Overview of the CKM MatrixOverview of the CKM Matrix in Fig. 2, the precision is such that...
17
PRAMANA c Indian Academy of Sciences — journal of physics Overview of the CKM Matrix TIM GERSHON a,b, * a Department of Physics, University of Warwick, Coventry, United Kingdom b European Organization for Nuclear Research (CERN), Geneva, Switzerland Abstract. The current status of the determination of the elements of the Cabibbo-Kobayashi- Maskawa quark-mixing matrix is reviewed. Tensions in the global fits are highlighted. Particular attention is paid to progress in, and prospects for, measurements of CP violation effects. 1. Introduction The Cabibbo-Kobayashi-Maskawa (CKM) matrix [1, 2] describes the mixing between the three different families of quark in the Standard Model (SM) of particle physics. It is therefore a 3 × 3 unitary matrix, and can be written in terms of four real parameters. For example, in the Wolfenstein parametrisation [3, 4] it can be expressed V CKM = V ud V us V ub V cd V cs V cb V td V ts V tb (1) = 1 - λ 2 /2 λ Aλ 3 (ρ - iη) -λ 1 - λ 2 /2 Aλ 2 Aλ 3 (1 - ρ - iη) -Aλ 2 1 + O ( λ 4 ) , (2) where the expansion parameter λ is the sine of the Cabibbo angle (λ = sin θ C ≈ V us ). With four independent parameters, a 3 × 3 unitary matrix cannot be forced to be real- valued, and hence CP violation arises as a consequence of the fact that the couplings for quarks and antiquarks have different phases, i.e. V CKM 6= V * CKM . In the SM, all CP violation in the quark sector arises from this fact, which is encoded in the Wolfenstein parameter η. Moreover, all flavour-changing interactions of the quarks are described by the four parameters of the CKM matrix, which makes it a remarkably predictive paradigm, describing phenomena from the lowest energies (such as nuclear transitions and pion decays) to the highest (W boson and top quark decays) within the realm of accelerator- based particle physics. Inevitably, a very broad range of theoretical tools (such as chiral perturbation theory, lattice quantum chromodynamics, and heavy quark effective theories) is needed to relate such diverse processes to the underlying physical parameters. Only a brief summary of the current status is given here, with most attention to exper- imental progress (discussions of progress in theory can be found in Refs. [5, 6]). More * [email protected] 1 arXiv:1112.1984v1 [hep-ex] 8 Dec 2011
Transcript of Overview of the CKM MatrixOverview of the CKM Matrix in Fig. 2, the precision is such that...
PRAMANA ccopy Indian Academy of Sciencesmdash journal of
physics
Overview of the CKM Matrix
TIM GERSHONab lowastaDepartment of Physics University of Warwick Coventry United KingdombEuropean Organization for Nuclear Research (CERN) Geneva Switzerland
Abstract The current status of the determination of the elements of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix is reviewed Tensions in the global fits are highlighted Particularattention is paid to progress in and prospects for measurements of CP violation effects
1 Introduction
The Cabibbo-Kobayashi-Maskawa (CKM) matrix [1 2] describes the mixing betweenthe three different families of quark in the Standard Model (SM) of particle physics It istherefore a 3times 3 unitary matrix and can be written in terms of four real parameters Forexample in the Wolfenstein parametrisation [3 4] it can be expressed
VCKM =
Vud Vus VubVcd Vcs VcbVtd Vts Vtb
(1)
=
1minus λ22 λ Aλ3(ρminus iη)minusλ 1minus λ22 Aλ2
Aλ3(1minus ρminus iη) minusAλ2 1
+O(λ4) (2)
where the expansion parameter λ is the sine of the Cabibbo angle (λ = sin θC asymp Vus)With four independent parameters a 3 times 3 unitary matrix cannot be forced to be real-valued and hence CP violation arises as a consequence of the fact that the couplings forquarks and antiquarks have different phases ie VCKM 6= V lowastCKM In the SM all CPviolation in the quark sector arises from this fact which is encoded in the Wolfensteinparameter η Moreover all flavour-changing interactions of the quarks are described bythe four parameters of the CKM matrix which makes it a remarkably predictive paradigmdescribing phenomena from the lowest energies (such as nuclear transitions and piondecays) to the highest (W boson and top quark decays) within the realm of accelerator-based particle physics Inevitably a very broad range of theoretical tools (such as chiralperturbation theory lattice quantum chromodynamics and heavy quark effective theories)is needed to relate such diverse processes to the underlying physical parameters
Only a brief summary of the current status is given here with most attention to exper-imental progress (discussions of progress in theory can be found in Refs [5 6]) More
lowastTJGershonwarwickacuk
1
arX
iv1
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1984
v1 [
hep-
ex]
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ec 2
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Tim Gershon
detailed reviews can be found for example in Refs [7ndash11] and in the summaries ofCKM2010 the 6th International Workshop on the CKM Unitarity Triangle [12ndash17]
ij
ijVF
G
()W
(uct)
(dsb)
s)microLifetime (
219695 219700 219705 219710 219715
Balandin shy 1974
Giovanetti shy 1984
Bardin shy 1984
Chitwood shy 2007
Barczyk shy 2008
MuLan shy R06
MuLan shy R07
Figure 1 (Left) Diagram for a flavour-changing charged current interaction thestrength of which involves the Fermi constant GF and the CKM matrix element Vij (Right) Progress in the determination of the muon lifetime over the past forty yearsfrom Ref [18]
2 CP conserving parameters ndash magnitudes of CKM matrix elements
21 The Fermi constant
As shown in Fig 1 any absolute determination of the magnitude of a CKM matrix el-ement requires knowledge of the Fermi constant GF The most precise information onGF is obtained from measurement of the lifetime of the muon τmicro since
1
τmicro=G2Fm
5micro
192π3(1 + ∆q) (3)
where mmicro is the mass of the muon (known to better than 50 parts per billion [19]) and ∆qaccounts for phase-space QED and hadronic radiative corrections (known to better than1 part per million [20 21]) A recent measurement of the positive muon lifetime by theMuLan collaboration [18] set in its historical context in Fig 1 gives
τmicro+ = (21969803plusmn 22) ps (4)
from which a determination of the Fermi constant to better than 1 part per million isobtained
GF = (11663788plusmn 7)times 10minus5 GeVminus2 (5)
22 Determination of |Vud|
The most precise determination of |Vud| is from super-allowed 0+ rarr 0+ nuclear betadecays The relation
ft =K
2G2F |Vud|
2 (6)
where the parameters f and t are obtained from measurements of the energy gap and fromthe half-life and branching fraction respectively is expected to be nucleus-independent tofirst order (K is a known constant K(hc)6 = 2π3h ln 2(mec
2)5) However as shown
2
Overview of the CKM Matrix
in Fig 2 the precision is such that second-order effects related to the nuclear medium(radiative and isospin-breaking corrections) need to be accounted for This is achievedby obtaining a corrected quantity labelled Ft [22] that is confirmed to be constant to3times 10minus4 (see Fig 2) This allows |Vud| to be extracted
|Vud| = 097425plusmn 000022 (7)
3030
ft(s
)
3040
3060
3080
3050
3070
3090
Z of daughter
2010 30 400
3070
3080
3090
3060
Ft
(s)
C10
O14
Mg22
Cl34
Al26 mAr34
K38 m
Sc42
V46
Mn50
Co54
Ga62 Rb74
Figure 2 Uncorrected (ft) and corrected (Ft) values obtained from different0+ rarr 0+ transitions from Ref [22]
Various alternative approaches allow determinations of |Vud| with different meritsNuclear mirror decays (transitions between states with nuclear isospin 12) and neutronlifetime measurements are sensitive to both vector and axial-vector couplings and thelatter does not require nucleus dependent or isospin breaking corrections to be knownThe current experimental status of the neutron lifetime is controversial [7 23] (see alsoRefs [24 25]) but future experiments should reduce its uncertainty Determinationsfrom pion beta decay (which has only vector couplings) have the smallest theoreticaluncertainty though significantly increased data samples would be necessary to approachthe current sensitivity on |Vud|
23 Determination of |Vus|
The past few years have seen significant progress in the determination of |Vus| fromsemileptonic kaon decays as reviewed in Ref [26 27] Fig 3 summarises the valuesof f+(0) |Vus| determined experimentally using data from the BNL-E865 KLOE KTeVISTRA+ and NA48 experiments (the latest preliminary results from the NA48 collabora-tion [28] are not included) as well as the calculations of f+(0) mainly using lattice QCDtechniques Using f+(0) = 0959plusmn 0005 [29] the average value is obtained
|Vus| = 02254plusmn 00013 (8)
A result with comparable precision on the ratio of CKM matrix elements is obtainedfrom the widths of leptonic kaon and pion decays The experimental data together with
3
Tim Gershon
0213 0214 0215 0216 0217
0213 0214 0215 0216 0217
KL e3
KL micro3
KS e3
Kplusmn e3
Kplusmn micro3
094095
096097
098099
100
Nf=2
Nf=2+1
SPQcdR
RBC
JLQCD
QCDSF
HPQCD-FNAL
RBC-UKQCD-07
0960(5)(7)
0968(9)(6)
0967(6)
09647(15)stat
0984(12)
0962(11)
09644(49)
0974(11)
Clover
Clover
0976(10)
0961(8)
Cirigliano et al
Jamin et al
Bijnens amp Talavera
Leutwyler amp Roos 84
ETMC-09 09560(84)
Clover
TWMF
RBC-UKQCD-10 +3109599(37)-43
f+
Κ0π
+
(0)
Nf=0
DWF
- L
AT
TIC
E -
DWF
Stag
-χP
T+
LE
Cs-
χPT + 1Nc
χPT + disp
χPT + LR
Quark M
QM
Figure 3 (Left) Values of f+(0) |Vus| obtained from different semileptonic kaondecays giving an average f+(0) |Vus| = 02163 plusmn 00005 (Right) Calculations offK
0π+
+ (0) From Ref [26]
lattice QCD input fKfπ = 1193plusmn0006 [26] and accounting for isospin violation [30]gives
|VusVud| = 02316plusmn 00012 (9)
where both experimental and theoretical uncertainties are essentially uncorrelated withthose in the average for |Vus| given above This then allows a comparison of the differentdeterminations as well as a test of the unitarity of the first row of the CKM matrix Asshown in Fig 4 unitarity is found to hold to better than one part in 103 An alternative wayof viewing this result is that the Fermi constant measured in the quark sector is consistentwith the determination from the muon lifetime This is thus a beautiful demonstration ofthe universality of the weak interaction
0224
0226
0228
0972 0974 0976
Vud
Vu
s
0224
0226
0228
0972 0974 0976
Vud
(0+ rarr 0
+)
VusVud
(Kmicro2)
Vus
(Kl3
)
fit withunitarity
fit
un
itarity
Figure 4 Combination of constraints on the magnitudes of the elements of the firstrow of the CKM matrix From Ref [26]
Alternative approaches to measure |Vus| are possible using hyperon decays or hadronictau lepton decays For the latter the method relies on comparison of the inclusive strange
4
Overview of the CKM Matrix
and non-strange branching fractions These are determined experimentally from sums ofexclusive measurements and since not all decays have yet been measured rely somewhaton extrapolations (see Ref [31] for a detailed review) A recent study [32] estimates thevalue from hadronic tau decays to be
|Vus| = 02166plusmn 00019 (exp)plusmn 00005 (th) (10)
which is discrepant from the value from semileptonic kaon decays at the level of 37σTwo important points are to be noted firstly the intrinsic theoretical uncertainty in thisapproach is very small secondly the central value may change as the B factories com-plete their programmes of study of multibody hadronic tau decays1
24 Determination of |Vcd| and |Vcs|
For several years the benchmark determination of |Vcd| has been that based on charmproduction in neutrino interactions
|Vcd| = 0230plusmn 0011 (11)
However improved measurements of charm semileptonic decaysD rarr πlν from CLEO-c [35] provide the potential for further improvements The CLEO-c data is shown inFig 5 A recent review [13] gives a value based on this approach
|Vcd| = 0234plusmn 0007plusmn 0002plusmn 0025 (12)
where the last uncertainty is from lattice QCD determinations of the form factors [36 37]With reduced uncertainties from the lattice calculations this promises to provide a moreprecise value of this CKM matrix element2
Figure 5 Differential branching fraction for semileptonic charm decays as a functionof eν invariant mass squared q2 from CLEO-c [35] The results of fits to parametrisedform factors are also shown
Semileptonic charm decays this time D rarr Klν also provide the most precise de-termination of |Vcs| Using inputs from CLEO-c [35] (Fig 5) and lattice QCD calcula-tions [36] the current value is
|Vcs| = 0961plusmn 0011plusmn 0024 (13)1 As pointed out by A Hoecker at Lepton Photon there is a significant discrepancy between the BaBar [33]
and Belle [34] measurements of τ rarr 3 tracks + ν branching fractions that should also be resolved2 While these proceedings were in preparation improved lattice calculations became available [38]
5
Tim Gershon
where the uncertainties are experimental and from the lattice respectivelyLeptonic charm meson decays provide an alternative approach to determine the magni-
tudes of these CKM matrix elements Their decay rates involve also the decay constantswhich can be determined from lattice QCD and helicity suppression factors for example
Γ(D+s rarr l+ν
)=G2F
8πf2D+
sm2lMD+
s
(1minus m2
l
M2D+
s
)2
|Vcs|2 (14)
Significant improvements in the measurements ofD+s decays have come from BaBar [39]
Belle [40] and CLEO-c [41] These are usually expressed in terms of fD+s
using the valueof |Vcs| given above and can be compared to the lattice QCD calculations Equally thiscan be recast using the input from the lattice [42] to obtain
|Vcs| = 1005plusmn 0026plusmn 0016 (15)
where the uncertainties are experimental and from the lattice respectively It should benoted that a discrepancy that was apparent a few years ago (see for example Ref [43])has disappeared Moreover the dominant uncertainty is experimental so improved mea-surements from BES and current or future e+eminus B factory experiments would be wel-come
25 Determination of |Vcb| and |Vub|
Both exclusive and inclusive studies of semileptonic B decays have been used to obtain|Vcb| and |Vub| (for a detailed recent review see Ref [44]) For the former the reviewin the 2010 edition of the Particle Data Group review of particle physics [7] quotes a 2σtension between the two determinations
|Vcb| (excl) = (387plusmn 11)times 10minus3 |Vcb| (incl) = (415plusmn 07)times 10minus3
(16)
Updated data from Belle on B0d rarr Dlowastminuslν decays [45] and improved lattice QCD cal-
culations of the form-factor at zero recoil [46] reduce slightly both the uncertainty of theexclusive determination and the tension with the inclusive determination
It is also worth noting that the semitauonic decays B rarr D(lowast)τν have recently beenseen for the first time by BaBar [47ndash49] (see Fig 6) and Belle [50 51] The rates of thesedecays depend on |Vcb| but it is more common to measure their ratios relative to thosefor B rarr D(lowast)lν (l = e micro) decays These ratios are precisely predicted in the SM andare sensitive to potential contributions beyond the SM for example from charged Higgsbosons The isospin averaged ratios are determined to be
R(D) = 0456plusmn 0053plusmn 0056 RSM(D) = 031plusmn 002 R(Dlowast) = 0325plusmn 0023plusmn 0027 RSM(Dlowast) = 025plusmn 007
(17)
The excess over the SM is about 18σ (see also Ref [52] where determinations of |Vub|from leptonic B decays are also discussed)
The b rarr ulν decays can similarly be used to obtain measurements of |Vub| by eitherexclusive or inclusive methods Most recent progress has been on the exclusive B rarr πlνdecays where new results have become available from both BaBar [53 54] and Belle [55]as shown in Fig 7 The updated HFAG [8] average is [56]
|Vub| = (326plusmn 030)times 10minus3 (18)
6
Overview of the CKM Matrix
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60 f) + D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80 g) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40h) + D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
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ents
(9
6 M
eV)
0
20
40
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(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
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)2 (Gevmiss2m
0 5
)2
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ents
(0
38
GeV
0
20
40
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80
)2 (Gevmiss2m
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)2
Ev
ents
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38
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0
20
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80 g) +D
(Gev)l
p0 05 1 15 2
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ents
(9
6 M
eV)
0
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40
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p0 05 1 15 2
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ents
(9
6 M
eV)
0
10
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40h) + D2 lt 120 GeVmiss
2 mle10
Figure 6 Signal for B rarr D(lowast)τν decays from BaBar [47] Note that the large peaksare due to backgrounds from D(lowast)lν (l = e micro) decays while the signals appears astails to large values of the missing mass squared variable m2
miss
where the dominant source of uncertainty is from the lattice QCD calculations of the formfactors [57]
)2 (GeV2Unfolded q
0 5 10 15 20 25
)2
(2 G
eV
times 2
q∆
)2
B(q
∆
0
2
4
6
8
10
12
14
16
shy610times
LCSR
FNALMILC
HPQCD
BGL fit to data
BK fit to data
data
)2c2 (GeV2Unfolded q0 5 10 15 20 25
2c
2)
2
Ge
V2
B(q
∆
0
2
4
6
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12
14
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18
20
shy610times
ISGW2
HPQCD
FNAL
LCSR
Data
Figure 7 Differential branching fractions of B0d rarr πminusl+ν decays as a function of
l+ν invariant mass squared q2 from (left) BaBar [53] and (right) Belle [55]
As was the case for |Vcb| there is a tension between inclusive and exclusive determi-nations (the world average value using the inclusive approach is |Vub| = (427plusmn 038)times10minus3 Although some commentators have pointed out that the large amount of theoreticalwork dedicated to the extraction of |Vub|may have led to an underestimation of the uncer-tainties [58] it is this authorrsquos view that more theoretical attention is necessary to resolvethe situation On the exclusive side improvements in lattice QCD calculations can beexpected while on the inclusive side an initiative to reduce uncertainties using global fitsis underway [59]
7
Tim Gershon
3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
As is widely known CP violation is one of the three ldquoSakharov conditionsrdquo [60] nec-essary for the evolution of a baryon asymmetry in the Universe Moreover the SM CPviolation encoded in the CKM matrix is not sufficient to explain the observed asym-metry Therefore there must be more sources of matter-antimatter asymmetry in natureThese could arise in almost any conceivable extension of the SM such as in an extendedquark sector in the lepton sector (leptogenesis) from anomalous gauge couplings in anextended Higgs sector and so on While all of these must be investigated testing theconsistency of the CKM mechanism in the quark sector provides the best chance to findnew sources of CP violation in the short term
Although the understanding of CP violation has advanced dramatically over the pastdecade it is important to realise that it remains a rarely observed phenomenon To dateit is only been observed (with gt 5σ significance) in the K0 and B0
d systems (Discus-sions of searches for CP violation in D0 and B0
s mixing can be found in Refs [61 62])In the B system the only 5σ significant measurements are of the parameters sin(2β)from JψKSL and similar decays from BaBar [63] and Belle [64] S(ηprimeKSL) fromBaBar [65] and Belle [66] S(π+πminus) from BaBar [67] and Belle [68] C(π+πminus) fromBelle [68] and ACP (K+πminus) from BaBar [67] Belle [69] and LHCb [70] (see alsoRef [52] on this last topic) The LHCb result on B0
d rarr K+πminus is thus the first 5σobservation of CP violation in the B system at a hadron collider experimentCP violation results are often expressed in terms of the so-called Unitarity Triangle
which is a graphical representation of one of the relations implied by the unitarity of theCKM matrix
VudVlowastub + VcdV
lowastcb + VtdV
lowasttb = 0 (19)
The angles of this triangle are usually denoted (α β γ) while its apex (after normalisingso that its base is unit length along the real axis) is given in terms of the Wolfensteinparameters (ρ η) [3 4]
31 Searches for CP violation in the charm sector
Almost all CP violation effects in the charm system are expected to be negligible inthe SM This therefore provides an excellent testing ground to look for unexpected ef-fects Various searches for direct CP violation effects (studies of mixing and indirectCP violation are discussed in Ref [62]) have been carried out recently for example inD+
(s) rarr KSπ+ and KSK
+ decays [71 72] in triple product asymmetries in four-bodyhadronic decays [73 74] and in Dalitz plot asymmetries in three-body decays [75] At thetime of Lepton Photon no significant signal for CP violation in charm had yet been seenalthough the world average asymmetry in D+ rarr KSπ
+ is more than 3σ from zero [8]this is consistent with originating from the CP violation in the neutral kaon system (seeRef [76] and references therein) However while these proceedings were being preparedLHCb announced a 35σ signal for the difference in time-integrated CP asymmetries be-tween D0 rarr K+Kminus and D0 rarr π+πminus decays [77] (CDF have also released less preciseresults on the same observable [78])
32 Measurement of sin(2β)
Both e+eminus B factory experiments BaBar and Belle have completed data taking Theresult on sin(2β) from B0
d rarr JψKSL (etc) with BaBarrsquos final data set (445 million
8
Overview of the CKM Matrix
BB pairs) has been published [63] while preliminary results following a reprocessing ofthe Belle data (772 million BB pairs) are available [64] A first analysis from LHCb isalso available [79] The results are compiled in Fig 8 At the level of precision that theexperiments are reaching it is important to check for effects that may perturb the naıveSM expectation S(JψKSL) = minusηCP sin(2β) where ηCP is the CP eigenvalue ofthe final state This can be done using channels that are related by flavour symmetries ndashB0d rarr Jψπ0 (related by SU(3)) orB0
s rarr JψK0S (related by U-spin) First observations
of the latter decay have recently been reported by CDF and LHCb [80 81] suggestingthat this approach will be possible with larger datasets
sin(2β) equiv sin(2φ1)
-2 -1 0 1 2 3
BaBarPRD 79 (2009) 072009
069 plusmn 003 plusmn 001
BaBar χc0 KSPRD 80 (2009) 112001
069 plusmn 052 plusmn 004 plusmn 007
BaBar Jψ (hadronic) KSPRD 69 (2004) 052001
156 plusmn 042 plusmn 021
BelleMoriond EW 2011 preliminary
067 plusmn 002 plusmn 001
ALEPHPLB 492 259 (2000)
084 +-018024 plusmn 016
OPALEPJ C5 379 (1998)
320 +-128000 plusmn 050
CDFPRD 61 072005 (2000)
079 +-004414
LHCbLHCb-CONF-2011-004
053 +-002289 plusmn 005
AverageHFAG
068 plusmn 002
H F A GH F A GBeauty 2011
PRELIMINARYβ equiv φ
1
ρndash
ηndash
-02 0 02 04 06 08 1-02
0
02
04
06
08
1
β equiv φ1 = (214 plusmn 08)˚
β equiv
φ1 =
(686
plusmn 0
8)˚
DIS
FA
VO
UR
ED
BY
Jψ
K D
DK
S amp D
h0
H F A GH F A GBeauty 2011
PRELIMINARY
Figure 8 (Left) Compilation of results on sin(2β) from B0d rarr JψKSL (etc) [8]
(Right) Corresponding constraint on ρndashη plane
The B factories have carried out a substantial programme of alternative measurementsof sin(2β) using different quark level transitions such as b rarr qqs (q = u d s egB0d rarr ηprimeK0
S) and b rarr ccd (eg B0d rarr D+Dminus) Compilations are shown in Fig 9 A
few years ago hints of deviations were apparent between the value of sin(2βeff) measuredin brarr qqs transitions and the reference value from brarr ccs These have diminished withthe latest data but effects of non-SM contributions at the O(10) level are not ruled outOne notable update is the new Belle result on B0
d rarr D+Dminus [82] which improves theconsistency between the results of the two B factories as well as with the SM
33 Measurement of α
The unitarity triangle angle α is constrained by measurements of and isospin relationsbetween B rarr ππ ρπ and ρρ decays [83 84] The situation has been stable for the lastfew years though the final results from both B factory experiments in all three systemsare still awaited Combining all available information the world average is [10]
α =(890 +44
minus42
) (20)
Since the average is dominated by results from the ρρ system two small comments arein order First the apparently high branching fraction of B+ rarr ρ+ρ0 which comesessentially from a single measurement [85] stretches the isospin triangle and reduces theuncertainty Secondly analyses to date while allowing CP violation in the rates haveassumed the longitudinal polarisation fraction is the same for B and B ndash but the mostgeneral analysis would allow a difference between the two
9
Tim Gershon
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
brarrccs
φ K
0
ηprime K
0
KS K
S K
S
π0 K
0
ρ0 K
S
ω K
S
f 0 K
S
K+ K
- K0
-08 -06 -04 -02 0 02 04 06 08 1 12 14 16
World Average 068 plusmn 002
BaBar 026 plusmn 026 plusmn 003
Belle 090 +-00
01
99
Average 056 +-00
11
68
BaBar 057 plusmn 008 plusmn 002
Belle 064 plusmn 010 plusmn 004
Average 059 plusmn 007
BaBar 094 +-00
22
14 plusmn 006
Belle 030 plusmn 032 plusmn 008
Average 072 plusmn 019
BaBar 055 plusmn 020 plusmn 003
Belle 067 plusmn 031 plusmn 008
Average 057 plusmn 017
BaBar 035 +-00
23
61 plusmn 006 plusmn 003
Belle 064 +-00
12
95 plusmn 009 plusmn 010
Average 054 +-00
12
81
BaBar 055 +-00
22
69 plusmn 002
Belle 011 plusmn 046 plusmn 007
Average 045 plusmn 024
BaBar 060 +-00
11
68
Belle 063 +-00
11
69
Average 062 +-00
11
13
BaBar 086 plusmn 008 plusmn 003
Belle 068 plusmn 015 plusmn 003 +-00
21
13
Average 082 plusmn 007
H F A GH F A GEndOfYear 2011
PRELIMINARY
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
brarrccs SCP
Jψ
π0 S
CP
D+ D
- SC
P
D+
D- S
CP
D+
- D-+
S+
-
D+
- D-+
S-+
-1 0 1 2
World AverageHFAG (EPS 2011)
068 plusmn 002
BaBarPRL 101 (2008) 021801
123 plusmn 021 plusmn 004
BellePRD 77 (2008) 071101(R)
065 plusmn 021 plusmn 005
AverageHFAG correlated average
093 plusmn 015
BaBarPRD 79 032002 (2009)
065 plusmn 036 plusmn 005
BelleEPS 2011 preliminary
106 plusmn 021 plusmn 007
AverageHFAG correlated average
096 plusmn 019
BaBarPRD 79 032002 (2009)
071 plusmn 016 plusmn 003
BelleEPS 2011 preliminary
079 plusmn 013 plusmn 003
AverageHFAG correlated average
077 plusmn 010
BaBarPRD 79 032002 (2009)
063 plusmn 021 plusmn 003
BellePRL 93 (2004) 201802
055 plusmn 039 plusmn 012
AverageHFAG
061 plusmn 019
BaBarPRD 79 032002 (2009)
074 plusmn 023 plusmn 005
BellePRL 93 (2004) 201802
096 plusmn 043 plusmn 012
AverageHFAG
079 plusmn 021
H F A GH F A GEPS 2011
PRELIMINARY
Figure 9 Compilation of results on sin(2βeff) from (left) b rarr qqs and (right)brarr ccd transitions [8]
34 Measurement of γ
The angle γ is unique among CP violating observables in that it can be determined us-ing tree-level processes only exploiting the interference between (typically) b rarr cudand brarr ucd transitions that occurs when the process involves a neutral D meson recon-structed in a final state accessible to both D0 and D0 decays It therefore provides a SMbenchmark and its precise measurement is crucial in order to disentangle any non-SMcontributions to other processes via global CKM fits
Several different D decay final states have been studied in order to maximise the sen-sitivity to γ The archetype is the use of D decays to CP eigenstates the so-called GLWmethod [86 87] New results with this approach have recently become available fromBaBar [88] CDF [89] and LHCb [90] while the very latest results from Belle [91] areshown in Fig 10 The world average for the CP asymmetry in the processes involvingCP -even D decay final states including all these new results and illustrated in Fig 11(left) shows that CP violation in Bplusmn rarr DKplusmn decays is clearly established though nosingle measurement exceeds 5σ significance
Another powerful approach to constrain γ the so-called ADS method [92 93] comesfrom the use of doubly-Cabibbo-suppressed D decays (for example to the final stateK+πminus) Recent new results come from BaBar [94] Belle [95] and CDF [96] whilethe very latest results from LHCb [97] are shown in Fig 12 The world average for theparameter RADS which is the ratio of decay rates to the suppressed states compared tothose for the favoured channels including all these new results and illustrated in Fig 11(right) shows that the suppressed decay is now clearly established though no single mea-surement exceeds 5σ significance This is very promising for future γ determinations
Although the analyses withBplusmn rarr DKplusmn decays give the most precise results differentB decays have also been studied The use of both possible decays Dlowast rarr Dπ0 andDlowast rarr Dγ provides an extra handle on the extraction of γ fromBplusmn rarr DlowastKplusmn [98] that isbecoming visible in the most recent results [91 94] In addition theB0
d rarr DKlowast0 channel
10
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
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16
Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Tim Gershon
detailed reviews can be found for example in Refs [7ndash11] and in the summaries ofCKM2010 the 6th International Workshop on the CKM Unitarity Triangle [12ndash17]
ij
ijVF
G
()W
(uct)
(dsb)
s)microLifetime (
219695 219700 219705 219710 219715
Balandin shy 1974
Giovanetti shy 1984
Bardin shy 1984
Chitwood shy 2007
Barczyk shy 2008
MuLan shy R06
MuLan shy R07
Figure 1 (Left) Diagram for a flavour-changing charged current interaction thestrength of which involves the Fermi constant GF and the CKM matrix element Vij (Right) Progress in the determination of the muon lifetime over the past forty yearsfrom Ref [18]
2 CP conserving parameters ndash magnitudes of CKM matrix elements
21 The Fermi constant
As shown in Fig 1 any absolute determination of the magnitude of a CKM matrix el-ement requires knowledge of the Fermi constant GF The most precise information onGF is obtained from measurement of the lifetime of the muon τmicro since
1
τmicro=G2Fm
5micro
192π3(1 + ∆q) (3)
where mmicro is the mass of the muon (known to better than 50 parts per billion [19]) and ∆qaccounts for phase-space QED and hadronic radiative corrections (known to better than1 part per million [20 21]) A recent measurement of the positive muon lifetime by theMuLan collaboration [18] set in its historical context in Fig 1 gives
τmicro+ = (21969803plusmn 22) ps (4)
from which a determination of the Fermi constant to better than 1 part per million isobtained
GF = (11663788plusmn 7)times 10minus5 GeVminus2 (5)
22 Determination of |Vud|
The most precise determination of |Vud| is from super-allowed 0+ rarr 0+ nuclear betadecays The relation
ft =K
2G2F |Vud|
2 (6)
where the parameters f and t are obtained from measurements of the energy gap and fromthe half-life and branching fraction respectively is expected to be nucleus-independent tofirst order (K is a known constant K(hc)6 = 2π3h ln 2(mec
2)5) However as shown
2
Overview of the CKM Matrix
in Fig 2 the precision is such that second-order effects related to the nuclear medium(radiative and isospin-breaking corrections) need to be accounted for This is achievedby obtaining a corrected quantity labelled Ft [22] that is confirmed to be constant to3times 10minus4 (see Fig 2) This allows |Vud| to be extracted
|Vud| = 097425plusmn 000022 (7)
3030
ft(s
)
3040
3060
3080
3050
3070
3090
Z of daughter
2010 30 400
3070
3080
3090
3060
Ft
(s)
C10
O14
Mg22
Cl34
Al26 mAr34
K38 m
Sc42
V46
Mn50
Co54
Ga62 Rb74
Figure 2 Uncorrected (ft) and corrected (Ft) values obtained from different0+ rarr 0+ transitions from Ref [22]
Various alternative approaches allow determinations of |Vud| with different meritsNuclear mirror decays (transitions between states with nuclear isospin 12) and neutronlifetime measurements are sensitive to both vector and axial-vector couplings and thelatter does not require nucleus dependent or isospin breaking corrections to be knownThe current experimental status of the neutron lifetime is controversial [7 23] (see alsoRefs [24 25]) but future experiments should reduce its uncertainty Determinationsfrom pion beta decay (which has only vector couplings) have the smallest theoreticaluncertainty though significantly increased data samples would be necessary to approachthe current sensitivity on |Vud|
23 Determination of |Vus|
The past few years have seen significant progress in the determination of |Vus| fromsemileptonic kaon decays as reviewed in Ref [26 27] Fig 3 summarises the valuesof f+(0) |Vus| determined experimentally using data from the BNL-E865 KLOE KTeVISTRA+ and NA48 experiments (the latest preliminary results from the NA48 collabora-tion [28] are not included) as well as the calculations of f+(0) mainly using lattice QCDtechniques Using f+(0) = 0959plusmn 0005 [29] the average value is obtained
|Vus| = 02254plusmn 00013 (8)
A result with comparable precision on the ratio of CKM matrix elements is obtainedfrom the widths of leptonic kaon and pion decays The experimental data together with
3
Tim Gershon
0213 0214 0215 0216 0217
0213 0214 0215 0216 0217
KL e3
KL micro3
KS e3
Kplusmn e3
Kplusmn micro3
094095
096097
098099
100
Nf=2
Nf=2+1
SPQcdR
RBC
JLQCD
QCDSF
HPQCD-FNAL
RBC-UKQCD-07
0960(5)(7)
0968(9)(6)
0967(6)
09647(15)stat
0984(12)
0962(11)
09644(49)
0974(11)
Clover
Clover
0976(10)
0961(8)
Cirigliano et al
Jamin et al
Bijnens amp Talavera
Leutwyler amp Roos 84
ETMC-09 09560(84)
Clover
TWMF
RBC-UKQCD-10 +3109599(37)-43
f+
Κ0π
+
(0)
Nf=0
DWF
- L
AT
TIC
E -
DWF
Stag
-χP
T+
LE
Cs-
χPT + 1Nc
χPT + disp
χPT + LR
Quark M
QM
Figure 3 (Left) Values of f+(0) |Vus| obtained from different semileptonic kaondecays giving an average f+(0) |Vus| = 02163 plusmn 00005 (Right) Calculations offK
0π+
+ (0) From Ref [26]
lattice QCD input fKfπ = 1193plusmn0006 [26] and accounting for isospin violation [30]gives
|VusVud| = 02316plusmn 00012 (9)
where both experimental and theoretical uncertainties are essentially uncorrelated withthose in the average for |Vus| given above This then allows a comparison of the differentdeterminations as well as a test of the unitarity of the first row of the CKM matrix Asshown in Fig 4 unitarity is found to hold to better than one part in 103 An alternative wayof viewing this result is that the Fermi constant measured in the quark sector is consistentwith the determination from the muon lifetime This is thus a beautiful demonstration ofthe universality of the weak interaction
0224
0226
0228
0972 0974 0976
Vud
Vu
s
0224
0226
0228
0972 0974 0976
Vud
(0+ rarr 0
+)
VusVud
(Kmicro2)
Vus
(Kl3
)
fit withunitarity
fit
un
itarity
Figure 4 Combination of constraints on the magnitudes of the elements of the firstrow of the CKM matrix From Ref [26]
Alternative approaches to measure |Vus| are possible using hyperon decays or hadronictau lepton decays For the latter the method relies on comparison of the inclusive strange
4
Overview of the CKM Matrix
and non-strange branching fractions These are determined experimentally from sums ofexclusive measurements and since not all decays have yet been measured rely somewhaton extrapolations (see Ref [31] for a detailed review) A recent study [32] estimates thevalue from hadronic tau decays to be
|Vus| = 02166plusmn 00019 (exp)plusmn 00005 (th) (10)
which is discrepant from the value from semileptonic kaon decays at the level of 37σTwo important points are to be noted firstly the intrinsic theoretical uncertainty in thisapproach is very small secondly the central value may change as the B factories com-plete their programmes of study of multibody hadronic tau decays1
24 Determination of |Vcd| and |Vcs|
For several years the benchmark determination of |Vcd| has been that based on charmproduction in neutrino interactions
|Vcd| = 0230plusmn 0011 (11)
However improved measurements of charm semileptonic decaysD rarr πlν from CLEO-c [35] provide the potential for further improvements The CLEO-c data is shown inFig 5 A recent review [13] gives a value based on this approach
|Vcd| = 0234plusmn 0007plusmn 0002plusmn 0025 (12)
where the last uncertainty is from lattice QCD determinations of the form factors [36 37]With reduced uncertainties from the lattice calculations this promises to provide a moreprecise value of this CKM matrix element2
Figure 5 Differential branching fraction for semileptonic charm decays as a functionof eν invariant mass squared q2 from CLEO-c [35] The results of fits to parametrisedform factors are also shown
Semileptonic charm decays this time D rarr Klν also provide the most precise de-termination of |Vcs| Using inputs from CLEO-c [35] (Fig 5) and lattice QCD calcula-tions [36] the current value is
|Vcs| = 0961plusmn 0011plusmn 0024 (13)1 As pointed out by A Hoecker at Lepton Photon there is a significant discrepancy between the BaBar [33]
and Belle [34] measurements of τ rarr 3 tracks + ν branching fractions that should also be resolved2 While these proceedings were in preparation improved lattice calculations became available [38]
5
Tim Gershon
where the uncertainties are experimental and from the lattice respectivelyLeptonic charm meson decays provide an alternative approach to determine the magni-
tudes of these CKM matrix elements Their decay rates involve also the decay constantswhich can be determined from lattice QCD and helicity suppression factors for example
Γ(D+s rarr l+ν
)=G2F
8πf2D+
sm2lMD+
s
(1minus m2
l
M2D+
s
)2
|Vcs|2 (14)
Significant improvements in the measurements ofD+s decays have come from BaBar [39]
Belle [40] and CLEO-c [41] These are usually expressed in terms of fD+s
using the valueof |Vcs| given above and can be compared to the lattice QCD calculations Equally thiscan be recast using the input from the lattice [42] to obtain
|Vcs| = 1005plusmn 0026plusmn 0016 (15)
where the uncertainties are experimental and from the lattice respectively It should benoted that a discrepancy that was apparent a few years ago (see for example Ref [43])has disappeared Moreover the dominant uncertainty is experimental so improved mea-surements from BES and current or future e+eminus B factory experiments would be wel-come
25 Determination of |Vcb| and |Vub|
Both exclusive and inclusive studies of semileptonic B decays have been used to obtain|Vcb| and |Vub| (for a detailed recent review see Ref [44]) For the former the reviewin the 2010 edition of the Particle Data Group review of particle physics [7] quotes a 2σtension between the two determinations
|Vcb| (excl) = (387plusmn 11)times 10minus3 |Vcb| (incl) = (415plusmn 07)times 10minus3
(16)
Updated data from Belle on B0d rarr Dlowastminuslν decays [45] and improved lattice QCD cal-
culations of the form-factor at zero recoil [46] reduce slightly both the uncertainty of theexclusive determination and the tension with the inclusive determination
It is also worth noting that the semitauonic decays B rarr D(lowast)τν have recently beenseen for the first time by BaBar [47ndash49] (see Fig 6) and Belle [50 51] The rates of thesedecays depend on |Vcb| but it is more common to measure their ratios relative to thosefor B rarr D(lowast)lν (l = e micro) decays These ratios are precisely predicted in the SM andare sensitive to potential contributions beyond the SM for example from charged Higgsbosons The isospin averaged ratios are determined to be
R(D) = 0456plusmn 0053plusmn 0056 RSM(D) = 031plusmn 002 R(Dlowast) = 0325plusmn 0023plusmn 0027 RSM(Dlowast) = 025plusmn 007
(17)
The excess over the SM is about 18σ (see also Ref [52] where determinations of |Vub|from leptonic B decays are also discussed)
The b rarr ulν decays can similarly be used to obtain measurements of |Vub| by eitherexclusive or inclusive methods Most recent progress has been on the exclusive B rarr πlνdecays where new results have become available from both BaBar [53 54] and Belle [55]as shown in Fig 7 The updated HFAG [8] average is [56]
|Vub| = (326plusmn 030)times 10minus3 (18)
6
Overview of the CKM Matrix
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60 f) + D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80 g) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40h) + D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60 f) + D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80 g) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40h) + D2 lt 120 GeVmiss
2 mle10
Figure 6 Signal for B rarr D(lowast)τν decays from BaBar [47] Note that the large peaksare due to backgrounds from D(lowast)lν (l = e micro) decays while the signals appears astails to large values of the missing mass squared variable m2
miss
where the dominant source of uncertainty is from the lattice QCD calculations of the formfactors [57]
)2 (GeV2Unfolded q
0 5 10 15 20 25
)2
(2 G
eV
times 2
q∆
)2
B(q
∆
0
2
4
6
8
10
12
14
16
shy610times
LCSR
FNALMILC
HPQCD
BGL fit to data
BK fit to data
data
)2c2 (GeV2Unfolded q0 5 10 15 20 25
2c
2)
2
Ge
V2
B(q
∆
0
2
4
6
8
10
12
14
16
18
20
shy610times
ISGW2
HPQCD
FNAL
LCSR
Data
Figure 7 Differential branching fractions of B0d rarr πminusl+ν decays as a function of
l+ν invariant mass squared q2 from (left) BaBar [53] and (right) Belle [55]
As was the case for |Vcb| there is a tension between inclusive and exclusive determi-nations (the world average value using the inclusive approach is |Vub| = (427plusmn 038)times10minus3 Although some commentators have pointed out that the large amount of theoreticalwork dedicated to the extraction of |Vub|may have led to an underestimation of the uncer-tainties [58] it is this authorrsquos view that more theoretical attention is necessary to resolvethe situation On the exclusive side improvements in lattice QCD calculations can beexpected while on the inclusive side an initiative to reduce uncertainties using global fitsis underway [59]
7
Tim Gershon
3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
As is widely known CP violation is one of the three ldquoSakharov conditionsrdquo [60] nec-essary for the evolution of a baryon asymmetry in the Universe Moreover the SM CPviolation encoded in the CKM matrix is not sufficient to explain the observed asym-metry Therefore there must be more sources of matter-antimatter asymmetry in natureThese could arise in almost any conceivable extension of the SM such as in an extendedquark sector in the lepton sector (leptogenesis) from anomalous gauge couplings in anextended Higgs sector and so on While all of these must be investigated testing theconsistency of the CKM mechanism in the quark sector provides the best chance to findnew sources of CP violation in the short term
Although the understanding of CP violation has advanced dramatically over the pastdecade it is important to realise that it remains a rarely observed phenomenon To dateit is only been observed (with gt 5σ significance) in the K0 and B0
d systems (Discus-sions of searches for CP violation in D0 and B0
s mixing can be found in Refs [61 62])In the B system the only 5σ significant measurements are of the parameters sin(2β)from JψKSL and similar decays from BaBar [63] and Belle [64] S(ηprimeKSL) fromBaBar [65] and Belle [66] S(π+πminus) from BaBar [67] and Belle [68] C(π+πminus) fromBelle [68] and ACP (K+πminus) from BaBar [67] Belle [69] and LHCb [70] (see alsoRef [52] on this last topic) The LHCb result on B0
d rarr K+πminus is thus the first 5σobservation of CP violation in the B system at a hadron collider experimentCP violation results are often expressed in terms of the so-called Unitarity Triangle
which is a graphical representation of one of the relations implied by the unitarity of theCKM matrix
VudVlowastub + VcdV
lowastcb + VtdV
lowasttb = 0 (19)
The angles of this triangle are usually denoted (α β γ) while its apex (after normalisingso that its base is unit length along the real axis) is given in terms of the Wolfensteinparameters (ρ η) [3 4]
31 Searches for CP violation in the charm sector
Almost all CP violation effects in the charm system are expected to be negligible inthe SM This therefore provides an excellent testing ground to look for unexpected ef-fects Various searches for direct CP violation effects (studies of mixing and indirectCP violation are discussed in Ref [62]) have been carried out recently for example inD+
(s) rarr KSπ+ and KSK
+ decays [71 72] in triple product asymmetries in four-bodyhadronic decays [73 74] and in Dalitz plot asymmetries in three-body decays [75] At thetime of Lepton Photon no significant signal for CP violation in charm had yet been seenalthough the world average asymmetry in D+ rarr KSπ
+ is more than 3σ from zero [8]this is consistent with originating from the CP violation in the neutral kaon system (seeRef [76] and references therein) However while these proceedings were being preparedLHCb announced a 35σ signal for the difference in time-integrated CP asymmetries be-tween D0 rarr K+Kminus and D0 rarr π+πminus decays [77] (CDF have also released less preciseresults on the same observable [78])
32 Measurement of sin(2β)
Both e+eminus B factory experiments BaBar and Belle have completed data taking Theresult on sin(2β) from B0
d rarr JψKSL (etc) with BaBarrsquos final data set (445 million
8
Overview of the CKM Matrix
BB pairs) has been published [63] while preliminary results following a reprocessing ofthe Belle data (772 million BB pairs) are available [64] A first analysis from LHCb isalso available [79] The results are compiled in Fig 8 At the level of precision that theexperiments are reaching it is important to check for effects that may perturb the naıveSM expectation S(JψKSL) = minusηCP sin(2β) where ηCP is the CP eigenvalue ofthe final state This can be done using channels that are related by flavour symmetries ndashB0d rarr Jψπ0 (related by SU(3)) orB0
s rarr JψK0S (related by U-spin) First observations
of the latter decay have recently been reported by CDF and LHCb [80 81] suggestingthat this approach will be possible with larger datasets
sin(2β) equiv sin(2φ1)
-2 -1 0 1 2 3
BaBarPRD 79 (2009) 072009
069 plusmn 003 plusmn 001
BaBar χc0 KSPRD 80 (2009) 112001
069 plusmn 052 plusmn 004 plusmn 007
BaBar Jψ (hadronic) KSPRD 69 (2004) 052001
156 plusmn 042 plusmn 021
BelleMoriond EW 2011 preliminary
067 plusmn 002 plusmn 001
ALEPHPLB 492 259 (2000)
084 +-018024 plusmn 016
OPALEPJ C5 379 (1998)
320 +-128000 plusmn 050
CDFPRD 61 072005 (2000)
079 +-004414
LHCbLHCb-CONF-2011-004
053 +-002289 plusmn 005
AverageHFAG
068 plusmn 002
H F A GH F A GBeauty 2011
PRELIMINARYβ equiv φ
1
ρndash
ηndash
-02 0 02 04 06 08 1-02
0
02
04
06
08
1
β equiv φ1 = (214 plusmn 08)˚
β equiv
φ1 =
(686
plusmn 0
8)˚
DIS
FA
VO
UR
ED
BY
Jψ
K D
DK
S amp D
h0
H F A GH F A GBeauty 2011
PRELIMINARY
Figure 8 (Left) Compilation of results on sin(2β) from B0d rarr JψKSL (etc) [8]
(Right) Corresponding constraint on ρndashη plane
The B factories have carried out a substantial programme of alternative measurementsof sin(2β) using different quark level transitions such as b rarr qqs (q = u d s egB0d rarr ηprimeK0
S) and b rarr ccd (eg B0d rarr D+Dminus) Compilations are shown in Fig 9 A
few years ago hints of deviations were apparent between the value of sin(2βeff) measuredin brarr qqs transitions and the reference value from brarr ccs These have diminished withthe latest data but effects of non-SM contributions at the O(10) level are not ruled outOne notable update is the new Belle result on B0
d rarr D+Dminus [82] which improves theconsistency between the results of the two B factories as well as with the SM
33 Measurement of α
The unitarity triangle angle α is constrained by measurements of and isospin relationsbetween B rarr ππ ρπ and ρρ decays [83 84] The situation has been stable for the lastfew years though the final results from both B factory experiments in all three systemsare still awaited Combining all available information the world average is [10]
α =(890 +44
minus42
) (20)
Since the average is dominated by results from the ρρ system two small comments arein order First the apparently high branching fraction of B+ rarr ρ+ρ0 which comesessentially from a single measurement [85] stretches the isospin triangle and reduces theuncertainty Secondly analyses to date while allowing CP violation in the rates haveassumed the longitudinal polarisation fraction is the same for B and B ndash but the mostgeneral analysis would allow a difference between the two
9
Tim Gershon
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
brarrccs
φ K
0
ηprime K
0
KS K
S K
S
π0 K
0
ρ0 K
S
ω K
S
f 0 K
S
K+ K
- K0
-08 -06 -04 -02 0 02 04 06 08 1 12 14 16
World Average 068 plusmn 002
BaBar 026 plusmn 026 plusmn 003
Belle 090 +-00
01
99
Average 056 +-00
11
68
BaBar 057 plusmn 008 plusmn 002
Belle 064 plusmn 010 plusmn 004
Average 059 plusmn 007
BaBar 094 +-00
22
14 plusmn 006
Belle 030 plusmn 032 plusmn 008
Average 072 plusmn 019
BaBar 055 plusmn 020 plusmn 003
Belle 067 plusmn 031 plusmn 008
Average 057 plusmn 017
BaBar 035 +-00
23
61 plusmn 006 plusmn 003
Belle 064 +-00
12
95 plusmn 009 plusmn 010
Average 054 +-00
12
81
BaBar 055 +-00
22
69 plusmn 002
Belle 011 plusmn 046 plusmn 007
Average 045 plusmn 024
BaBar 060 +-00
11
68
Belle 063 +-00
11
69
Average 062 +-00
11
13
BaBar 086 plusmn 008 plusmn 003
Belle 068 plusmn 015 plusmn 003 +-00
21
13
Average 082 plusmn 007
H F A GH F A GEndOfYear 2011
PRELIMINARY
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
brarrccs SCP
Jψ
π0 S
CP
D+ D
- SC
P
D+
D- S
CP
D+
- D-+
S+
-
D+
- D-+
S-+
-1 0 1 2
World AverageHFAG (EPS 2011)
068 plusmn 002
BaBarPRL 101 (2008) 021801
123 plusmn 021 plusmn 004
BellePRD 77 (2008) 071101(R)
065 plusmn 021 plusmn 005
AverageHFAG correlated average
093 plusmn 015
BaBarPRD 79 032002 (2009)
065 plusmn 036 plusmn 005
BelleEPS 2011 preliminary
106 plusmn 021 plusmn 007
AverageHFAG correlated average
096 plusmn 019
BaBarPRD 79 032002 (2009)
071 plusmn 016 plusmn 003
BelleEPS 2011 preliminary
079 plusmn 013 plusmn 003
AverageHFAG correlated average
077 plusmn 010
BaBarPRD 79 032002 (2009)
063 plusmn 021 plusmn 003
BellePRL 93 (2004) 201802
055 plusmn 039 plusmn 012
AverageHFAG
061 plusmn 019
BaBarPRD 79 032002 (2009)
074 plusmn 023 plusmn 005
BellePRL 93 (2004) 201802
096 plusmn 043 plusmn 012
AverageHFAG
079 plusmn 021
H F A GH F A GEPS 2011
PRELIMINARY
Figure 9 Compilation of results on sin(2βeff) from (left) b rarr qqs and (right)brarr ccd transitions [8]
34 Measurement of γ
The angle γ is unique among CP violating observables in that it can be determined us-ing tree-level processes only exploiting the interference between (typically) b rarr cudand brarr ucd transitions that occurs when the process involves a neutral D meson recon-structed in a final state accessible to both D0 and D0 decays It therefore provides a SMbenchmark and its precise measurement is crucial in order to disentangle any non-SMcontributions to other processes via global CKM fits
Several different D decay final states have been studied in order to maximise the sen-sitivity to γ The archetype is the use of D decays to CP eigenstates the so-called GLWmethod [86 87] New results with this approach have recently become available fromBaBar [88] CDF [89] and LHCb [90] while the very latest results from Belle [91] areshown in Fig 10 The world average for the CP asymmetry in the processes involvingCP -even D decay final states including all these new results and illustrated in Fig 11(left) shows that CP violation in Bplusmn rarr DKplusmn decays is clearly established though nosingle measurement exceeds 5σ significance
Another powerful approach to constrain γ the so-called ADS method [92 93] comesfrom the use of doubly-Cabibbo-suppressed D decays (for example to the final stateK+πminus) Recent new results come from BaBar [94] Belle [95] and CDF [96] whilethe very latest results from LHCb [97] are shown in Fig 12 The world average for theparameter RADS which is the ratio of decay rates to the suppressed states compared tothose for the favoured channels including all these new results and illustrated in Fig 11(right) shows that the suppressed decay is now clearly established though no single mea-surement exceeds 5σ significance This is very promising for future γ determinations
Although the analyses withBplusmn rarr DKplusmn decays give the most precise results differentB decays have also been studied The use of both possible decays Dlowast rarr Dπ0 andDlowast rarr Dγ provides an extra handle on the extraction of γ fromBplusmn rarr DlowastKplusmn [98] that isbecoming visible in the most recent results [91 94] In addition theB0
d rarr DKlowast0 channel
10
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
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001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Overview of the CKM Matrix
in Fig 2 the precision is such that second-order effects related to the nuclear medium(radiative and isospin-breaking corrections) need to be accounted for This is achievedby obtaining a corrected quantity labelled Ft [22] that is confirmed to be constant to3times 10minus4 (see Fig 2) This allows |Vud| to be extracted
|Vud| = 097425plusmn 000022 (7)
3030
ft(s
)
3040
3060
3080
3050
3070
3090
Z of daughter
2010 30 400
3070
3080
3090
3060
Ft
(s)
C10
O14
Mg22
Cl34
Al26 mAr34
K38 m
Sc42
V46
Mn50
Co54
Ga62 Rb74
Figure 2 Uncorrected (ft) and corrected (Ft) values obtained from different0+ rarr 0+ transitions from Ref [22]
Various alternative approaches allow determinations of |Vud| with different meritsNuclear mirror decays (transitions between states with nuclear isospin 12) and neutronlifetime measurements are sensitive to both vector and axial-vector couplings and thelatter does not require nucleus dependent or isospin breaking corrections to be knownThe current experimental status of the neutron lifetime is controversial [7 23] (see alsoRefs [24 25]) but future experiments should reduce its uncertainty Determinationsfrom pion beta decay (which has only vector couplings) have the smallest theoreticaluncertainty though significantly increased data samples would be necessary to approachthe current sensitivity on |Vud|
23 Determination of |Vus|
The past few years have seen significant progress in the determination of |Vus| fromsemileptonic kaon decays as reviewed in Ref [26 27] Fig 3 summarises the valuesof f+(0) |Vus| determined experimentally using data from the BNL-E865 KLOE KTeVISTRA+ and NA48 experiments (the latest preliminary results from the NA48 collabora-tion [28] are not included) as well as the calculations of f+(0) mainly using lattice QCDtechniques Using f+(0) = 0959plusmn 0005 [29] the average value is obtained
|Vus| = 02254plusmn 00013 (8)
A result with comparable precision on the ratio of CKM matrix elements is obtainedfrom the widths of leptonic kaon and pion decays The experimental data together with
3
Tim Gershon
0213 0214 0215 0216 0217
0213 0214 0215 0216 0217
KL e3
KL micro3
KS e3
Kplusmn e3
Kplusmn micro3
094095
096097
098099
100
Nf=2
Nf=2+1
SPQcdR
RBC
JLQCD
QCDSF
HPQCD-FNAL
RBC-UKQCD-07
0960(5)(7)
0968(9)(6)
0967(6)
09647(15)stat
0984(12)
0962(11)
09644(49)
0974(11)
Clover
Clover
0976(10)
0961(8)
Cirigliano et al
Jamin et al
Bijnens amp Talavera
Leutwyler amp Roos 84
ETMC-09 09560(84)
Clover
TWMF
RBC-UKQCD-10 +3109599(37)-43
f+
Κ0π
+
(0)
Nf=0
DWF
- L
AT
TIC
E -
DWF
Stag
-χP
T+
LE
Cs-
χPT + 1Nc
χPT + disp
χPT + LR
Quark M
QM
Figure 3 (Left) Values of f+(0) |Vus| obtained from different semileptonic kaondecays giving an average f+(0) |Vus| = 02163 plusmn 00005 (Right) Calculations offK
0π+
+ (0) From Ref [26]
lattice QCD input fKfπ = 1193plusmn0006 [26] and accounting for isospin violation [30]gives
|VusVud| = 02316plusmn 00012 (9)
where both experimental and theoretical uncertainties are essentially uncorrelated withthose in the average for |Vus| given above This then allows a comparison of the differentdeterminations as well as a test of the unitarity of the first row of the CKM matrix Asshown in Fig 4 unitarity is found to hold to better than one part in 103 An alternative wayof viewing this result is that the Fermi constant measured in the quark sector is consistentwith the determination from the muon lifetime This is thus a beautiful demonstration ofthe universality of the weak interaction
0224
0226
0228
0972 0974 0976
Vud
Vu
s
0224
0226
0228
0972 0974 0976
Vud
(0+ rarr 0
+)
VusVud
(Kmicro2)
Vus
(Kl3
)
fit withunitarity
fit
un
itarity
Figure 4 Combination of constraints on the magnitudes of the elements of the firstrow of the CKM matrix From Ref [26]
Alternative approaches to measure |Vus| are possible using hyperon decays or hadronictau lepton decays For the latter the method relies on comparison of the inclusive strange
4
Overview of the CKM Matrix
and non-strange branching fractions These are determined experimentally from sums ofexclusive measurements and since not all decays have yet been measured rely somewhaton extrapolations (see Ref [31] for a detailed review) A recent study [32] estimates thevalue from hadronic tau decays to be
|Vus| = 02166plusmn 00019 (exp)plusmn 00005 (th) (10)
which is discrepant from the value from semileptonic kaon decays at the level of 37σTwo important points are to be noted firstly the intrinsic theoretical uncertainty in thisapproach is very small secondly the central value may change as the B factories com-plete their programmes of study of multibody hadronic tau decays1
24 Determination of |Vcd| and |Vcs|
For several years the benchmark determination of |Vcd| has been that based on charmproduction in neutrino interactions
|Vcd| = 0230plusmn 0011 (11)
However improved measurements of charm semileptonic decaysD rarr πlν from CLEO-c [35] provide the potential for further improvements The CLEO-c data is shown inFig 5 A recent review [13] gives a value based on this approach
|Vcd| = 0234plusmn 0007plusmn 0002plusmn 0025 (12)
where the last uncertainty is from lattice QCD determinations of the form factors [36 37]With reduced uncertainties from the lattice calculations this promises to provide a moreprecise value of this CKM matrix element2
Figure 5 Differential branching fraction for semileptonic charm decays as a functionof eν invariant mass squared q2 from CLEO-c [35] The results of fits to parametrisedform factors are also shown
Semileptonic charm decays this time D rarr Klν also provide the most precise de-termination of |Vcs| Using inputs from CLEO-c [35] (Fig 5) and lattice QCD calcula-tions [36] the current value is
|Vcs| = 0961plusmn 0011plusmn 0024 (13)1 As pointed out by A Hoecker at Lepton Photon there is a significant discrepancy between the BaBar [33]
and Belle [34] measurements of τ rarr 3 tracks + ν branching fractions that should also be resolved2 While these proceedings were in preparation improved lattice calculations became available [38]
5
Tim Gershon
where the uncertainties are experimental and from the lattice respectivelyLeptonic charm meson decays provide an alternative approach to determine the magni-
tudes of these CKM matrix elements Their decay rates involve also the decay constantswhich can be determined from lattice QCD and helicity suppression factors for example
Γ(D+s rarr l+ν
)=G2F
8πf2D+
sm2lMD+
s
(1minus m2
l
M2D+
s
)2
|Vcs|2 (14)
Significant improvements in the measurements ofD+s decays have come from BaBar [39]
Belle [40] and CLEO-c [41] These are usually expressed in terms of fD+s
using the valueof |Vcs| given above and can be compared to the lattice QCD calculations Equally thiscan be recast using the input from the lattice [42] to obtain
|Vcs| = 1005plusmn 0026plusmn 0016 (15)
where the uncertainties are experimental and from the lattice respectively It should benoted that a discrepancy that was apparent a few years ago (see for example Ref [43])has disappeared Moreover the dominant uncertainty is experimental so improved mea-surements from BES and current or future e+eminus B factory experiments would be wel-come
25 Determination of |Vcb| and |Vub|
Both exclusive and inclusive studies of semileptonic B decays have been used to obtain|Vcb| and |Vub| (for a detailed recent review see Ref [44]) For the former the reviewin the 2010 edition of the Particle Data Group review of particle physics [7] quotes a 2σtension between the two determinations
|Vcb| (excl) = (387plusmn 11)times 10minus3 |Vcb| (incl) = (415plusmn 07)times 10minus3
(16)
Updated data from Belle on B0d rarr Dlowastminuslν decays [45] and improved lattice QCD cal-
culations of the form-factor at zero recoil [46] reduce slightly both the uncertainty of theexclusive determination and the tension with the inclusive determination
It is also worth noting that the semitauonic decays B rarr D(lowast)τν have recently beenseen for the first time by BaBar [47ndash49] (see Fig 6) and Belle [50 51] The rates of thesedecays depend on |Vcb| but it is more common to measure their ratios relative to thosefor B rarr D(lowast)lν (l = e micro) decays These ratios are precisely predicted in the SM andare sensitive to potential contributions beyond the SM for example from charged Higgsbosons The isospin averaged ratios are determined to be
R(D) = 0456plusmn 0053plusmn 0056 RSM(D) = 031plusmn 002 R(Dlowast) = 0325plusmn 0023plusmn 0027 RSM(Dlowast) = 025plusmn 007
(17)
The excess over the SM is about 18σ (see also Ref [52] where determinations of |Vub|from leptonic B decays are also discussed)
The b rarr ulν decays can similarly be used to obtain measurements of |Vub| by eitherexclusive or inclusive methods Most recent progress has been on the exclusive B rarr πlνdecays where new results have become available from both BaBar [53 54] and Belle [55]as shown in Fig 7 The updated HFAG [8] average is [56]
|Vub| = (326plusmn 030)times 10minus3 (18)
6
Overview of the CKM Matrix
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60 f) + D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80 g) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40h) + D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60 f) + D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80 g) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40h) + D2 lt 120 GeVmiss
2 mle10
Figure 6 Signal for B rarr D(lowast)τν decays from BaBar [47] Note that the large peaksare due to backgrounds from D(lowast)lν (l = e micro) decays while the signals appears astails to large values of the missing mass squared variable m2
miss
where the dominant source of uncertainty is from the lattice QCD calculations of the formfactors [57]
)2 (GeV2Unfolded q
0 5 10 15 20 25
)2
(2 G
eV
times 2
q∆
)2
B(q
∆
0
2
4
6
8
10
12
14
16
shy610times
LCSR
FNALMILC
HPQCD
BGL fit to data
BK fit to data
data
)2c2 (GeV2Unfolded q0 5 10 15 20 25
2c
2)
2
Ge
V2
B(q
∆
0
2
4
6
8
10
12
14
16
18
20
shy610times
ISGW2
HPQCD
FNAL
LCSR
Data
Figure 7 Differential branching fractions of B0d rarr πminusl+ν decays as a function of
l+ν invariant mass squared q2 from (left) BaBar [53] and (right) Belle [55]
As was the case for |Vcb| there is a tension between inclusive and exclusive determi-nations (the world average value using the inclusive approach is |Vub| = (427plusmn 038)times10minus3 Although some commentators have pointed out that the large amount of theoreticalwork dedicated to the extraction of |Vub|may have led to an underestimation of the uncer-tainties [58] it is this authorrsquos view that more theoretical attention is necessary to resolvethe situation On the exclusive side improvements in lattice QCD calculations can beexpected while on the inclusive side an initiative to reduce uncertainties using global fitsis underway [59]
7
Tim Gershon
3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
As is widely known CP violation is one of the three ldquoSakharov conditionsrdquo [60] nec-essary for the evolution of a baryon asymmetry in the Universe Moreover the SM CPviolation encoded in the CKM matrix is not sufficient to explain the observed asym-metry Therefore there must be more sources of matter-antimatter asymmetry in natureThese could arise in almost any conceivable extension of the SM such as in an extendedquark sector in the lepton sector (leptogenesis) from anomalous gauge couplings in anextended Higgs sector and so on While all of these must be investigated testing theconsistency of the CKM mechanism in the quark sector provides the best chance to findnew sources of CP violation in the short term
Although the understanding of CP violation has advanced dramatically over the pastdecade it is important to realise that it remains a rarely observed phenomenon To dateit is only been observed (with gt 5σ significance) in the K0 and B0
d systems (Discus-sions of searches for CP violation in D0 and B0
s mixing can be found in Refs [61 62])In the B system the only 5σ significant measurements are of the parameters sin(2β)from JψKSL and similar decays from BaBar [63] and Belle [64] S(ηprimeKSL) fromBaBar [65] and Belle [66] S(π+πminus) from BaBar [67] and Belle [68] C(π+πminus) fromBelle [68] and ACP (K+πminus) from BaBar [67] Belle [69] and LHCb [70] (see alsoRef [52] on this last topic) The LHCb result on B0
d rarr K+πminus is thus the first 5σobservation of CP violation in the B system at a hadron collider experimentCP violation results are often expressed in terms of the so-called Unitarity Triangle
which is a graphical representation of one of the relations implied by the unitarity of theCKM matrix
VudVlowastub + VcdV
lowastcb + VtdV
lowasttb = 0 (19)
The angles of this triangle are usually denoted (α β γ) while its apex (after normalisingso that its base is unit length along the real axis) is given in terms of the Wolfensteinparameters (ρ η) [3 4]
31 Searches for CP violation in the charm sector
Almost all CP violation effects in the charm system are expected to be negligible inthe SM This therefore provides an excellent testing ground to look for unexpected ef-fects Various searches for direct CP violation effects (studies of mixing and indirectCP violation are discussed in Ref [62]) have been carried out recently for example inD+
(s) rarr KSπ+ and KSK
+ decays [71 72] in triple product asymmetries in four-bodyhadronic decays [73 74] and in Dalitz plot asymmetries in three-body decays [75] At thetime of Lepton Photon no significant signal for CP violation in charm had yet been seenalthough the world average asymmetry in D+ rarr KSπ
+ is more than 3σ from zero [8]this is consistent with originating from the CP violation in the neutral kaon system (seeRef [76] and references therein) However while these proceedings were being preparedLHCb announced a 35σ signal for the difference in time-integrated CP asymmetries be-tween D0 rarr K+Kminus and D0 rarr π+πminus decays [77] (CDF have also released less preciseresults on the same observable [78])
32 Measurement of sin(2β)
Both e+eminus B factory experiments BaBar and Belle have completed data taking Theresult on sin(2β) from B0
d rarr JψKSL (etc) with BaBarrsquos final data set (445 million
8
Overview of the CKM Matrix
BB pairs) has been published [63] while preliminary results following a reprocessing ofthe Belle data (772 million BB pairs) are available [64] A first analysis from LHCb isalso available [79] The results are compiled in Fig 8 At the level of precision that theexperiments are reaching it is important to check for effects that may perturb the naıveSM expectation S(JψKSL) = minusηCP sin(2β) where ηCP is the CP eigenvalue ofthe final state This can be done using channels that are related by flavour symmetries ndashB0d rarr Jψπ0 (related by SU(3)) orB0
s rarr JψK0S (related by U-spin) First observations
of the latter decay have recently been reported by CDF and LHCb [80 81] suggestingthat this approach will be possible with larger datasets
sin(2β) equiv sin(2φ1)
-2 -1 0 1 2 3
BaBarPRD 79 (2009) 072009
069 plusmn 003 plusmn 001
BaBar χc0 KSPRD 80 (2009) 112001
069 plusmn 052 plusmn 004 plusmn 007
BaBar Jψ (hadronic) KSPRD 69 (2004) 052001
156 plusmn 042 plusmn 021
BelleMoriond EW 2011 preliminary
067 plusmn 002 plusmn 001
ALEPHPLB 492 259 (2000)
084 +-018024 plusmn 016
OPALEPJ C5 379 (1998)
320 +-128000 plusmn 050
CDFPRD 61 072005 (2000)
079 +-004414
LHCbLHCb-CONF-2011-004
053 +-002289 plusmn 005
AverageHFAG
068 plusmn 002
H F A GH F A GBeauty 2011
PRELIMINARYβ equiv φ
1
ρndash
ηndash
-02 0 02 04 06 08 1-02
0
02
04
06
08
1
β equiv φ1 = (214 plusmn 08)˚
β equiv
φ1 =
(686
plusmn 0
8)˚
DIS
FA
VO
UR
ED
BY
Jψ
K D
DK
S amp D
h0
H F A GH F A GBeauty 2011
PRELIMINARY
Figure 8 (Left) Compilation of results on sin(2β) from B0d rarr JψKSL (etc) [8]
(Right) Corresponding constraint on ρndashη plane
The B factories have carried out a substantial programme of alternative measurementsof sin(2β) using different quark level transitions such as b rarr qqs (q = u d s egB0d rarr ηprimeK0
S) and b rarr ccd (eg B0d rarr D+Dminus) Compilations are shown in Fig 9 A
few years ago hints of deviations were apparent between the value of sin(2βeff) measuredin brarr qqs transitions and the reference value from brarr ccs These have diminished withthe latest data but effects of non-SM contributions at the O(10) level are not ruled outOne notable update is the new Belle result on B0
d rarr D+Dminus [82] which improves theconsistency between the results of the two B factories as well as with the SM
33 Measurement of α
The unitarity triangle angle α is constrained by measurements of and isospin relationsbetween B rarr ππ ρπ and ρρ decays [83 84] The situation has been stable for the lastfew years though the final results from both B factory experiments in all three systemsare still awaited Combining all available information the world average is [10]
α =(890 +44
minus42
) (20)
Since the average is dominated by results from the ρρ system two small comments arein order First the apparently high branching fraction of B+ rarr ρ+ρ0 which comesessentially from a single measurement [85] stretches the isospin triangle and reduces theuncertainty Secondly analyses to date while allowing CP violation in the rates haveassumed the longitudinal polarisation fraction is the same for B and B ndash but the mostgeneral analysis would allow a difference between the two
9
Tim Gershon
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
brarrccs
φ K
0
ηprime K
0
KS K
S K
S
π0 K
0
ρ0 K
S
ω K
S
f 0 K
S
K+ K
- K0
-08 -06 -04 -02 0 02 04 06 08 1 12 14 16
World Average 068 plusmn 002
BaBar 026 plusmn 026 plusmn 003
Belle 090 +-00
01
99
Average 056 +-00
11
68
BaBar 057 plusmn 008 plusmn 002
Belle 064 plusmn 010 plusmn 004
Average 059 plusmn 007
BaBar 094 +-00
22
14 plusmn 006
Belle 030 plusmn 032 plusmn 008
Average 072 plusmn 019
BaBar 055 plusmn 020 plusmn 003
Belle 067 plusmn 031 plusmn 008
Average 057 plusmn 017
BaBar 035 +-00
23
61 plusmn 006 plusmn 003
Belle 064 +-00
12
95 plusmn 009 plusmn 010
Average 054 +-00
12
81
BaBar 055 +-00
22
69 plusmn 002
Belle 011 plusmn 046 plusmn 007
Average 045 plusmn 024
BaBar 060 +-00
11
68
Belle 063 +-00
11
69
Average 062 +-00
11
13
BaBar 086 plusmn 008 plusmn 003
Belle 068 plusmn 015 plusmn 003 +-00
21
13
Average 082 plusmn 007
H F A GH F A GEndOfYear 2011
PRELIMINARY
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
brarrccs SCP
Jψ
π0 S
CP
D+ D
- SC
P
D+
D- S
CP
D+
- D-+
S+
-
D+
- D-+
S-+
-1 0 1 2
World AverageHFAG (EPS 2011)
068 plusmn 002
BaBarPRL 101 (2008) 021801
123 plusmn 021 plusmn 004
BellePRD 77 (2008) 071101(R)
065 plusmn 021 plusmn 005
AverageHFAG correlated average
093 plusmn 015
BaBarPRD 79 032002 (2009)
065 plusmn 036 plusmn 005
BelleEPS 2011 preliminary
106 plusmn 021 plusmn 007
AverageHFAG correlated average
096 plusmn 019
BaBarPRD 79 032002 (2009)
071 plusmn 016 plusmn 003
BelleEPS 2011 preliminary
079 plusmn 013 plusmn 003
AverageHFAG correlated average
077 plusmn 010
BaBarPRD 79 032002 (2009)
063 plusmn 021 plusmn 003
BellePRL 93 (2004) 201802
055 plusmn 039 plusmn 012
AverageHFAG
061 plusmn 019
BaBarPRD 79 032002 (2009)
074 plusmn 023 plusmn 005
BellePRL 93 (2004) 201802
096 plusmn 043 plusmn 012
AverageHFAG
079 plusmn 021
H F A GH F A GEPS 2011
PRELIMINARY
Figure 9 Compilation of results on sin(2βeff) from (left) b rarr qqs and (right)brarr ccd transitions [8]
34 Measurement of γ
The angle γ is unique among CP violating observables in that it can be determined us-ing tree-level processes only exploiting the interference between (typically) b rarr cudand brarr ucd transitions that occurs when the process involves a neutral D meson recon-structed in a final state accessible to both D0 and D0 decays It therefore provides a SMbenchmark and its precise measurement is crucial in order to disentangle any non-SMcontributions to other processes via global CKM fits
Several different D decay final states have been studied in order to maximise the sen-sitivity to γ The archetype is the use of D decays to CP eigenstates the so-called GLWmethod [86 87] New results with this approach have recently become available fromBaBar [88] CDF [89] and LHCb [90] while the very latest results from Belle [91] areshown in Fig 10 The world average for the CP asymmetry in the processes involvingCP -even D decay final states including all these new results and illustrated in Fig 11(left) shows that CP violation in Bplusmn rarr DKplusmn decays is clearly established though nosingle measurement exceeds 5σ significance
Another powerful approach to constrain γ the so-called ADS method [92 93] comesfrom the use of doubly-Cabibbo-suppressed D decays (for example to the final stateK+πminus) Recent new results come from BaBar [94] Belle [95] and CDF [96] whilethe very latest results from LHCb [97] are shown in Fig 12 The world average for theparameter RADS which is the ratio of decay rates to the suppressed states compared tothose for the favoured channels including all these new results and illustrated in Fig 11(right) shows that the suppressed decay is now clearly established though no single mea-surement exceeds 5σ significance This is very promising for future γ determinations
Although the analyses withBplusmn rarr DKplusmn decays give the most precise results differentB decays have also been studied The use of both possible decays Dlowast rarr Dπ0 andDlowast rarr Dγ provides an extra handle on the extraction of γ fromBplusmn rarr DlowastKplusmn [98] that isbecoming visible in the most recent results [91 94] In addition theB0
d rarr DKlowast0 channel
10
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
References
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Overview of the CKM Matrix
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[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
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Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
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001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Tim Gershon
0213 0214 0215 0216 0217
0213 0214 0215 0216 0217
KL e3
KL micro3
KS e3
Kplusmn e3
Kplusmn micro3
094095
096097
098099
100
Nf=2
Nf=2+1
SPQcdR
RBC
JLQCD
QCDSF
HPQCD-FNAL
RBC-UKQCD-07
0960(5)(7)
0968(9)(6)
0967(6)
09647(15)stat
0984(12)
0962(11)
09644(49)
0974(11)
Clover
Clover
0976(10)
0961(8)
Cirigliano et al
Jamin et al
Bijnens amp Talavera
Leutwyler amp Roos 84
ETMC-09 09560(84)
Clover
TWMF
RBC-UKQCD-10 +3109599(37)-43
f+
Κ0π
+
(0)
Nf=0
DWF
- L
AT
TIC
E -
DWF
Stag
-χP
T+
LE
Cs-
χPT + 1Nc
χPT + disp
χPT + LR
Quark M
QM
Figure 3 (Left) Values of f+(0) |Vus| obtained from different semileptonic kaondecays giving an average f+(0) |Vus| = 02163 plusmn 00005 (Right) Calculations offK
0π+
+ (0) From Ref [26]
lattice QCD input fKfπ = 1193plusmn0006 [26] and accounting for isospin violation [30]gives
|VusVud| = 02316plusmn 00012 (9)
where both experimental and theoretical uncertainties are essentially uncorrelated withthose in the average for |Vus| given above This then allows a comparison of the differentdeterminations as well as a test of the unitarity of the first row of the CKM matrix Asshown in Fig 4 unitarity is found to hold to better than one part in 103 An alternative wayof viewing this result is that the Fermi constant measured in the quark sector is consistentwith the determination from the muon lifetime This is thus a beautiful demonstration ofthe universality of the weak interaction
0224
0226
0228
0972 0974 0976
Vud
Vu
s
0224
0226
0228
0972 0974 0976
Vud
(0+ rarr 0
+)
VusVud
(Kmicro2)
Vus
(Kl3
)
fit withunitarity
fit
un
itarity
Figure 4 Combination of constraints on the magnitudes of the elements of the firstrow of the CKM matrix From Ref [26]
Alternative approaches to measure |Vus| are possible using hyperon decays or hadronictau lepton decays For the latter the method relies on comparison of the inclusive strange
4
Overview of the CKM Matrix
and non-strange branching fractions These are determined experimentally from sums ofexclusive measurements and since not all decays have yet been measured rely somewhaton extrapolations (see Ref [31] for a detailed review) A recent study [32] estimates thevalue from hadronic tau decays to be
|Vus| = 02166plusmn 00019 (exp)plusmn 00005 (th) (10)
which is discrepant from the value from semileptonic kaon decays at the level of 37σTwo important points are to be noted firstly the intrinsic theoretical uncertainty in thisapproach is very small secondly the central value may change as the B factories com-plete their programmes of study of multibody hadronic tau decays1
24 Determination of |Vcd| and |Vcs|
For several years the benchmark determination of |Vcd| has been that based on charmproduction in neutrino interactions
|Vcd| = 0230plusmn 0011 (11)
However improved measurements of charm semileptonic decaysD rarr πlν from CLEO-c [35] provide the potential for further improvements The CLEO-c data is shown inFig 5 A recent review [13] gives a value based on this approach
|Vcd| = 0234plusmn 0007plusmn 0002plusmn 0025 (12)
where the last uncertainty is from lattice QCD determinations of the form factors [36 37]With reduced uncertainties from the lattice calculations this promises to provide a moreprecise value of this CKM matrix element2
Figure 5 Differential branching fraction for semileptonic charm decays as a functionof eν invariant mass squared q2 from CLEO-c [35] The results of fits to parametrisedform factors are also shown
Semileptonic charm decays this time D rarr Klν also provide the most precise de-termination of |Vcs| Using inputs from CLEO-c [35] (Fig 5) and lattice QCD calcula-tions [36] the current value is
|Vcs| = 0961plusmn 0011plusmn 0024 (13)1 As pointed out by A Hoecker at Lepton Photon there is a significant discrepancy between the BaBar [33]
and Belle [34] measurements of τ rarr 3 tracks + ν branching fractions that should also be resolved2 While these proceedings were in preparation improved lattice calculations became available [38]
5
Tim Gershon
where the uncertainties are experimental and from the lattice respectivelyLeptonic charm meson decays provide an alternative approach to determine the magni-
tudes of these CKM matrix elements Their decay rates involve also the decay constantswhich can be determined from lattice QCD and helicity suppression factors for example
Γ(D+s rarr l+ν
)=G2F
8πf2D+
sm2lMD+
s
(1minus m2
l
M2D+
s
)2
|Vcs|2 (14)
Significant improvements in the measurements ofD+s decays have come from BaBar [39]
Belle [40] and CLEO-c [41] These are usually expressed in terms of fD+s
using the valueof |Vcs| given above and can be compared to the lattice QCD calculations Equally thiscan be recast using the input from the lattice [42] to obtain
|Vcs| = 1005plusmn 0026plusmn 0016 (15)
where the uncertainties are experimental and from the lattice respectively It should benoted that a discrepancy that was apparent a few years ago (see for example Ref [43])has disappeared Moreover the dominant uncertainty is experimental so improved mea-surements from BES and current or future e+eminus B factory experiments would be wel-come
25 Determination of |Vcb| and |Vub|
Both exclusive and inclusive studies of semileptonic B decays have been used to obtain|Vcb| and |Vub| (for a detailed recent review see Ref [44]) For the former the reviewin the 2010 edition of the Particle Data Group review of particle physics [7] quotes a 2σtension between the two determinations
|Vcb| (excl) = (387plusmn 11)times 10minus3 |Vcb| (incl) = (415plusmn 07)times 10minus3
(16)
Updated data from Belle on B0d rarr Dlowastminuslν decays [45] and improved lattice QCD cal-
culations of the form-factor at zero recoil [46] reduce slightly both the uncertainty of theexclusive determination and the tension with the inclusive determination
It is also worth noting that the semitauonic decays B rarr D(lowast)τν have recently beenseen for the first time by BaBar [47ndash49] (see Fig 6) and Belle [50 51] The rates of thesedecays depend on |Vcb| but it is more common to measure their ratios relative to thosefor B rarr D(lowast)lν (l = e micro) decays These ratios are precisely predicted in the SM andare sensitive to potential contributions beyond the SM for example from charged Higgsbosons The isospin averaged ratios are determined to be
R(D) = 0456plusmn 0053plusmn 0056 RSM(D) = 031plusmn 002 R(Dlowast) = 0325plusmn 0023plusmn 0027 RSM(Dlowast) = 025plusmn 007
(17)
The excess over the SM is about 18σ (see also Ref [52] where determinations of |Vub|from leptonic B decays are also discussed)
The b rarr ulν decays can similarly be used to obtain measurements of |Vub| by eitherexclusive or inclusive methods Most recent progress has been on the exclusive B rarr πlνdecays where new results have become available from both BaBar [53 54] and Belle [55]as shown in Fig 7 The updated HFAG [8] average is [56]
|Vub| = (326plusmn 030)times 10minus3 (18)
6
Overview of the CKM Matrix
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60 f) + D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80 g) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40h) + D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60 f) + D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80 g) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40h) + D2 lt 120 GeVmiss
2 mle10
Figure 6 Signal for B rarr D(lowast)τν decays from BaBar [47] Note that the large peaksare due to backgrounds from D(lowast)lν (l = e micro) decays while the signals appears astails to large values of the missing mass squared variable m2
miss
where the dominant source of uncertainty is from the lattice QCD calculations of the formfactors [57]
)2 (GeV2Unfolded q
0 5 10 15 20 25
)2
(2 G
eV
times 2
q∆
)2
B(q
∆
0
2
4
6
8
10
12
14
16
shy610times
LCSR
FNALMILC
HPQCD
BGL fit to data
BK fit to data
data
)2c2 (GeV2Unfolded q0 5 10 15 20 25
2c
2)
2
Ge
V2
B(q
∆
0
2
4
6
8
10
12
14
16
18
20
shy610times
ISGW2
HPQCD
FNAL
LCSR
Data
Figure 7 Differential branching fractions of B0d rarr πminusl+ν decays as a function of
l+ν invariant mass squared q2 from (left) BaBar [53] and (right) Belle [55]
As was the case for |Vcb| there is a tension between inclusive and exclusive determi-nations (the world average value using the inclusive approach is |Vub| = (427plusmn 038)times10minus3 Although some commentators have pointed out that the large amount of theoreticalwork dedicated to the extraction of |Vub|may have led to an underestimation of the uncer-tainties [58] it is this authorrsquos view that more theoretical attention is necessary to resolvethe situation On the exclusive side improvements in lattice QCD calculations can beexpected while on the inclusive side an initiative to reduce uncertainties using global fitsis underway [59]
7
Tim Gershon
3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
As is widely known CP violation is one of the three ldquoSakharov conditionsrdquo [60] nec-essary for the evolution of a baryon asymmetry in the Universe Moreover the SM CPviolation encoded in the CKM matrix is not sufficient to explain the observed asym-metry Therefore there must be more sources of matter-antimatter asymmetry in natureThese could arise in almost any conceivable extension of the SM such as in an extendedquark sector in the lepton sector (leptogenesis) from anomalous gauge couplings in anextended Higgs sector and so on While all of these must be investigated testing theconsistency of the CKM mechanism in the quark sector provides the best chance to findnew sources of CP violation in the short term
Although the understanding of CP violation has advanced dramatically over the pastdecade it is important to realise that it remains a rarely observed phenomenon To dateit is only been observed (with gt 5σ significance) in the K0 and B0
d systems (Discus-sions of searches for CP violation in D0 and B0
s mixing can be found in Refs [61 62])In the B system the only 5σ significant measurements are of the parameters sin(2β)from JψKSL and similar decays from BaBar [63] and Belle [64] S(ηprimeKSL) fromBaBar [65] and Belle [66] S(π+πminus) from BaBar [67] and Belle [68] C(π+πminus) fromBelle [68] and ACP (K+πminus) from BaBar [67] Belle [69] and LHCb [70] (see alsoRef [52] on this last topic) The LHCb result on B0
d rarr K+πminus is thus the first 5σobservation of CP violation in the B system at a hadron collider experimentCP violation results are often expressed in terms of the so-called Unitarity Triangle
which is a graphical representation of one of the relations implied by the unitarity of theCKM matrix
VudVlowastub + VcdV
lowastcb + VtdV
lowasttb = 0 (19)
The angles of this triangle are usually denoted (α β γ) while its apex (after normalisingso that its base is unit length along the real axis) is given in terms of the Wolfensteinparameters (ρ η) [3 4]
31 Searches for CP violation in the charm sector
Almost all CP violation effects in the charm system are expected to be negligible inthe SM This therefore provides an excellent testing ground to look for unexpected ef-fects Various searches for direct CP violation effects (studies of mixing and indirectCP violation are discussed in Ref [62]) have been carried out recently for example inD+
(s) rarr KSπ+ and KSK
+ decays [71 72] in triple product asymmetries in four-bodyhadronic decays [73 74] and in Dalitz plot asymmetries in three-body decays [75] At thetime of Lepton Photon no significant signal for CP violation in charm had yet been seenalthough the world average asymmetry in D+ rarr KSπ
+ is more than 3σ from zero [8]this is consistent with originating from the CP violation in the neutral kaon system (seeRef [76] and references therein) However while these proceedings were being preparedLHCb announced a 35σ signal for the difference in time-integrated CP asymmetries be-tween D0 rarr K+Kminus and D0 rarr π+πminus decays [77] (CDF have also released less preciseresults on the same observable [78])
32 Measurement of sin(2β)
Both e+eminus B factory experiments BaBar and Belle have completed data taking Theresult on sin(2β) from B0
d rarr JψKSL (etc) with BaBarrsquos final data set (445 million
8
Overview of the CKM Matrix
BB pairs) has been published [63] while preliminary results following a reprocessing ofthe Belle data (772 million BB pairs) are available [64] A first analysis from LHCb isalso available [79] The results are compiled in Fig 8 At the level of precision that theexperiments are reaching it is important to check for effects that may perturb the naıveSM expectation S(JψKSL) = minusηCP sin(2β) where ηCP is the CP eigenvalue ofthe final state This can be done using channels that are related by flavour symmetries ndashB0d rarr Jψπ0 (related by SU(3)) orB0
s rarr JψK0S (related by U-spin) First observations
of the latter decay have recently been reported by CDF and LHCb [80 81] suggestingthat this approach will be possible with larger datasets
sin(2β) equiv sin(2φ1)
-2 -1 0 1 2 3
BaBarPRD 79 (2009) 072009
069 plusmn 003 plusmn 001
BaBar χc0 KSPRD 80 (2009) 112001
069 plusmn 052 plusmn 004 plusmn 007
BaBar Jψ (hadronic) KSPRD 69 (2004) 052001
156 plusmn 042 plusmn 021
BelleMoriond EW 2011 preliminary
067 plusmn 002 plusmn 001
ALEPHPLB 492 259 (2000)
084 +-018024 plusmn 016
OPALEPJ C5 379 (1998)
320 +-128000 plusmn 050
CDFPRD 61 072005 (2000)
079 +-004414
LHCbLHCb-CONF-2011-004
053 +-002289 plusmn 005
AverageHFAG
068 plusmn 002
H F A GH F A GBeauty 2011
PRELIMINARYβ equiv φ
1
ρndash
ηndash
-02 0 02 04 06 08 1-02
0
02
04
06
08
1
β equiv φ1 = (214 plusmn 08)˚
β equiv
φ1 =
(686
plusmn 0
8)˚
DIS
FA
VO
UR
ED
BY
Jψ
K D
DK
S amp D
h0
H F A GH F A GBeauty 2011
PRELIMINARY
Figure 8 (Left) Compilation of results on sin(2β) from B0d rarr JψKSL (etc) [8]
(Right) Corresponding constraint on ρndashη plane
The B factories have carried out a substantial programme of alternative measurementsof sin(2β) using different quark level transitions such as b rarr qqs (q = u d s egB0d rarr ηprimeK0
S) and b rarr ccd (eg B0d rarr D+Dminus) Compilations are shown in Fig 9 A
few years ago hints of deviations were apparent between the value of sin(2βeff) measuredin brarr qqs transitions and the reference value from brarr ccs These have diminished withthe latest data but effects of non-SM contributions at the O(10) level are not ruled outOne notable update is the new Belle result on B0
d rarr D+Dminus [82] which improves theconsistency between the results of the two B factories as well as with the SM
33 Measurement of α
The unitarity triangle angle α is constrained by measurements of and isospin relationsbetween B rarr ππ ρπ and ρρ decays [83 84] The situation has been stable for the lastfew years though the final results from both B factory experiments in all three systemsare still awaited Combining all available information the world average is [10]
α =(890 +44
minus42
) (20)
Since the average is dominated by results from the ρρ system two small comments arein order First the apparently high branching fraction of B+ rarr ρ+ρ0 which comesessentially from a single measurement [85] stretches the isospin triangle and reduces theuncertainty Secondly analyses to date while allowing CP violation in the rates haveassumed the longitudinal polarisation fraction is the same for B and B ndash but the mostgeneral analysis would allow a difference between the two
9
Tim Gershon
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
brarrccs
φ K
0
ηprime K
0
KS K
S K
S
π0 K
0
ρ0 K
S
ω K
S
f 0 K
S
K+ K
- K0
-08 -06 -04 -02 0 02 04 06 08 1 12 14 16
World Average 068 plusmn 002
BaBar 026 plusmn 026 plusmn 003
Belle 090 +-00
01
99
Average 056 +-00
11
68
BaBar 057 plusmn 008 plusmn 002
Belle 064 plusmn 010 plusmn 004
Average 059 plusmn 007
BaBar 094 +-00
22
14 plusmn 006
Belle 030 plusmn 032 plusmn 008
Average 072 plusmn 019
BaBar 055 plusmn 020 plusmn 003
Belle 067 plusmn 031 plusmn 008
Average 057 plusmn 017
BaBar 035 +-00
23
61 plusmn 006 plusmn 003
Belle 064 +-00
12
95 plusmn 009 plusmn 010
Average 054 +-00
12
81
BaBar 055 +-00
22
69 plusmn 002
Belle 011 plusmn 046 plusmn 007
Average 045 plusmn 024
BaBar 060 +-00
11
68
Belle 063 +-00
11
69
Average 062 +-00
11
13
BaBar 086 plusmn 008 plusmn 003
Belle 068 plusmn 015 plusmn 003 +-00
21
13
Average 082 plusmn 007
H F A GH F A GEndOfYear 2011
PRELIMINARY
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
brarrccs SCP
Jψ
π0 S
CP
D+ D
- SC
P
D+
D- S
CP
D+
- D-+
S+
-
D+
- D-+
S-+
-1 0 1 2
World AverageHFAG (EPS 2011)
068 plusmn 002
BaBarPRL 101 (2008) 021801
123 plusmn 021 plusmn 004
BellePRD 77 (2008) 071101(R)
065 plusmn 021 plusmn 005
AverageHFAG correlated average
093 plusmn 015
BaBarPRD 79 032002 (2009)
065 plusmn 036 plusmn 005
BelleEPS 2011 preliminary
106 plusmn 021 plusmn 007
AverageHFAG correlated average
096 plusmn 019
BaBarPRD 79 032002 (2009)
071 plusmn 016 plusmn 003
BelleEPS 2011 preliminary
079 plusmn 013 plusmn 003
AverageHFAG correlated average
077 plusmn 010
BaBarPRD 79 032002 (2009)
063 plusmn 021 plusmn 003
BellePRL 93 (2004) 201802
055 plusmn 039 plusmn 012
AverageHFAG
061 plusmn 019
BaBarPRD 79 032002 (2009)
074 plusmn 023 plusmn 005
BellePRL 93 (2004) 201802
096 plusmn 043 plusmn 012
AverageHFAG
079 plusmn 021
H F A GH F A GEPS 2011
PRELIMINARY
Figure 9 Compilation of results on sin(2βeff) from (left) b rarr qqs and (right)brarr ccd transitions [8]
34 Measurement of γ
The angle γ is unique among CP violating observables in that it can be determined us-ing tree-level processes only exploiting the interference between (typically) b rarr cudand brarr ucd transitions that occurs when the process involves a neutral D meson recon-structed in a final state accessible to both D0 and D0 decays It therefore provides a SMbenchmark and its precise measurement is crucial in order to disentangle any non-SMcontributions to other processes via global CKM fits
Several different D decay final states have been studied in order to maximise the sen-sitivity to γ The archetype is the use of D decays to CP eigenstates the so-called GLWmethod [86 87] New results with this approach have recently become available fromBaBar [88] CDF [89] and LHCb [90] while the very latest results from Belle [91] areshown in Fig 10 The world average for the CP asymmetry in the processes involvingCP -even D decay final states including all these new results and illustrated in Fig 11(left) shows that CP violation in Bplusmn rarr DKplusmn decays is clearly established though nosingle measurement exceeds 5σ significance
Another powerful approach to constrain γ the so-called ADS method [92 93] comesfrom the use of doubly-Cabibbo-suppressed D decays (for example to the final stateK+πminus) Recent new results come from BaBar [94] Belle [95] and CDF [96] whilethe very latest results from LHCb [97] are shown in Fig 12 The world average for theparameter RADS which is the ratio of decay rates to the suppressed states compared tothose for the favoured channels including all these new results and illustrated in Fig 11(right) shows that the suppressed decay is now clearly established though no single mea-surement exceeds 5σ significance This is very promising for future γ determinations
Although the analyses withBplusmn rarr DKplusmn decays give the most precise results differentB decays have also been studied The use of both possible decays Dlowast rarr Dπ0 andDlowast rarr Dγ provides an extra handle on the extraction of γ fromBplusmn rarr DlowastKplusmn [98] that isbecoming visible in the most recent results [91 94] In addition theB0
d rarr DKlowast0 channel
10
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
References
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[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
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Overview of the CKM Matrix
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08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Overview of the CKM Matrix
and non-strange branching fractions These are determined experimentally from sums ofexclusive measurements and since not all decays have yet been measured rely somewhaton extrapolations (see Ref [31] for a detailed review) A recent study [32] estimates thevalue from hadronic tau decays to be
|Vus| = 02166plusmn 00019 (exp)plusmn 00005 (th) (10)
which is discrepant from the value from semileptonic kaon decays at the level of 37σTwo important points are to be noted firstly the intrinsic theoretical uncertainty in thisapproach is very small secondly the central value may change as the B factories com-plete their programmes of study of multibody hadronic tau decays1
24 Determination of |Vcd| and |Vcs|
For several years the benchmark determination of |Vcd| has been that based on charmproduction in neutrino interactions
|Vcd| = 0230plusmn 0011 (11)
However improved measurements of charm semileptonic decaysD rarr πlν from CLEO-c [35] provide the potential for further improvements The CLEO-c data is shown inFig 5 A recent review [13] gives a value based on this approach
|Vcd| = 0234plusmn 0007plusmn 0002plusmn 0025 (12)
where the last uncertainty is from lattice QCD determinations of the form factors [36 37]With reduced uncertainties from the lattice calculations this promises to provide a moreprecise value of this CKM matrix element2
Figure 5 Differential branching fraction for semileptonic charm decays as a functionof eν invariant mass squared q2 from CLEO-c [35] The results of fits to parametrisedform factors are also shown
Semileptonic charm decays this time D rarr Klν also provide the most precise de-termination of |Vcs| Using inputs from CLEO-c [35] (Fig 5) and lattice QCD calcula-tions [36] the current value is
|Vcs| = 0961plusmn 0011plusmn 0024 (13)1 As pointed out by A Hoecker at Lepton Photon there is a significant discrepancy between the BaBar [33]
and Belle [34] measurements of τ rarr 3 tracks + ν branching fractions that should also be resolved2 While these proceedings were in preparation improved lattice calculations became available [38]
5
Tim Gershon
where the uncertainties are experimental and from the lattice respectivelyLeptonic charm meson decays provide an alternative approach to determine the magni-
tudes of these CKM matrix elements Their decay rates involve also the decay constantswhich can be determined from lattice QCD and helicity suppression factors for example
Γ(D+s rarr l+ν
)=G2F
8πf2D+
sm2lMD+
s
(1minus m2
l
M2D+
s
)2
|Vcs|2 (14)
Significant improvements in the measurements ofD+s decays have come from BaBar [39]
Belle [40] and CLEO-c [41] These are usually expressed in terms of fD+s
using the valueof |Vcs| given above and can be compared to the lattice QCD calculations Equally thiscan be recast using the input from the lattice [42] to obtain
|Vcs| = 1005plusmn 0026plusmn 0016 (15)
where the uncertainties are experimental and from the lattice respectively It should benoted that a discrepancy that was apparent a few years ago (see for example Ref [43])has disappeared Moreover the dominant uncertainty is experimental so improved mea-surements from BES and current or future e+eminus B factory experiments would be wel-come
25 Determination of |Vcb| and |Vub|
Both exclusive and inclusive studies of semileptonic B decays have been used to obtain|Vcb| and |Vub| (for a detailed recent review see Ref [44]) For the former the reviewin the 2010 edition of the Particle Data Group review of particle physics [7] quotes a 2σtension between the two determinations
|Vcb| (excl) = (387plusmn 11)times 10minus3 |Vcb| (incl) = (415plusmn 07)times 10minus3
(16)
Updated data from Belle on B0d rarr Dlowastminuslν decays [45] and improved lattice QCD cal-
culations of the form-factor at zero recoil [46] reduce slightly both the uncertainty of theexclusive determination and the tension with the inclusive determination
It is also worth noting that the semitauonic decays B rarr D(lowast)τν have recently beenseen for the first time by BaBar [47ndash49] (see Fig 6) and Belle [50 51] The rates of thesedecays depend on |Vcb| but it is more common to measure their ratios relative to thosefor B rarr D(lowast)lν (l = e micro) decays These ratios are precisely predicted in the SM andare sensitive to potential contributions beyond the SM for example from charged Higgsbosons The isospin averaged ratios are determined to be
R(D) = 0456plusmn 0053plusmn 0056 RSM(D) = 031plusmn 002 R(Dlowast) = 0325plusmn 0023plusmn 0027 RSM(Dlowast) = 025plusmn 007
(17)
The excess over the SM is about 18σ (see also Ref [52] where determinations of |Vub|from leptonic B decays are also discussed)
The b rarr ulν decays can similarly be used to obtain measurements of |Vub| by eitherexclusive or inclusive methods Most recent progress has been on the exclusive B rarr πlνdecays where new results have become available from both BaBar [53 54] and Belle [55]as shown in Fig 7 The updated HFAG [8] average is [56]
|Vub| = (326plusmn 030)times 10minus3 (18)
6
Overview of the CKM Matrix
)2 (Gevmiss2m
0 5
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ents
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40h) + D2 lt 120 GeVmiss
2 mle10
Figure 6 Signal for B rarr D(lowast)τν decays from BaBar [47] Note that the large peaksare due to backgrounds from D(lowast)lν (l = e micro) decays while the signals appears astails to large values of the missing mass squared variable m2
miss
where the dominant source of uncertainty is from the lattice QCD calculations of the formfactors [57]
)2 (GeV2Unfolded q
0 5 10 15 20 25
)2
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LCSR
Data
Figure 7 Differential branching fractions of B0d rarr πminusl+ν decays as a function of
l+ν invariant mass squared q2 from (left) BaBar [53] and (right) Belle [55]
As was the case for |Vcb| there is a tension between inclusive and exclusive determi-nations (the world average value using the inclusive approach is |Vub| = (427plusmn 038)times10minus3 Although some commentators have pointed out that the large amount of theoreticalwork dedicated to the extraction of |Vub|may have led to an underestimation of the uncer-tainties [58] it is this authorrsquos view that more theoretical attention is necessary to resolvethe situation On the exclusive side improvements in lattice QCD calculations can beexpected while on the inclusive side an initiative to reduce uncertainties using global fitsis underway [59]
7
Tim Gershon
3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
As is widely known CP violation is one of the three ldquoSakharov conditionsrdquo [60] nec-essary for the evolution of a baryon asymmetry in the Universe Moreover the SM CPviolation encoded in the CKM matrix is not sufficient to explain the observed asym-metry Therefore there must be more sources of matter-antimatter asymmetry in natureThese could arise in almost any conceivable extension of the SM such as in an extendedquark sector in the lepton sector (leptogenesis) from anomalous gauge couplings in anextended Higgs sector and so on While all of these must be investigated testing theconsistency of the CKM mechanism in the quark sector provides the best chance to findnew sources of CP violation in the short term
Although the understanding of CP violation has advanced dramatically over the pastdecade it is important to realise that it remains a rarely observed phenomenon To dateit is only been observed (with gt 5σ significance) in the K0 and B0
d systems (Discus-sions of searches for CP violation in D0 and B0
s mixing can be found in Refs [61 62])In the B system the only 5σ significant measurements are of the parameters sin(2β)from JψKSL and similar decays from BaBar [63] and Belle [64] S(ηprimeKSL) fromBaBar [65] and Belle [66] S(π+πminus) from BaBar [67] and Belle [68] C(π+πminus) fromBelle [68] and ACP (K+πminus) from BaBar [67] Belle [69] and LHCb [70] (see alsoRef [52] on this last topic) The LHCb result on B0
d rarr K+πminus is thus the first 5σobservation of CP violation in the B system at a hadron collider experimentCP violation results are often expressed in terms of the so-called Unitarity Triangle
which is a graphical representation of one of the relations implied by the unitarity of theCKM matrix
VudVlowastub + VcdV
lowastcb + VtdV
lowasttb = 0 (19)
The angles of this triangle are usually denoted (α β γ) while its apex (after normalisingso that its base is unit length along the real axis) is given in terms of the Wolfensteinparameters (ρ η) [3 4]
31 Searches for CP violation in the charm sector
Almost all CP violation effects in the charm system are expected to be negligible inthe SM This therefore provides an excellent testing ground to look for unexpected ef-fects Various searches for direct CP violation effects (studies of mixing and indirectCP violation are discussed in Ref [62]) have been carried out recently for example inD+
(s) rarr KSπ+ and KSK
+ decays [71 72] in triple product asymmetries in four-bodyhadronic decays [73 74] and in Dalitz plot asymmetries in three-body decays [75] At thetime of Lepton Photon no significant signal for CP violation in charm had yet been seenalthough the world average asymmetry in D+ rarr KSπ
+ is more than 3σ from zero [8]this is consistent with originating from the CP violation in the neutral kaon system (seeRef [76] and references therein) However while these proceedings were being preparedLHCb announced a 35σ signal for the difference in time-integrated CP asymmetries be-tween D0 rarr K+Kminus and D0 rarr π+πminus decays [77] (CDF have also released less preciseresults on the same observable [78])
32 Measurement of sin(2β)
Both e+eminus B factory experiments BaBar and Belle have completed data taking Theresult on sin(2β) from B0
d rarr JψKSL (etc) with BaBarrsquos final data set (445 million
8
Overview of the CKM Matrix
BB pairs) has been published [63] while preliminary results following a reprocessing ofthe Belle data (772 million BB pairs) are available [64] A first analysis from LHCb isalso available [79] The results are compiled in Fig 8 At the level of precision that theexperiments are reaching it is important to check for effects that may perturb the naıveSM expectation S(JψKSL) = minusηCP sin(2β) where ηCP is the CP eigenvalue ofthe final state This can be done using channels that are related by flavour symmetries ndashB0d rarr Jψπ0 (related by SU(3)) orB0
s rarr JψK0S (related by U-spin) First observations
of the latter decay have recently been reported by CDF and LHCb [80 81] suggestingthat this approach will be possible with larger datasets
sin(2β) equiv sin(2φ1)
-2 -1 0 1 2 3
BaBarPRD 79 (2009) 072009
069 plusmn 003 plusmn 001
BaBar χc0 KSPRD 80 (2009) 112001
069 plusmn 052 plusmn 004 plusmn 007
BaBar Jψ (hadronic) KSPRD 69 (2004) 052001
156 plusmn 042 plusmn 021
BelleMoriond EW 2011 preliminary
067 plusmn 002 plusmn 001
ALEPHPLB 492 259 (2000)
084 +-018024 plusmn 016
OPALEPJ C5 379 (1998)
320 +-128000 plusmn 050
CDFPRD 61 072005 (2000)
079 +-004414
LHCbLHCb-CONF-2011-004
053 +-002289 plusmn 005
AverageHFAG
068 plusmn 002
H F A GH F A GBeauty 2011
PRELIMINARYβ equiv φ
1
ρndash
ηndash
-02 0 02 04 06 08 1-02
0
02
04
06
08
1
β equiv φ1 = (214 plusmn 08)˚
β equiv
φ1 =
(686
plusmn 0
8)˚
DIS
FA
VO
UR
ED
BY
Jψ
K D
DK
S amp D
h0
H F A GH F A GBeauty 2011
PRELIMINARY
Figure 8 (Left) Compilation of results on sin(2β) from B0d rarr JψKSL (etc) [8]
(Right) Corresponding constraint on ρndashη plane
The B factories have carried out a substantial programme of alternative measurementsof sin(2β) using different quark level transitions such as b rarr qqs (q = u d s egB0d rarr ηprimeK0
S) and b rarr ccd (eg B0d rarr D+Dminus) Compilations are shown in Fig 9 A
few years ago hints of deviations were apparent between the value of sin(2βeff) measuredin brarr qqs transitions and the reference value from brarr ccs These have diminished withthe latest data but effects of non-SM contributions at the O(10) level are not ruled outOne notable update is the new Belle result on B0
d rarr D+Dminus [82] which improves theconsistency between the results of the two B factories as well as with the SM
33 Measurement of α
The unitarity triangle angle α is constrained by measurements of and isospin relationsbetween B rarr ππ ρπ and ρρ decays [83 84] The situation has been stable for the lastfew years though the final results from both B factory experiments in all three systemsare still awaited Combining all available information the world average is [10]
α =(890 +44
minus42
) (20)
Since the average is dominated by results from the ρρ system two small comments arein order First the apparently high branching fraction of B+ rarr ρ+ρ0 which comesessentially from a single measurement [85] stretches the isospin triangle and reduces theuncertainty Secondly analyses to date while allowing CP violation in the rates haveassumed the longitudinal polarisation fraction is the same for B and B ndash but the mostgeneral analysis would allow a difference between the two
9
Tim Gershon
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
brarrccs
φ K
0
ηprime K
0
KS K
S K
S
π0 K
0
ρ0 K
S
ω K
S
f 0 K
S
K+ K
- K0
-08 -06 -04 -02 0 02 04 06 08 1 12 14 16
World Average 068 plusmn 002
BaBar 026 plusmn 026 plusmn 003
Belle 090 +-00
01
99
Average 056 +-00
11
68
BaBar 057 plusmn 008 plusmn 002
Belle 064 plusmn 010 plusmn 004
Average 059 plusmn 007
BaBar 094 +-00
22
14 plusmn 006
Belle 030 plusmn 032 plusmn 008
Average 072 plusmn 019
BaBar 055 plusmn 020 plusmn 003
Belle 067 plusmn 031 plusmn 008
Average 057 plusmn 017
BaBar 035 +-00
23
61 plusmn 006 plusmn 003
Belle 064 +-00
12
95 plusmn 009 plusmn 010
Average 054 +-00
12
81
BaBar 055 +-00
22
69 plusmn 002
Belle 011 plusmn 046 plusmn 007
Average 045 plusmn 024
BaBar 060 +-00
11
68
Belle 063 +-00
11
69
Average 062 +-00
11
13
BaBar 086 plusmn 008 plusmn 003
Belle 068 plusmn 015 plusmn 003 +-00
21
13
Average 082 plusmn 007
H F A GH F A GEndOfYear 2011
PRELIMINARY
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
brarrccs SCP
Jψ
π0 S
CP
D+ D
- SC
P
D+
D- S
CP
D+
- D-+
S+
-
D+
- D-+
S-+
-1 0 1 2
World AverageHFAG (EPS 2011)
068 plusmn 002
BaBarPRL 101 (2008) 021801
123 plusmn 021 plusmn 004
BellePRD 77 (2008) 071101(R)
065 plusmn 021 plusmn 005
AverageHFAG correlated average
093 plusmn 015
BaBarPRD 79 032002 (2009)
065 plusmn 036 plusmn 005
BelleEPS 2011 preliminary
106 plusmn 021 plusmn 007
AverageHFAG correlated average
096 plusmn 019
BaBarPRD 79 032002 (2009)
071 plusmn 016 plusmn 003
BelleEPS 2011 preliminary
079 plusmn 013 plusmn 003
AverageHFAG correlated average
077 plusmn 010
BaBarPRD 79 032002 (2009)
063 plusmn 021 plusmn 003
BellePRL 93 (2004) 201802
055 plusmn 039 plusmn 012
AverageHFAG
061 plusmn 019
BaBarPRD 79 032002 (2009)
074 plusmn 023 plusmn 005
BellePRL 93 (2004) 201802
096 plusmn 043 plusmn 012
AverageHFAG
079 plusmn 021
H F A GH F A GEPS 2011
PRELIMINARY
Figure 9 Compilation of results on sin(2βeff) from (left) b rarr qqs and (right)brarr ccd transitions [8]
34 Measurement of γ
The angle γ is unique among CP violating observables in that it can be determined us-ing tree-level processes only exploiting the interference between (typically) b rarr cudand brarr ucd transitions that occurs when the process involves a neutral D meson recon-structed in a final state accessible to both D0 and D0 decays It therefore provides a SMbenchmark and its precise measurement is crucial in order to disentangle any non-SMcontributions to other processes via global CKM fits
Several different D decay final states have been studied in order to maximise the sen-sitivity to γ The archetype is the use of D decays to CP eigenstates the so-called GLWmethod [86 87] New results with this approach have recently become available fromBaBar [88] CDF [89] and LHCb [90] while the very latest results from Belle [91] areshown in Fig 10 The world average for the CP asymmetry in the processes involvingCP -even D decay final states including all these new results and illustrated in Fig 11(left) shows that CP violation in Bplusmn rarr DKplusmn decays is clearly established though nosingle measurement exceeds 5σ significance
Another powerful approach to constrain γ the so-called ADS method [92 93] comesfrom the use of doubly-Cabibbo-suppressed D decays (for example to the final stateK+πminus) Recent new results come from BaBar [94] Belle [95] and CDF [96] whilethe very latest results from LHCb [97] are shown in Fig 12 The world average for theparameter RADS which is the ratio of decay rates to the suppressed states compared tothose for the favoured channels including all these new results and illustrated in Fig 11(right) shows that the suppressed decay is now clearly established though no single mea-surement exceeds 5σ significance This is very promising for future γ determinations
Although the analyses withBplusmn rarr DKplusmn decays give the most precise results differentB decays have also been studied The use of both possible decays Dlowast rarr Dπ0 andDlowast rarr Dγ provides an extra handle on the extraction of γ fromBplusmn rarr DlowastKplusmn [98] that isbecoming visible in the most recent results [91 94] In addition theB0
d rarr DKlowast0 channel
10
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
References
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9403384[5] A Dighe (2011) these proceeedings[6] V Lubicz (2011) these proceeedings[7] K Nakamura et al (Particle Data Group) J Phys G37 075021 (2010)[8] D Asner et al (Heavy Flavor Averaging Group) (2010) 10101589 URL http
wwwslacstanfordeduxorghfag[9] M Antonelli et al PhysRept 494 197 (2010) 09075386
[10] J Charles et al (CKMfitter) EurPhysJ C41 1 (2005) hep-ph0406184 URL httpckmfitterin2p3fr
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[12] T Spadaro and A Young (2011) 11120238[13] J Laiho BD Pecjak and C Schwanda (2011) 11073934[14] M Gorbahn M Patel and S Robertson (2011) 11040826[15] M Kreps A Lenz and O Leroy (2011) 11034962[16] R Fleischer and S Ricciardi (2011) 11044029[17] MT Graham D Tonelli and J Zupan (2011) 11050179[18] DM Webber et al (MuLan) PhysRevLett 106 041803 (2011) 10100991[19] PJ Mohr BN Taylor and DB Newell RevModPhys 80 633 (2008) 08010028[20] WJ Marciano PhysRev D60 093006 (1999) hep-ph9903451[21] A Pak and A Czarnecki PhysRevLett 100 241807 (2008) 08030960[22] JC Hardy and IS Towner PhysRev C79 055502 (2009) 08121202[23] A Pichlmaier V Varlamov K Schreckenbach and P Geltenbort PhysLett B693 221
(2010)
5 At Lepton Photon 2011 the author compared the long wait to discover effects beyond the SM to that forIndian batting hero Sachin Tendulkar to achieve his 100th century in international cricket Sadly at the time ofwriting these proceedings and despite some close calls we are still waiting for both historic achievements
14
Overview of the CKM Matrix
[24] JS Nico J Phys G36 104001 (2009)[25] S Paul NuclInstrumMeth A611 157 (2009) 09020169[26] M Antonelli et al EurPhysJ C69 399 (2010) 10052323[27] V Cirigliano G Ecker H Neufeld A Pich and J Portoles (2011) 11076001[28] M Veltri (2011) 11015031[29] PA Boyle et al EurPhysJ C69 159 (2010) 10040886[30] V Cirigliano and H Neufeld PhysLett B700 7 (2011) 11020563[31] M Davier A Hocker and Z Zhang RevModPhys 78 1043 (2006) hep-ph0507078[32] A Pich NuclPhysProcSuppl 218 89 (2011) 11012107[33] B Aubert et al (BABAR) Phys Rev Lett 100 011801 (2008) 07072981[34] MJ Lee et al (Belle) Phys Rev D81 113007 (2010) 10010083[35] D Besson et al (CLEO) PhysRev D80 032005 (2009) 09062983[36] H Na CTH Davies E Follana GP Lepage and J Shigemitsu PhysRev D82 114506
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(2010) 10112166[47] BABAR collaboration (2011) Preliminary results presented at EPS2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=30ampsessionId=2ampmaterialId=slidesampconfId=5116
[48] B Aubert et al (BABAR) PhysRevLett 100 021801 (2008) 07091698[49] B Aubert et al (BABAR) PhysRev D79 092002 (2009) 09022660[50] A Matyja et al (Belle) PhysRevLett 99 191807 (2007) 07064429[51] A Bozek et al (Belle) PhysRev D82 072005 (2010) 10052302[52] YJ Kwon (2011) these proceeedings[53] P del Amo Sanchez et al (BABAR) PhysRev D83 052011 (2011) 10100987[54] P del Amo Sanchez et al (BABAR) PhysRev D83 032007 (2011) 10053288[55] H Ha et al (Belle) PhysRev D83 071101 (2011) 10120090[56] P Urquijo (2011) Preliminary results presented at EPS2011 URL http
indicoin2p3frmaterialDisplaypycontribId=1016ampsessionId=2ampmaterialId=slidesampconfId=5116
[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
httpindicoin2p3frgetFilepyaccesscontribId=114ampsessionId=7ampresId=0ampmaterialId=slidesampconfId=4403
[65] B Aubert et al (BABAR) Phys Rev D79 052003 (2009) 08091174[66] K-F Chen et al (Belle) Phys Rev Lett 98 031802 (2007) hep-ex0608039[67] B Aubert et al (BABAR) PhysRevLett 99 021603 (2007) hep-ex0703016[68] H Ishino et al (Belle) Phys Rev Lett 98 211801 (2007) hep-ex0608035
15
Tim Gershon
[69] P Chang (Belle) (2011) Preliminary results presented at EPS 2011 URLhttpindicoin2p3frmaterialDisplaypycontribId=1019ampsessionId=2ampmaterialId=slidesampconfId=5116
[70] LHCb collaboration (2011) LHCb-CONF-2011-042[71] BR Ko et al (Belle) PhysRevLett 104 181602 (2010) 10013202[72] P del Amo Sanchez et al (BABAR) PhysRev D83 071103 (2011) 10115477[73] P del Amo Sanchez et al (BABAR) PhysRev D81 111103 (2010) 10033397[74] JP Lees et al (BABAR) PhysRev D84 031103 (2011) 11054410[75] R Aaij et al (LHCb) (2011) 11103970[76] Y Grossman and Y Nir (2011) 11103790[77] R Aaij et al (LHCb) (2011) 11120938[78] T Aaltonen et al (CDF) PhysRevD (2011) 11115023[79] LHCb collaboration (2011) LHCb-CONF-2011-004[80] T Aaltonen et al (CDF) PhysRev D83 052012 (2011) 11021961[81] LHCb collaboration (2011) LHCb-CONF-2011-048[82] T Higuchi (Belle) (2011) Preliminary results presented at EPS 2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=1017ampsessionId=2ampmaterialId=slidesampconfId=5116
[83] M Gronau and D London PhysRevLett 65 3381 (1990)[84] AE Snyder and HR Quinn PhysRev D48 2139 (1993)[85] B Aubert et al (BABAR) Phys Rev Lett 102 141802 (2009) 09013522[86] M Gronau and D London PhysLett B253 483 (1991)[87] M Gronau and D Wyler PhysLett B265 172 (1991)[88] P del Amo Sanchez et al (BABAR) Phys Rev D82 072004 (2010) 10070504[89] T Aaltonen et al (CDF) Phys Rev D81 031105 (2010) 09110425[90] LHCb collaboration (2011) LHCb-CONF-2011-031[91] Belle collaboration (2011) Preliminary results presented at Lepton Photon 2011
(BELLE-CONF-1112) URL httpwwwinotifrresinMaKaCgetFilepyaccesscontribId=150ampsessionId=21ampresId=1ampmaterialId=slidesampconfId=79
[92] D Atwood I Dunietz and A Soni PhysRevLett 78 3257 (1997) hep-ph9612433[93] D Atwood I Dunietz and A Soni PhysRev D63 036005 (2001) hep-ph0008090[94] P del Amo Sanchez et al (BABAR) Phys Rev D82 072006 (2010) 10064241[95] Y Horii et al (Belle) Phys Rev Lett 106 231803 (2011) 11035951[96] T Aaltonen et al (CDF) PhysRevD (2011) 11085765[97] LHCb collaboration (2011) LHCb-CONF-2011-044[98] A Bondar and T Gershon PhysRev D70 091503 (2004) hep-ph0409281[99] I Dunietz PhysLett B270 75 (1991)
[100] M Gronau PhysLett B557 198 (2003) hep-ph0211282[101] T Gershon PhysRev D79 051301 (2009) 08102706[102] T Gershon and M Williams PhysRev D80 092002 (2009) 09091495[103] A Giri Y Grossman A Soffer and J Zupan PhysRev D68 054018 (2003) hep-ph
0303187[104] P del Amo Sanchez et al (BABAR) Phys Rev Lett 105 121801 (2010) 10051096[105] A Poluektov et al (Belle) Phys Rev D81 112002 (2010) 10033360[106] A Bondar and A Poluektov EurPhysJ C47 347 (2006) hep-ph0510246[107] A Bondar and A Poluektov EurPhysJ C55 51 (2008) 08010840[108] J Libby et al (CLEO) PhysRev D82 112006 (2010) 10102817[109] I Adachi K Adamczyk and H Aihara (Belle) (2011) 11064046[110] R Aleksan I Dunietz and B Kayser ZPhys C54 653 (1992)[111] T Aaltonen et al (CDF) PhysRevLett 103 191802 (2009) 08090080[112] LHCb collaboration (2011) LHCb-CONF-2011-057[113] J Dalseno et al (Belle) Phys Rev D79 072004 (2009) 08113665[114] B Aubert et al (BABAR) Phys Rev D80 112001 (2009) 09053615
16
Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Tim Gershon
where the uncertainties are experimental and from the lattice respectivelyLeptonic charm meson decays provide an alternative approach to determine the magni-
tudes of these CKM matrix elements Their decay rates involve also the decay constantswhich can be determined from lattice QCD and helicity suppression factors for example
Γ(D+s rarr l+ν
)=G2F
8πf2D+
sm2lMD+
s
(1minus m2
l
M2D+
s
)2
|Vcs|2 (14)
Significant improvements in the measurements ofD+s decays have come from BaBar [39]
Belle [40] and CLEO-c [41] These are usually expressed in terms of fD+s
using the valueof |Vcs| given above and can be compared to the lattice QCD calculations Equally thiscan be recast using the input from the lattice [42] to obtain
|Vcs| = 1005plusmn 0026plusmn 0016 (15)
where the uncertainties are experimental and from the lattice respectively It should benoted that a discrepancy that was apparent a few years ago (see for example Ref [43])has disappeared Moreover the dominant uncertainty is experimental so improved mea-surements from BES and current or future e+eminus B factory experiments would be wel-come
25 Determination of |Vcb| and |Vub|
Both exclusive and inclusive studies of semileptonic B decays have been used to obtain|Vcb| and |Vub| (for a detailed recent review see Ref [44]) For the former the reviewin the 2010 edition of the Particle Data Group review of particle physics [7] quotes a 2σtension between the two determinations
|Vcb| (excl) = (387plusmn 11)times 10minus3 |Vcb| (incl) = (415plusmn 07)times 10minus3
(16)
Updated data from Belle on B0d rarr Dlowastminuslν decays [45] and improved lattice QCD cal-
culations of the form-factor at zero recoil [46] reduce slightly both the uncertainty of theexclusive determination and the tension with the inclusive determination
It is also worth noting that the semitauonic decays B rarr D(lowast)τν have recently beenseen for the first time by BaBar [47ndash49] (see Fig 6) and Belle [50 51] The rates of thesedecays depend on |Vcb| but it is more common to measure their ratios relative to thosefor B rarr D(lowast)lν (l = e micro) decays These ratios are precisely predicted in the SM andare sensitive to potential contributions beyond the SM for example from charged Higgsbosons The isospin averaged ratios are determined to be
R(D) = 0456plusmn 0053plusmn 0056 RSM(D) = 031plusmn 002 R(Dlowast) = 0325plusmn 0023plusmn 0027 RSM(Dlowast) = 025plusmn 007
(17)
The excess over the SM is about 18σ (see also Ref [52] where determinations of |Vub|from leptonic B decays are also discussed)
The b rarr ulν decays can similarly be used to obtain measurements of |Vub| by eitherexclusive or inclusive methods Most recent progress has been on the exclusive B rarr πlνdecays where new results have become available from both BaBar [53 54] and Belle [55]as shown in Fig 7 The updated HFAG [8] average is [56]
|Vub| = (326plusmn 030)times 10minus3 (18)
6
Overview of the CKM Matrix
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60 f) + D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80 g) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40h) + D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60 f) + D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80 g) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40h) + D2 lt 120 GeVmiss
2 mle10
Figure 6 Signal for B rarr D(lowast)τν decays from BaBar [47] Note that the large peaksare due to backgrounds from D(lowast)lν (l = e micro) decays while the signals appears astails to large values of the missing mass squared variable m2
miss
where the dominant source of uncertainty is from the lattice QCD calculations of the formfactors [57]
)2 (GeV2Unfolded q
0 5 10 15 20 25
)2
(2 G
eV
times 2
q∆
)2
B(q
∆
0
2
4
6
8
10
12
14
16
shy610times
LCSR
FNALMILC
HPQCD
BGL fit to data
BK fit to data
data
)2c2 (GeV2Unfolded q0 5 10 15 20 25
2c
2)
2
Ge
V2
B(q
∆
0
2
4
6
8
10
12
14
16
18
20
shy610times
ISGW2
HPQCD
FNAL
LCSR
Data
Figure 7 Differential branching fractions of B0d rarr πminusl+ν decays as a function of
l+ν invariant mass squared q2 from (left) BaBar [53] and (right) Belle [55]
As was the case for |Vcb| there is a tension between inclusive and exclusive determi-nations (the world average value using the inclusive approach is |Vub| = (427plusmn 038)times10minus3 Although some commentators have pointed out that the large amount of theoreticalwork dedicated to the extraction of |Vub|may have led to an underestimation of the uncer-tainties [58] it is this authorrsquos view that more theoretical attention is necessary to resolvethe situation On the exclusive side improvements in lattice QCD calculations can beexpected while on the inclusive side an initiative to reduce uncertainties using global fitsis underway [59]
7
Tim Gershon
3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
As is widely known CP violation is one of the three ldquoSakharov conditionsrdquo [60] nec-essary for the evolution of a baryon asymmetry in the Universe Moreover the SM CPviolation encoded in the CKM matrix is not sufficient to explain the observed asym-metry Therefore there must be more sources of matter-antimatter asymmetry in natureThese could arise in almost any conceivable extension of the SM such as in an extendedquark sector in the lepton sector (leptogenesis) from anomalous gauge couplings in anextended Higgs sector and so on While all of these must be investigated testing theconsistency of the CKM mechanism in the quark sector provides the best chance to findnew sources of CP violation in the short term
Although the understanding of CP violation has advanced dramatically over the pastdecade it is important to realise that it remains a rarely observed phenomenon To dateit is only been observed (with gt 5σ significance) in the K0 and B0
d systems (Discus-sions of searches for CP violation in D0 and B0
s mixing can be found in Refs [61 62])In the B system the only 5σ significant measurements are of the parameters sin(2β)from JψKSL and similar decays from BaBar [63] and Belle [64] S(ηprimeKSL) fromBaBar [65] and Belle [66] S(π+πminus) from BaBar [67] and Belle [68] C(π+πminus) fromBelle [68] and ACP (K+πminus) from BaBar [67] Belle [69] and LHCb [70] (see alsoRef [52] on this last topic) The LHCb result on B0
d rarr K+πminus is thus the first 5σobservation of CP violation in the B system at a hadron collider experimentCP violation results are often expressed in terms of the so-called Unitarity Triangle
which is a graphical representation of one of the relations implied by the unitarity of theCKM matrix
VudVlowastub + VcdV
lowastcb + VtdV
lowasttb = 0 (19)
The angles of this triangle are usually denoted (α β γ) while its apex (after normalisingso that its base is unit length along the real axis) is given in terms of the Wolfensteinparameters (ρ η) [3 4]
31 Searches for CP violation in the charm sector
Almost all CP violation effects in the charm system are expected to be negligible inthe SM This therefore provides an excellent testing ground to look for unexpected ef-fects Various searches for direct CP violation effects (studies of mixing and indirectCP violation are discussed in Ref [62]) have been carried out recently for example inD+
(s) rarr KSπ+ and KSK
+ decays [71 72] in triple product asymmetries in four-bodyhadronic decays [73 74] and in Dalitz plot asymmetries in three-body decays [75] At thetime of Lepton Photon no significant signal for CP violation in charm had yet been seenalthough the world average asymmetry in D+ rarr KSπ
+ is more than 3σ from zero [8]this is consistent with originating from the CP violation in the neutral kaon system (seeRef [76] and references therein) However while these proceedings were being preparedLHCb announced a 35σ signal for the difference in time-integrated CP asymmetries be-tween D0 rarr K+Kminus and D0 rarr π+πminus decays [77] (CDF have also released less preciseresults on the same observable [78])
32 Measurement of sin(2β)
Both e+eminus B factory experiments BaBar and Belle have completed data taking Theresult on sin(2β) from B0
d rarr JψKSL (etc) with BaBarrsquos final data set (445 million
8
Overview of the CKM Matrix
BB pairs) has been published [63] while preliminary results following a reprocessing ofthe Belle data (772 million BB pairs) are available [64] A first analysis from LHCb isalso available [79] The results are compiled in Fig 8 At the level of precision that theexperiments are reaching it is important to check for effects that may perturb the naıveSM expectation S(JψKSL) = minusηCP sin(2β) where ηCP is the CP eigenvalue ofthe final state This can be done using channels that are related by flavour symmetries ndashB0d rarr Jψπ0 (related by SU(3)) orB0
s rarr JψK0S (related by U-spin) First observations
of the latter decay have recently been reported by CDF and LHCb [80 81] suggestingthat this approach will be possible with larger datasets
sin(2β) equiv sin(2φ1)
-2 -1 0 1 2 3
BaBarPRD 79 (2009) 072009
069 plusmn 003 plusmn 001
BaBar χc0 KSPRD 80 (2009) 112001
069 plusmn 052 plusmn 004 plusmn 007
BaBar Jψ (hadronic) KSPRD 69 (2004) 052001
156 plusmn 042 plusmn 021
BelleMoriond EW 2011 preliminary
067 plusmn 002 plusmn 001
ALEPHPLB 492 259 (2000)
084 +-018024 plusmn 016
OPALEPJ C5 379 (1998)
320 +-128000 plusmn 050
CDFPRD 61 072005 (2000)
079 +-004414
LHCbLHCb-CONF-2011-004
053 +-002289 plusmn 005
AverageHFAG
068 plusmn 002
H F A GH F A GBeauty 2011
PRELIMINARYβ equiv φ
1
ρndash
ηndash
-02 0 02 04 06 08 1-02
0
02
04
06
08
1
β equiv φ1 = (214 plusmn 08)˚
β equiv
φ1 =
(686
plusmn 0
8)˚
DIS
FA
VO
UR
ED
BY
Jψ
K D
DK
S amp D
h0
H F A GH F A GBeauty 2011
PRELIMINARY
Figure 8 (Left) Compilation of results on sin(2β) from B0d rarr JψKSL (etc) [8]
(Right) Corresponding constraint on ρndashη plane
The B factories have carried out a substantial programme of alternative measurementsof sin(2β) using different quark level transitions such as b rarr qqs (q = u d s egB0d rarr ηprimeK0
S) and b rarr ccd (eg B0d rarr D+Dminus) Compilations are shown in Fig 9 A
few years ago hints of deviations were apparent between the value of sin(2βeff) measuredin brarr qqs transitions and the reference value from brarr ccs These have diminished withthe latest data but effects of non-SM contributions at the O(10) level are not ruled outOne notable update is the new Belle result on B0
d rarr D+Dminus [82] which improves theconsistency between the results of the two B factories as well as with the SM
33 Measurement of α
The unitarity triangle angle α is constrained by measurements of and isospin relationsbetween B rarr ππ ρπ and ρρ decays [83 84] The situation has been stable for the lastfew years though the final results from both B factory experiments in all three systemsare still awaited Combining all available information the world average is [10]
α =(890 +44
minus42
) (20)
Since the average is dominated by results from the ρρ system two small comments arein order First the apparently high branching fraction of B+ rarr ρ+ρ0 which comesessentially from a single measurement [85] stretches the isospin triangle and reduces theuncertainty Secondly analyses to date while allowing CP violation in the rates haveassumed the longitudinal polarisation fraction is the same for B and B ndash but the mostgeneral analysis would allow a difference between the two
9
Tim Gershon
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
brarrccs
φ K
0
ηprime K
0
KS K
S K
S
π0 K
0
ρ0 K
S
ω K
S
f 0 K
S
K+ K
- K0
-08 -06 -04 -02 0 02 04 06 08 1 12 14 16
World Average 068 plusmn 002
BaBar 026 plusmn 026 plusmn 003
Belle 090 +-00
01
99
Average 056 +-00
11
68
BaBar 057 plusmn 008 plusmn 002
Belle 064 plusmn 010 plusmn 004
Average 059 plusmn 007
BaBar 094 +-00
22
14 plusmn 006
Belle 030 plusmn 032 plusmn 008
Average 072 plusmn 019
BaBar 055 plusmn 020 plusmn 003
Belle 067 plusmn 031 plusmn 008
Average 057 plusmn 017
BaBar 035 +-00
23
61 plusmn 006 plusmn 003
Belle 064 +-00
12
95 plusmn 009 plusmn 010
Average 054 +-00
12
81
BaBar 055 +-00
22
69 plusmn 002
Belle 011 plusmn 046 plusmn 007
Average 045 plusmn 024
BaBar 060 +-00
11
68
Belle 063 +-00
11
69
Average 062 +-00
11
13
BaBar 086 plusmn 008 plusmn 003
Belle 068 plusmn 015 plusmn 003 +-00
21
13
Average 082 plusmn 007
H F A GH F A GEndOfYear 2011
PRELIMINARY
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
brarrccs SCP
Jψ
π0 S
CP
D+ D
- SC
P
D+
D- S
CP
D+
- D-+
S+
-
D+
- D-+
S-+
-1 0 1 2
World AverageHFAG (EPS 2011)
068 plusmn 002
BaBarPRL 101 (2008) 021801
123 plusmn 021 plusmn 004
BellePRD 77 (2008) 071101(R)
065 plusmn 021 plusmn 005
AverageHFAG correlated average
093 plusmn 015
BaBarPRD 79 032002 (2009)
065 plusmn 036 plusmn 005
BelleEPS 2011 preliminary
106 plusmn 021 plusmn 007
AverageHFAG correlated average
096 plusmn 019
BaBarPRD 79 032002 (2009)
071 plusmn 016 plusmn 003
BelleEPS 2011 preliminary
079 plusmn 013 plusmn 003
AverageHFAG correlated average
077 plusmn 010
BaBarPRD 79 032002 (2009)
063 plusmn 021 plusmn 003
BellePRL 93 (2004) 201802
055 plusmn 039 plusmn 012
AverageHFAG
061 plusmn 019
BaBarPRD 79 032002 (2009)
074 plusmn 023 plusmn 005
BellePRL 93 (2004) 201802
096 plusmn 043 plusmn 012
AverageHFAG
079 plusmn 021
H F A GH F A GEPS 2011
PRELIMINARY
Figure 9 Compilation of results on sin(2βeff) from (left) b rarr qqs and (right)brarr ccd transitions [8]
34 Measurement of γ
The angle γ is unique among CP violating observables in that it can be determined us-ing tree-level processes only exploiting the interference between (typically) b rarr cudand brarr ucd transitions that occurs when the process involves a neutral D meson recon-structed in a final state accessible to both D0 and D0 decays It therefore provides a SMbenchmark and its precise measurement is crucial in order to disentangle any non-SMcontributions to other processes via global CKM fits
Several different D decay final states have been studied in order to maximise the sen-sitivity to γ The archetype is the use of D decays to CP eigenstates the so-called GLWmethod [86 87] New results with this approach have recently become available fromBaBar [88] CDF [89] and LHCb [90] while the very latest results from Belle [91] areshown in Fig 10 The world average for the CP asymmetry in the processes involvingCP -even D decay final states including all these new results and illustrated in Fig 11(left) shows that CP violation in Bplusmn rarr DKplusmn decays is clearly established though nosingle measurement exceeds 5σ significance
Another powerful approach to constrain γ the so-called ADS method [92 93] comesfrom the use of doubly-Cabibbo-suppressed D decays (for example to the final stateK+πminus) Recent new results come from BaBar [94] Belle [95] and CDF [96] whilethe very latest results from LHCb [97] are shown in Fig 12 The world average for theparameter RADS which is the ratio of decay rates to the suppressed states compared tothose for the favoured channels including all these new results and illustrated in Fig 11(right) shows that the suppressed decay is now clearly established though no single mea-surement exceeds 5σ significance This is very promising for future γ determinations
Although the analyses withBplusmn rarr DKplusmn decays give the most precise results differentB decays have also been studied The use of both possible decays Dlowast rarr Dπ0 andDlowast rarr Dγ provides an extra handle on the extraction of γ fromBplusmn rarr DlowastKplusmn [98] that isbecoming visible in the most recent results [91 94] In addition theB0
d rarr DKlowast0 channel
10
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
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001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Overview of the CKM Matrix
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
50
100ντD
ντDνDl
νDlνDl
Bkg
a) 0
D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
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2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
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0 5
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Ev
ents
(0
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0
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(Gev)l
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(9
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(9
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(9
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(Gev)l
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(9
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80
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0 5
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ents
(9
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0
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20
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(Gev)l
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ents
(9
6 M
eV)
0
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40h) + D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
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Ev
ents
(0
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0
50
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0 5
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Ev
ents
(0
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GeV
0
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100ντD
ντDνDl
νDlνDl
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a) 0
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(Gev)l
p0 05 1 15 2
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ents
(9
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eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
b) 0 D2 lt 120 GeVmiss
2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
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0
50
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0 5
)2
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ents
(0
38
GeV
0
50
100
c) 0D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
50
100d) 0
D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
e) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
20
40
60 f) + D2 lt 120 GeVmiss2 mle10
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80
)2 (Gevmiss2m
0 5
)2
Ev
ents
(0
38
GeV
0
20
40
60
80 g) +D
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40
(Gev)l
p0 05 1 15 2
Ev
ents
(9
6 M
eV)
0
10
20
30
40h) + D2 lt 120 GeVmiss
2 mle10
Figure 6 Signal for B rarr D(lowast)τν decays from BaBar [47] Note that the large peaksare due to backgrounds from D(lowast)lν (l = e micro) decays while the signals appears astails to large values of the missing mass squared variable m2
miss
where the dominant source of uncertainty is from the lattice QCD calculations of the formfactors [57]
)2 (GeV2Unfolded q
0 5 10 15 20 25
)2
(2 G
eV
times 2
q∆
)2
B(q
∆
0
2
4
6
8
10
12
14
16
shy610times
LCSR
FNALMILC
HPQCD
BGL fit to data
BK fit to data
data
)2c2 (GeV2Unfolded q0 5 10 15 20 25
2c
2)
2
Ge
V2
B(q
∆
0
2
4
6
8
10
12
14
16
18
20
shy610times
ISGW2
HPQCD
FNAL
LCSR
Data
Figure 7 Differential branching fractions of B0d rarr πminusl+ν decays as a function of
l+ν invariant mass squared q2 from (left) BaBar [53] and (right) Belle [55]
As was the case for |Vcb| there is a tension between inclusive and exclusive determi-nations (the world average value using the inclusive approach is |Vub| = (427plusmn 038)times10minus3 Although some commentators have pointed out that the large amount of theoreticalwork dedicated to the extraction of |Vub|may have led to an underestimation of the uncer-tainties [58] it is this authorrsquos view that more theoretical attention is necessary to resolvethe situation On the exclusive side improvements in lattice QCD calculations can beexpected while on the inclusive side an initiative to reduce uncertainties using global fitsis underway [59]
7
Tim Gershon
3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
As is widely known CP violation is one of the three ldquoSakharov conditionsrdquo [60] nec-essary for the evolution of a baryon asymmetry in the Universe Moreover the SM CPviolation encoded in the CKM matrix is not sufficient to explain the observed asym-metry Therefore there must be more sources of matter-antimatter asymmetry in natureThese could arise in almost any conceivable extension of the SM such as in an extendedquark sector in the lepton sector (leptogenesis) from anomalous gauge couplings in anextended Higgs sector and so on While all of these must be investigated testing theconsistency of the CKM mechanism in the quark sector provides the best chance to findnew sources of CP violation in the short term
Although the understanding of CP violation has advanced dramatically over the pastdecade it is important to realise that it remains a rarely observed phenomenon To dateit is only been observed (with gt 5σ significance) in the K0 and B0
d systems (Discus-sions of searches for CP violation in D0 and B0
s mixing can be found in Refs [61 62])In the B system the only 5σ significant measurements are of the parameters sin(2β)from JψKSL and similar decays from BaBar [63] and Belle [64] S(ηprimeKSL) fromBaBar [65] and Belle [66] S(π+πminus) from BaBar [67] and Belle [68] C(π+πminus) fromBelle [68] and ACP (K+πminus) from BaBar [67] Belle [69] and LHCb [70] (see alsoRef [52] on this last topic) The LHCb result on B0
d rarr K+πminus is thus the first 5σobservation of CP violation in the B system at a hadron collider experimentCP violation results are often expressed in terms of the so-called Unitarity Triangle
which is a graphical representation of one of the relations implied by the unitarity of theCKM matrix
VudVlowastub + VcdV
lowastcb + VtdV
lowasttb = 0 (19)
The angles of this triangle are usually denoted (α β γ) while its apex (after normalisingso that its base is unit length along the real axis) is given in terms of the Wolfensteinparameters (ρ η) [3 4]
31 Searches for CP violation in the charm sector
Almost all CP violation effects in the charm system are expected to be negligible inthe SM This therefore provides an excellent testing ground to look for unexpected ef-fects Various searches for direct CP violation effects (studies of mixing and indirectCP violation are discussed in Ref [62]) have been carried out recently for example inD+
(s) rarr KSπ+ and KSK
+ decays [71 72] in triple product asymmetries in four-bodyhadronic decays [73 74] and in Dalitz plot asymmetries in three-body decays [75] At thetime of Lepton Photon no significant signal for CP violation in charm had yet been seenalthough the world average asymmetry in D+ rarr KSπ
+ is more than 3σ from zero [8]this is consistent with originating from the CP violation in the neutral kaon system (seeRef [76] and references therein) However while these proceedings were being preparedLHCb announced a 35σ signal for the difference in time-integrated CP asymmetries be-tween D0 rarr K+Kminus and D0 rarr π+πminus decays [77] (CDF have also released less preciseresults on the same observable [78])
32 Measurement of sin(2β)
Both e+eminus B factory experiments BaBar and Belle have completed data taking Theresult on sin(2β) from B0
d rarr JψKSL (etc) with BaBarrsquos final data set (445 million
8
Overview of the CKM Matrix
BB pairs) has been published [63] while preliminary results following a reprocessing ofthe Belle data (772 million BB pairs) are available [64] A first analysis from LHCb isalso available [79] The results are compiled in Fig 8 At the level of precision that theexperiments are reaching it is important to check for effects that may perturb the naıveSM expectation S(JψKSL) = minusηCP sin(2β) where ηCP is the CP eigenvalue ofthe final state This can be done using channels that are related by flavour symmetries ndashB0d rarr Jψπ0 (related by SU(3)) orB0
s rarr JψK0S (related by U-spin) First observations
of the latter decay have recently been reported by CDF and LHCb [80 81] suggestingthat this approach will be possible with larger datasets
sin(2β) equiv sin(2φ1)
-2 -1 0 1 2 3
BaBarPRD 79 (2009) 072009
069 plusmn 003 plusmn 001
BaBar χc0 KSPRD 80 (2009) 112001
069 plusmn 052 plusmn 004 plusmn 007
BaBar Jψ (hadronic) KSPRD 69 (2004) 052001
156 plusmn 042 plusmn 021
BelleMoriond EW 2011 preliminary
067 plusmn 002 plusmn 001
ALEPHPLB 492 259 (2000)
084 +-018024 plusmn 016
OPALEPJ C5 379 (1998)
320 +-128000 plusmn 050
CDFPRD 61 072005 (2000)
079 +-004414
LHCbLHCb-CONF-2011-004
053 +-002289 plusmn 005
AverageHFAG
068 plusmn 002
H F A GH F A GBeauty 2011
PRELIMINARYβ equiv φ
1
ρndash
ηndash
-02 0 02 04 06 08 1-02
0
02
04
06
08
1
β equiv φ1 = (214 plusmn 08)˚
β equiv
φ1 =
(686
plusmn 0
8)˚
DIS
FA
VO
UR
ED
BY
Jψ
K D
DK
S amp D
h0
H F A GH F A GBeauty 2011
PRELIMINARY
Figure 8 (Left) Compilation of results on sin(2β) from B0d rarr JψKSL (etc) [8]
(Right) Corresponding constraint on ρndashη plane
The B factories have carried out a substantial programme of alternative measurementsof sin(2β) using different quark level transitions such as b rarr qqs (q = u d s egB0d rarr ηprimeK0
S) and b rarr ccd (eg B0d rarr D+Dminus) Compilations are shown in Fig 9 A
few years ago hints of deviations were apparent between the value of sin(2βeff) measuredin brarr qqs transitions and the reference value from brarr ccs These have diminished withthe latest data but effects of non-SM contributions at the O(10) level are not ruled outOne notable update is the new Belle result on B0
d rarr D+Dminus [82] which improves theconsistency between the results of the two B factories as well as with the SM
33 Measurement of α
The unitarity triangle angle α is constrained by measurements of and isospin relationsbetween B rarr ππ ρπ and ρρ decays [83 84] The situation has been stable for the lastfew years though the final results from both B factory experiments in all three systemsare still awaited Combining all available information the world average is [10]
α =(890 +44
minus42
) (20)
Since the average is dominated by results from the ρρ system two small comments arein order First the apparently high branching fraction of B+ rarr ρ+ρ0 which comesessentially from a single measurement [85] stretches the isospin triangle and reduces theuncertainty Secondly analyses to date while allowing CP violation in the rates haveassumed the longitudinal polarisation fraction is the same for B and B ndash but the mostgeneral analysis would allow a difference between the two
9
Tim Gershon
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
brarrccs
φ K
0
ηprime K
0
KS K
S K
S
π0 K
0
ρ0 K
S
ω K
S
f 0 K
S
K+ K
- K0
-08 -06 -04 -02 0 02 04 06 08 1 12 14 16
World Average 068 plusmn 002
BaBar 026 plusmn 026 plusmn 003
Belle 090 +-00
01
99
Average 056 +-00
11
68
BaBar 057 plusmn 008 plusmn 002
Belle 064 plusmn 010 plusmn 004
Average 059 plusmn 007
BaBar 094 +-00
22
14 plusmn 006
Belle 030 plusmn 032 plusmn 008
Average 072 plusmn 019
BaBar 055 plusmn 020 plusmn 003
Belle 067 plusmn 031 plusmn 008
Average 057 plusmn 017
BaBar 035 +-00
23
61 plusmn 006 plusmn 003
Belle 064 +-00
12
95 plusmn 009 plusmn 010
Average 054 +-00
12
81
BaBar 055 +-00
22
69 plusmn 002
Belle 011 plusmn 046 plusmn 007
Average 045 plusmn 024
BaBar 060 +-00
11
68
Belle 063 +-00
11
69
Average 062 +-00
11
13
BaBar 086 plusmn 008 plusmn 003
Belle 068 plusmn 015 plusmn 003 +-00
21
13
Average 082 plusmn 007
H F A GH F A GEndOfYear 2011
PRELIMINARY
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
brarrccs SCP
Jψ
π0 S
CP
D+ D
- SC
P
D+
D- S
CP
D+
- D-+
S+
-
D+
- D-+
S-+
-1 0 1 2
World AverageHFAG (EPS 2011)
068 plusmn 002
BaBarPRL 101 (2008) 021801
123 plusmn 021 plusmn 004
BellePRD 77 (2008) 071101(R)
065 plusmn 021 plusmn 005
AverageHFAG correlated average
093 plusmn 015
BaBarPRD 79 032002 (2009)
065 plusmn 036 plusmn 005
BelleEPS 2011 preliminary
106 plusmn 021 plusmn 007
AverageHFAG correlated average
096 plusmn 019
BaBarPRD 79 032002 (2009)
071 plusmn 016 plusmn 003
BelleEPS 2011 preliminary
079 plusmn 013 plusmn 003
AverageHFAG correlated average
077 plusmn 010
BaBarPRD 79 032002 (2009)
063 plusmn 021 plusmn 003
BellePRL 93 (2004) 201802
055 plusmn 039 plusmn 012
AverageHFAG
061 plusmn 019
BaBarPRD 79 032002 (2009)
074 plusmn 023 plusmn 005
BellePRL 93 (2004) 201802
096 plusmn 043 plusmn 012
AverageHFAG
079 plusmn 021
H F A GH F A GEPS 2011
PRELIMINARY
Figure 9 Compilation of results on sin(2βeff) from (left) b rarr qqs and (right)brarr ccd transitions [8]
34 Measurement of γ
The angle γ is unique among CP violating observables in that it can be determined us-ing tree-level processes only exploiting the interference between (typically) b rarr cudand brarr ucd transitions that occurs when the process involves a neutral D meson recon-structed in a final state accessible to both D0 and D0 decays It therefore provides a SMbenchmark and its precise measurement is crucial in order to disentangle any non-SMcontributions to other processes via global CKM fits
Several different D decay final states have been studied in order to maximise the sen-sitivity to γ The archetype is the use of D decays to CP eigenstates the so-called GLWmethod [86 87] New results with this approach have recently become available fromBaBar [88] CDF [89] and LHCb [90] while the very latest results from Belle [91] areshown in Fig 10 The world average for the CP asymmetry in the processes involvingCP -even D decay final states including all these new results and illustrated in Fig 11(left) shows that CP violation in Bplusmn rarr DKplusmn decays is clearly established though nosingle measurement exceeds 5σ significance
Another powerful approach to constrain γ the so-called ADS method [92 93] comesfrom the use of doubly-Cabibbo-suppressed D decays (for example to the final stateK+πminus) Recent new results come from BaBar [94] Belle [95] and CDF [96] whilethe very latest results from LHCb [97] are shown in Fig 12 The world average for theparameter RADS which is the ratio of decay rates to the suppressed states compared tothose for the favoured channels including all these new results and illustrated in Fig 11(right) shows that the suppressed decay is now clearly established though no single mea-surement exceeds 5σ significance This is very promising for future γ determinations
Although the analyses withBplusmn rarr DKplusmn decays give the most precise results differentB decays have also been studied The use of both possible decays Dlowast rarr Dπ0 andDlowast rarr Dγ provides an extra handle on the extraction of γ fromBplusmn rarr DlowastKplusmn [98] that isbecoming visible in the most recent results [91 94] In addition theB0
d rarr DKlowast0 channel
10
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
References
[1] N Cabibbo PhysRevLett 10 531 (1963)[2] M Kobayashi and T Maskawa ProgTheorPhys 49 652 (1973)[3] L Wolfenstein PhysRevLett 51 1945 (1983)[4] AJ Buras ME Lautenbacher and G Ostermaier PhysRev D50 3433 (1994) hep-ph
9403384[5] A Dighe (2011) these proceeedings[6] V Lubicz (2011) these proceeedings[7] K Nakamura et al (Particle Data Group) J Phys G37 075021 (2010)[8] D Asner et al (Heavy Flavor Averaging Group) (2010) 10101589 URL http
wwwslacstanfordeduxorghfag[9] M Antonelli et al PhysRept 494 197 (2010) 09075386
[10] J Charles et al (CKMfitter) EurPhysJ C41 1 (2005) hep-ph0406184 URL httpckmfitterin2p3fr
[11] M Bona et al (UTfit) JHEP 0507 028 (2005) hep-ph0501199 URL httpwwwutfitorgUTfit
[12] T Spadaro and A Young (2011) 11120238[13] J Laiho BD Pecjak and C Schwanda (2011) 11073934[14] M Gorbahn M Patel and S Robertson (2011) 11040826[15] M Kreps A Lenz and O Leroy (2011) 11034962[16] R Fleischer and S Ricciardi (2011) 11044029[17] MT Graham D Tonelli and J Zupan (2011) 11050179[18] DM Webber et al (MuLan) PhysRevLett 106 041803 (2011) 10100991[19] PJ Mohr BN Taylor and DB Newell RevModPhys 80 633 (2008) 08010028[20] WJ Marciano PhysRev D60 093006 (1999) hep-ph9903451[21] A Pak and A Czarnecki PhysRevLett 100 241807 (2008) 08030960[22] JC Hardy and IS Towner PhysRev C79 055502 (2009) 08121202[23] A Pichlmaier V Varlamov K Schreckenbach and P Geltenbort PhysLett B693 221
(2010)
5 At Lepton Photon 2011 the author compared the long wait to discover effects beyond the SM to that forIndian batting hero Sachin Tendulkar to achieve his 100th century in international cricket Sadly at the time ofwriting these proceedings and despite some close calls we are still waiting for both historic achievements
14
Overview of the CKM Matrix
[24] JS Nico J Phys G36 104001 (2009)[25] S Paul NuclInstrumMeth A611 157 (2009) 09020169[26] M Antonelli et al EurPhysJ C69 399 (2010) 10052323[27] V Cirigliano G Ecker H Neufeld A Pich and J Portoles (2011) 11076001[28] M Veltri (2011) 11015031[29] PA Boyle et al EurPhysJ C69 159 (2010) 10040886[30] V Cirigliano and H Neufeld PhysLett B700 7 (2011) 11020563[31] M Davier A Hocker and Z Zhang RevModPhys 78 1043 (2006) hep-ph0507078[32] A Pich NuclPhysProcSuppl 218 89 (2011) 11012107[33] B Aubert et al (BABAR) Phys Rev Lett 100 011801 (2008) 07072981[34] MJ Lee et al (Belle) Phys Rev D81 113007 (2010) 10010083[35] D Besson et al (CLEO) PhysRev D80 032005 (2009) 09062983[36] H Na CTH Davies E Follana GP Lepage and J Shigemitsu PhysRev D82 114506
(2010) 10084562[37] C Aubin et al (Fermilab Lattice MILC and HPQCD Collaborations) PhysRevLett 94
011601 (2005) hep-ph0408306[38] H Na et al (2011) 11091501[39] P del Amo Sanchez et al (BABAR) PhysRev D82 091103 (2010) 10084080[40] L Widhalm et al (Belle) PhysRevLett 100 241801 (2008) 07091340[41] P Naik et al (CLEO) PhysRev D80 112004 (2009) 09103602[42] J Laiho E Lunghi and RS Van de Water PhysRev D81 034503 (2010) 09102928[43] BA Dobrescu and AS Kronfeld PhysRevLett 100 241802 (2008) 08030512[44] VG Luth Annual Review of Nuclear and Particle Science 61 1 119 (2011)[45] W Dungel et al (Belle) PhysRev D82 112007 (2010) 10105620[46] JA Bailey et al (Fermilab Lattice and MILC Collaborations) PoS LATTICE2010 311
(2010) 10112166[47] BABAR collaboration (2011) Preliminary results presented at EPS2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=30ampsessionId=2ampmaterialId=slidesampconfId=5116
[48] B Aubert et al (BABAR) PhysRevLett 100 021801 (2008) 07091698[49] B Aubert et al (BABAR) PhysRev D79 092002 (2009) 09022660[50] A Matyja et al (Belle) PhysRevLett 99 191807 (2007) 07064429[51] A Bozek et al (Belle) PhysRev D82 072005 (2010) 10052302[52] YJ Kwon (2011) these proceeedings[53] P del Amo Sanchez et al (BABAR) PhysRev D83 052011 (2011) 10100987[54] P del Amo Sanchez et al (BABAR) PhysRev D83 032007 (2011) 10053288[55] H Ha et al (Belle) PhysRev D83 071101 (2011) 10120090[56] P Urquijo (2011) Preliminary results presented at EPS2011 URL http
indicoin2p3frmaterialDisplaypycontribId=1016ampsessionId=2ampmaterialId=slidesampconfId=5116
[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
httpindicoin2p3frgetFilepyaccesscontribId=114ampsessionId=7ampresId=0ampmaterialId=slidesampconfId=4403
[65] B Aubert et al (BABAR) Phys Rev D79 052003 (2009) 08091174[66] K-F Chen et al (Belle) Phys Rev Lett 98 031802 (2007) hep-ex0608039[67] B Aubert et al (BABAR) PhysRevLett 99 021603 (2007) hep-ex0703016[68] H Ishino et al (Belle) Phys Rev Lett 98 211801 (2007) hep-ex0608035
15
Tim Gershon
[69] P Chang (Belle) (2011) Preliminary results presented at EPS 2011 URLhttpindicoin2p3frmaterialDisplaypycontribId=1019ampsessionId=2ampmaterialId=slidesampconfId=5116
[70] LHCb collaboration (2011) LHCb-CONF-2011-042[71] BR Ko et al (Belle) PhysRevLett 104 181602 (2010) 10013202[72] P del Amo Sanchez et al (BABAR) PhysRev D83 071103 (2011) 10115477[73] P del Amo Sanchez et al (BABAR) PhysRev D81 111103 (2010) 10033397[74] JP Lees et al (BABAR) PhysRev D84 031103 (2011) 11054410[75] R Aaij et al (LHCb) (2011) 11103970[76] Y Grossman and Y Nir (2011) 11103790[77] R Aaij et al (LHCb) (2011) 11120938[78] T Aaltonen et al (CDF) PhysRevD (2011) 11115023[79] LHCb collaboration (2011) LHCb-CONF-2011-004[80] T Aaltonen et al (CDF) PhysRev D83 052012 (2011) 11021961[81] LHCb collaboration (2011) LHCb-CONF-2011-048[82] T Higuchi (Belle) (2011) Preliminary results presented at EPS 2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=1017ampsessionId=2ampmaterialId=slidesampconfId=5116
[83] M Gronau and D London PhysRevLett 65 3381 (1990)[84] AE Snyder and HR Quinn PhysRev D48 2139 (1993)[85] B Aubert et al (BABAR) Phys Rev Lett 102 141802 (2009) 09013522[86] M Gronau and D London PhysLett B253 483 (1991)[87] M Gronau and D Wyler PhysLett B265 172 (1991)[88] P del Amo Sanchez et al (BABAR) Phys Rev D82 072004 (2010) 10070504[89] T Aaltonen et al (CDF) Phys Rev D81 031105 (2010) 09110425[90] LHCb collaboration (2011) LHCb-CONF-2011-031[91] Belle collaboration (2011) Preliminary results presented at Lepton Photon 2011
(BELLE-CONF-1112) URL httpwwwinotifrresinMaKaCgetFilepyaccesscontribId=150ampsessionId=21ampresId=1ampmaterialId=slidesampconfId=79
[92] D Atwood I Dunietz and A Soni PhysRevLett 78 3257 (1997) hep-ph9612433[93] D Atwood I Dunietz and A Soni PhysRev D63 036005 (2001) hep-ph0008090[94] P del Amo Sanchez et al (BABAR) Phys Rev D82 072006 (2010) 10064241[95] Y Horii et al (Belle) Phys Rev Lett 106 231803 (2011) 11035951[96] T Aaltonen et al (CDF) PhysRevD (2011) 11085765[97] LHCb collaboration (2011) LHCb-CONF-2011-044[98] A Bondar and T Gershon PhysRev D70 091503 (2004) hep-ph0409281[99] I Dunietz PhysLett B270 75 (1991)
[100] M Gronau PhysLett B557 198 (2003) hep-ph0211282[101] T Gershon PhysRev D79 051301 (2009) 08102706[102] T Gershon and M Williams PhysRev D80 092002 (2009) 09091495[103] A Giri Y Grossman A Soffer and J Zupan PhysRev D68 054018 (2003) hep-ph
0303187[104] P del Amo Sanchez et al (BABAR) Phys Rev Lett 105 121801 (2010) 10051096[105] A Poluektov et al (Belle) Phys Rev D81 112002 (2010) 10033360[106] A Bondar and A Poluektov EurPhysJ C47 347 (2006) hep-ph0510246[107] A Bondar and A Poluektov EurPhysJ C55 51 (2008) 08010840[108] J Libby et al (CLEO) PhysRev D82 112006 (2010) 10102817[109] I Adachi K Adamczyk and H Aihara (Belle) (2011) 11064046[110] R Aleksan I Dunietz and B Kayser ZPhys C54 653 (1992)[111] T Aaltonen et al (CDF) PhysRevLett 103 191802 (2009) 08090080[112] LHCb collaboration (2011) LHCb-CONF-2011-057[113] J Dalseno et al (Belle) Phys Rev D79 072004 (2009) 08113665[114] B Aubert et al (BABAR) Phys Rev D80 112001 (2009) 09053615
16
Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Tim Gershon
3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
As is widely known CP violation is one of the three ldquoSakharov conditionsrdquo [60] nec-essary for the evolution of a baryon asymmetry in the Universe Moreover the SM CPviolation encoded in the CKM matrix is not sufficient to explain the observed asym-metry Therefore there must be more sources of matter-antimatter asymmetry in natureThese could arise in almost any conceivable extension of the SM such as in an extendedquark sector in the lepton sector (leptogenesis) from anomalous gauge couplings in anextended Higgs sector and so on While all of these must be investigated testing theconsistency of the CKM mechanism in the quark sector provides the best chance to findnew sources of CP violation in the short term
Although the understanding of CP violation has advanced dramatically over the pastdecade it is important to realise that it remains a rarely observed phenomenon To dateit is only been observed (with gt 5σ significance) in the K0 and B0
d systems (Discus-sions of searches for CP violation in D0 and B0
s mixing can be found in Refs [61 62])In the B system the only 5σ significant measurements are of the parameters sin(2β)from JψKSL and similar decays from BaBar [63] and Belle [64] S(ηprimeKSL) fromBaBar [65] and Belle [66] S(π+πminus) from BaBar [67] and Belle [68] C(π+πminus) fromBelle [68] and ACP (K+πminus) from BaBar [67] Belle [69] and LHCb [70] (see alsoRef [52] on this last topic) The LHCb result on B0
d rarr K+πminus is thus the first 5σobservation of CP violation in the B system at a hadron collider experimentCP violation results are often expressed in terms of the so-called Unitarity Triangle
which is a graphical representation of one of the relations implied by the unitarity of theCKM matrix
VudVlowastub + VcdV
lowastcb + VtdV
lowasttb = 0 (19)
The angles of this triangle are usually denoted (α β γ) while its apex (after normalisingso that its base is unit length along the real axis) is given in terms of the Wolfensteinparameters (ρ η) [3 4]
31 Searches for CP violation in the charm sector
Almost all CP violation effects in the charm system are expected to be negligible inthe SM This therefore provides an excellent testing ground to look for unexpected ef-fects Various searches for direct CP violation effects (studies of mixing and indirectCP violation are discussed in Ref [62]) have been carried out recently for example inD+
(s) rarr KSπ+ and KSK
+ decays [71 72] in triple product asymmetries in four-bodyhadronic decays [73 74] and in Dalitz plot asymmetries in three-body decays [75] At thetime of Lepton Photon no significant signal for CP violation in charm had yet been seenalthough the world average asymmetry in D+ rarr KSπ
+ is more than 3σ from zero [8]this is consistent with originating from the CP violation in the neutral kaon system (seeRef [76] and references therein) However while these proceedings were being preparedLHCb announced a 35σ signal for the difference in time-integrated CP asymmetries be-tween D0 rarr K+Kminus and D0 rarr π+πminus decays [77] (CDF have also released less preciseresults on the same observable [78])
32 Measurement of sin(2β)
Both e+eminus B factory experiments BaBar and Belle have completed data taking Theresult on sin(2β) from B0
d rarr JψKSL (etc) with BaBarrsquos final data set (445 million
8
Overview of the CKM Matrix
BB pairs) has been published [63] while preliminary results following a reprocessing ofthe Belle data (772 million BB pairs) are available [64] A first analysis from LHCb isalso available [79] The results are compiled in Fig 8 At the level of precision that theexperiments are reaching it is important to check for effects that may perturb the naıveSM expectation S(JψKSL) = minusηCP sin(2β) where ηCP is the CP eigenvalue ofthe final state This can be done using channels that are related by flavour symmetries ndashB0d rarr Jψπ0 (related by SU(3)) orB0
s rarr JψK0S (related by U-spin) First observations
of the latter decay have recently been reported by CDF and LHCb [80 81] suggestingthat this approach will be possible with larger datasets
sin(2β) equiv sin(2φ1)
-2 -1 0 1 2 3
BaBarPRD 79 (2009) 072009
069 plusmn 003 plusmn 001
BaBar χc0 KSPRD 80 (2009) 112001
069 plusmn 052 plusmn 004 plusmn 007
BaBar Jψ (hadronic) KSPRD 69 (2004) 052001
156 plusmn 042 plusmn 021
BelleMoriond EW 2011 preliminary
067 plusmn 002 plusmn 001
ALEPHPLB 492 259 (2000)
084 +-018024 plusmn 016
OPALEPJ C5 379 (1998)
320 +-128000 plusmn 050
CDFPRD 61 072005 (2000)
079 +-004414
LHCbLHCb-CONF-2011-004
053 +-002289 plusmn 005
AverageHFAG
068 plusmn 002
H F A GH F A GBeauty 2011
PRELIMINARYβ equiv φ
1
ρndash
ηndash
-02 0 02 04 06 08 1-02
0
02
04
06
08
1
β equiv φ1 = (214 plusmn 08)˚
β equiv
φ1 =
(686
plusmn 0
8)˚
DIS
FA
VO
UR
ED
BY
Jψ
K D
DK
S amp D
h0
H F A GH F A GBeauty 2011
PRELIMINARY
Figure 8 (Left) Compilation of results on sin(2β) from B0d rarr JψKSL (etc) [8]
(Right) Corresponding constraint on ρndashη plane
The B factories have carried out a substantial programme of alternative measurementsof sin(2β) using different quark level transitions such as b rarr qqs (q = u d s egB0d rarr ηprimeK0
S) and b rarr ccd (eg B0d rarr D+Dminus) Compilations are shown in Fig 9 A
few years ago hints of deviations were apparent between the value of sin(2βeff) measuredin brarr qqs transitions and the reference value from brarr ccs These have diminished withthe latest data but effects of non-SM contributions at the O(10) level are not ruled outOne notable update is the new Belle result on B0
d rarr D+Dminus [82] which improves theconsistency between the results of the two B factories as well as with the SM
33 Measurement of α
The unitarity triangle angle α is constrained by measurements of and isospin relationsbetween B rarr ππ ρπ and ρρ decays [83 84] The situation has been stable for the lastfew years though the final results from both B factory experiments in all three systemsare still awaited Combining all available information the world average is [10]
α =(890 +44
minus42
) (20)
Since the average is dominated by results from the ρρ system two small comments arein order First the apparently high branching fraction of B+ rarr ρ+ρ0 which comesessentially from a single measurement [85] stretches the isospin triangle and reduces theuncertainty Secondly analyses to date while allowing CP violation in the rates haveassumed the longitudinal polarisation fraction is the same for B and B ndash but the mostgeneral analysis would allow a difference between the two
9
Tim Gershon
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
brarrccs
φ K
0
ηprime K
0
KS K
S K
S
π0 K
0
ρ0 K
S
ω K
S
f 0 K
S
K+ K
- K0
-08 -06 -04 -02 0 02 04 06 08 1 12 14 16
World Average 068 plusmn 002
BaBar 026 plusmn 026 plusmn 003
Belle 090 +-00
01
99
Average 056 +-00
11
68
BaBar 057 plusmn 008 plusmn 002
Belle 064 plusmn 010 plusmn 004
Average 059 plusmn 007
BaBar 094 +-00
22
14 plusmn 006
Belle 030 plusmn 032 plusmn 008
Average 072 plusmn 019
BaBar 055 plusmn 020 plusmn 003
Belle 067 plusmn 031 plusmn 008
Average 057 plusmn 017
BaBar 035 +-00
23
61 plusmn 006 plusmn 003
Belle 064 +-00
12
95 plusmn 009 plusmn 010
Average 054 +-00
12
81
BaBar 055 +-00
22
69 plusmn 002
Belle 011 plusmn 046 plusmn 007
Average 045 plusmn 024
BaBar 060 +-00
11
68
Belle 063 +-00
11
69
Average 062 +-00
11
13
BaBar 086 plusmn 008 plusmn 003
Belle 068 plusmn 015 plusmn 003 +-00
21
13
Average 082 plusmn 007
H F A GH F A GEndOfYear 2011
PRELIMINARY
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
brarrccs SCP
Jψ
π0 S
CP
D+ D
- SC
P
D+
D- S
CP
D+
- D-+
S+
-
D+
- D-+
S-+
-1 0 1 2
World AverageHFAG (EPS 2011)
068 plusmn 002
BaBarPRL 101 (2008) 021801
123 plusmn 021 plusmn 004
BellePRD 77 (2008) 071101(R)
065 plusmn 021 plusmn 005
AverageHFAG correlated average
093 plusmn 015
BaBarPRD 79 032002 (2009)
065 plusmn 036 plusmn 005
BelleEPS 2011 preliminary
106 plusmn 021 plusmn 007
AverageHFAG correlated average
096 plusmn 019
BaBarPRD 79 032002 (2009)
071 plusmn 016 plusmn 003
BelleEPS 2011 preliminary
079 plusmn 013 plusmn 003
AverageHFAG correlated average
077 plusmn 010
BaBarPRD 79 032002 (2009)
063 plusmn 021 plusmn 003
BellePRL 93 (2004) 201802
055 plusmn 039 plusmn 012
AverageHFAG
061 plusmn 019
BaBarPRD 79 032002 (2009)
074 plusmn 023 plusmn 005
BellePRL 93 (2004) 201802
096 plusmn 043 plusmn 012
AverageHFAG
079 plusmn 021
H F A GH F A GEPS 2011
PRELIMINARY
Figure 9 Compilation of results on sin(2βeff) from (left) b rarr qqs and (right)brarr ccd transitions [8]
34 Measurement of γ
The angle γ is unique among CP violating observables in that it can be determined us-ing tree-level processes only exploiting the interference between (typically) b rarr cudand brarr ucd transitions that occurs when the process involves a neutral D meson recon-structed in a final state accessible to both D0 and D0 decays It therefore provides a SMbenchmark and its precise measurement is crucial in order to disentangle any non-SMcontributions to other processes via global CKM fits
Several different D decay final states have been studied in order to maximise the sen-sitivity to γ The archetype is the use of D decays to CP eigenstates the so-called GLWmethod [86 87] New results with this approach have recently become available fromBaBar [88] CDF [89] and LHCb [90] while the very latest results from Belle [91] areshown in Fig 10 The world average for the CP asymmetry in the processes involvingCP -even D decay final states including all these new results and illustrated in Fig 11(left) shows that CP violation in Bplusmn rarr DKplusmn decays is clearly established though nosingle measurement exceeds 5σ significance
Another powerful approach to constrain γ the so-called ADS method [92 93] comesfrom the use of doubly-Cabibbo-suppressed D decays (for example to the final stateK+πminus) Recent new results come from BaBar [94] Belle [95] and CDF [96] whilethe very latest results from LHCb [97] are shown in Fig 12 The world average for theparameter RADS which is the ratio of decay rates to the suppressed states compared tothose for the favoured channels including all these new results and illustrated in Fig 11(right) shows that the suppressed decay is now clearly established though no single mea-surement exceeds 5σ significance This is very promising for future γ determinations
Although the analyses withBplusmn rarr DKplusmn decays give the most precise results differentB decays have also been studied The use of both possible decays Dlowast rarr Dπ0 andDlowast rarr Dγ provides an extra handle on the extraction of γ fromBplusmn rarr DlowastKplusmn [98] that isbecoming visible in the most recent results [91 94] In addition theB0
d rarr DKlowast0 channel
10
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
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15
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Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
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08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Overview of the CKM Matrix
BB pairs) has been published [63] while preliminary results following a reprocessing ofthe Belle data (772 million BB pairs) are available [64] A first analysis from LHCb isalso available [79] The results are compiled in Fig 8 At the level of precision that theexperiments are reaching it is important to check for effects that may perturb the naıveSM expectation S(JψKSL) = minusηCP sin(2β) where ηCP is the CP eigenvalue ofthe final state This can be done using channels that are related by flavour symmetries ndashB0d rarr Jψπ0 (related by SU(3)) orB0
s rarr JψK0S (related by U-spin) First observations
of the latter decay have recently been reported by CDF and LHCb [80 81] suggestingthat this approach will be possible with larger datasets
sin(2β) equiv sin(2φ1)
-2 -1 0 1 2 3
BaBarPRD 79 (2009) 072009
069 plusmn 003 plusmn 001
BaBar χc0 KSPRD 80 (2009) 112001
069 plusmn 052 plusmn 004 plusmn 007
BaBar Jψ (hadronic) KSPRD 69 (2004) 052001
156 plusmn 042 plusmn 021
BelleMoriond EW 2011 preliminary
067 plusmn 002 plusmn 001
ALEPHPLB 492 259 (2000)
084 +-018024 plusmn 016
OPALEPJ C5 379 (1998)
320 +-128000 plusmn 050
CDFPRD 61 072005 (2000)
079 +-004414
LHCbLHCb-CONF-2011-004
053 +-002289 plusmn 005
AverageHFAG
068 plusmn 002
H F A GH F A GBeauty 2011
PRELIMINARYβ equiv φ
1
ρndash
ηndash
-02 0 02 04 06 08 1-02
0
02
04
06
08
1
β equiv φ1 = (214 plusmn 08)˚
β equiv
φ1 =
(686
plusmn 0
8)˚
DIS
FA
VO
UR
ED
BY
Jψ
K D
DK
S amp D
h0
H F A GH F A GBeauty 2011
PRELIMINARY
Figure 8 (Left) Compilation of results on sin(2β) from B0d rarr JψKSL (etc) [8]
(Right) Corresponding constraint on ρndashη plane
The B factories have carried out a substantial programme of alternative measurementsof sin(2β) using different quark level transitions such as b rarr qqs (q = u d s egB0d rarr ηprimeK0
S) and b rarr ccd (eg B0d rarr D+Dminus) Compilations are shown in Fig 9 A
few years ago hints of deviations were apparent between the value of sin(2βeff) measuredin brarr qqs transitions and the reference value from brarr ccs These have diminished withthe latest data but effects of non-SM contributions at the O(10) level are not ruled outOne notable update is the new Belle result on B0
d rarr D+Dminus [82] which improves theconsistency between the results of the two B factories as well as with the SM
33 Measurement of α
The unitarity triangle angle α is constrained by measurements of and isospin relationsbetween B rarr ππ ρπ and ρρ decays [83 84] The situation has been stable for the lastfew years though the final results from both B factory experiments in all three systemsare still awaited Combining all available information the world average is [10]
α =(890 +44
minus42
) (20)
Since the average is dominated by results from the ρρ system two small comments arein order First the apparently high branching fraction of B+ rarr ρ+ρ0 which comesessentially from a single measurement [85] stretches the isospin triangle and reduces theuncertainty Secondly analyses to date while allowing CP violation in the rates haveassumed the longitudinal polarisation fraction is the same for B and B ndash but the mostgeneral analysis would allow a difference between the two
9
Tim Gershon
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
brarrccs
φ K
0
ηprime K
0
KS K
S K
S
π0 K
0
ρ0 K
S
ω K
S
f 0 K
S
K+ K
- K0
-08 -06 -04 -02 0 02 04 06 08 1 12 14 16
World Average 068 plusmn 002
BaBar 026 plusmn 026 plusmn 003
Belle 090 +-00
01
99
Average 056 +-00
11
68
BaBar 057 plusmn 008 plusmn 002
Belle 064 plusmn 010 plusmn 004
Average 059 plusmn 007
BaBar 094 +-00
22
14 plusmn 006
Belle 030 plusmn 032 plusmn 008
Average 072 plusmn 019
BaBar 055 plusmn 020 plusmn 003
Belle 067 plusmn 031 plusmn 008
Average 057 plusmn 017
BaBar 035 +-00
23
61 plusmn 006 plusmn 003
Belle 064 +-00
12
95 plusmn 009 plusmn 010
Average 054 +-00
12
81
BaBar 055 +-00
22
69 plusmn 002
Belle 011 plusmn 046 plusmn 007
Average 045 plusmn 024
BaBar 060 +-00
11
68
Belle 063 +-00
11
69
Average 062 +-00
11
13
BaBar 086 plusmn 008 plusmn 003
Belle 068 plusmn 015 plusmn 003 +-00
21
13
Average 082 plusmn 007
H F A GH F A GEndOfYear 2011
PRELIMINARY
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
brarrccs SCP
Jψ
π0 S
CP
D+ D
- SC
P
D+
D- S
CP
D+
- D-+
S+
-
D+
- D-+
S-+
-1 0 1 2
World AverageHFAG (EPS 2011)
068 plusmn 002
BaBarPRL 101 (2008) 021801
123 plusmn 021 plusmn 004
BellePRD 77 (2008) 071101(R)
065 plusmn 021 plusmn 005
AverageHFAG correlated average
093 plusmn 015
BaBarPRD 79 032002 (2009)
065 plusmn 036 plusmn 005
BelleEPS 2011 preliminary
106 plusmn 021 plusmn 007
AverageHFAG correlated average
096 plusmn 019
BaBarPRD 79 032002 (2009)
071 plusmn 016 plusmn 003
BelleEPS 2011 preliminary
079 plusmn 013 plusmn 003
AverageHFAG correlated average
077 plusmn 010
BaBarPRD 79 032002 (2009)
063 plusmn 021 plusmn 003
BellePRL 93 (2004) 201802
055 plusmn 039 plusmn 012
AverageHFAG
061 plusmn 019
BaBarPRD 79 032002 (2009)
074 plusmn 023 plusmn 005
BellePRL 93 (2004) 201802
096 plusmn 043 plusmn 012
AverageHFAG
079 plusmn 021
H F A GH F A GEPS 2011
PRELIMINARY
Figure 9 Compilation of results on sin(2βeff) from (left) b rarr qqs and (right)brarr ccd transitions [8]
34 Measurement of γ
The angle γ is unique among CP violating observables in that it can be determined us-ing tree-level processes only exploiting the interference between (typically) b rarr cudand brarr ucd transitions that occurs when the process involves a neutral D meson recon-structed in a final state accessible to both D0 and D0 decays It therefore provides a SMbenchmark and its precise measurement is crucial in order to disentangle any non-SMcontributions to other processes via global CKM fits
Several different D decay final states have been studied in order to maximise the sen-sitivity to γ The archetype is the use of D decays to CP eigenstates the so-called GLWmethod [86 87] New results with this approach have recently become available fromBaBar [88] CDF [89] and LHCb [90] while the very latest results from Belle [91] areshown in Fig 10 The world average for the CP asymmetry in the processes involvingCP -even D decay final states including all these new results and illustrated in Fig 11(left) shows that CP violation in Bplusmn rarr DKplusmn decays is clearly established though nosingle measurement exceeds 5σ significance
Another powerful approach to constrain γ the so-called ADS method [92 93] comesfrom the use of doubly-Cabibbo-suppressed D decays (for example to the final stateK+πminus) Recent new results come from BaBar [94] Belle [95] and CDF [96] whilethe very latest results from LHCb [97] are shown in Fig 12 The world average for theparameter RADS which is the ratio of decay rates to the suppressed states compared tothose for the favoured channels including all these new results and illustrated in Fig 11(right) shows that the suppressed decay is now clearly established though no single mea-surement exceeds 5σ significance This is very promising for future γ determinations
Although the analyses withBplusmn rarr DKplusmn decays give the most precise results differentB decays have also been studied The use of both possible decays Dlowast rarr Dπ0 andDlowast rarr Dγ provides an extra handle on the extraction of γ fromBplusmn rarr DlowastKplusmn [98] that isbecoming visible in the most recent results [91 94] In addition theB0
d rarr DKlowast0 channel
10
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
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[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
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Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
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08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Tim Gershon
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
HF
AG
EndO
fYear
2011
brarrccs
φ K
0
ηprime K
0
KS K
S K
S
π0 K
0
ρ0 K
S
ω K
S
f 0 K
S
K+ K
- K0
-08 -06 -04 -02 0 02 04 06 08 1 12 14 16
World Average 068 plusmn 002
BaBar 026 plusmn 026 plusmn 003
Belle 090 +-00
01
99
Average 056 +-00
11
68
BaBar 057 plusmn 008 plusmn 002
Belle 064 plusmn 010 plusmn 004
Average 059 plusmn 007
BaBar 094 +-00
22
14 plusmn 006
Belle 030 plusmn 032 plusmn 008
Average 072 plusmn 019
BaBar 055 plusmn 020 plusmn 003
Belle 067 plusmn 031 plusmn 008
Average 057 plusmn 017
BaBar 035 +-00
23
61 plusmn 006 plusmn 003
Belle 064 +-00
12
95 plusmn 009 plusmn 010
Average 054 +-00
12
81
BaBar 055 +-00
22
69 plusmn 002
Belle 011 plusmn 046 plusmn 007
Average 045 plusmn 024
BaBar 060 +-00
11
68
Belle 063 +-00
11
69
Average 062 +-00
11
13
BaBar 086 plusmn 008 plusmn 003
Belle 068 plusmn 015 plusmn 003 +-00
21
13
Average 082 plusmn 007
H F A GH F A GEndOfYear 2011
PRELIMINARY
sin(2βeff
) equiv sin(2φe1ff)
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
HF
AG
EP
S 2
011
brarrccs SCP
Jψ
π0 S
CP
D+ D
- SC
P
D+
D- S
CP
D+
- D-+
S+
-
D+
- D-+
S-+
-1 0 1 2
World AverageHFAG (EPS 2011)
068 plusmn 002
BaBarPRL 101 (2008) 021801
123 plusmn 021 plusmn 004
BellePRD 77 (2008) 071101(R)
065 plusmn 021 plusmn 005
AverageHFAG correlated average
093 plusmn 015
BaBarPRD 79 032002 (2009)
065 plusmn 036 plusmn 005
BelleEPS 2011 preliminary
106 plusmn 021 plusmn 007
AverageHFAG correlated average
096 plusmn 019
BaBarPRD 79 032002 (2009)
071 plusmn 016 plusmn 003
BelleEPS 2011 preliminary
079 plusmn 013 plusmn 003
AverageHFAG correlated average
077 plusmn 010
BaBarPRD 79 032002 (2009)
063 plusmn 021 plusmn 003
BellePRL 93 (2004) 201802
055 plusmn 039 plusmn 012
AverageHFAG
061 plusmn 019
BaBarPRD 79 032002 (2009)
074 plusmn 023 plusmn 005
BellePRL 93 (2004) 201802
096 plusmn 043 plusmn 012
AverageHFAG
079 plusmn 021
H F A GH F A GEPS 2011
PRELIMINARY
Figure 9 Compilation of results on sin(2βeff) from (left) b rarr qqs and (right)brarr ccd transitions [8]
34 Measurement of γ
The angle γ is unique among CP violating observables in that it can be determined us-ing tree-level processes only exploiting the interference between (typically) b rarr cudand brarr ucd transitions that occurs when the process involves a neutral D meson recon-structed in a final state accessible to both D0 and D0 decays It therefore provides a SMbenchmark and its precise measurement is crucial in order to disentangle any non-SMcontributions to other processes via global CKM fits
Several different D decay final states have been studied in order to maximise the sen-sitivity to γ The archetype is the use of D decays to CP eigenstates the so-called GLWmethod [86 87] New results with this approach have recently become available fromBaBar [88] CDF [89] and LHCb [90] while the very latest results from Belle [91] areshown in Fig 10 The world average for the CP asymmetry in the processes involvingCP -even D decay final states including all these new results and illustrated in Fig 11(left) shows that CP violation in Bplusmn rarr DKplusmn decays is clearly established though nosingle measurement exceeds 5σ significance
Another powerful approach to constrain γ the so-called ADS method [92 93] comesfrom the use of doubly-Cabibbo-suppressed D decays (for example to the final stateK+πminus) Recent new results come from BaBar [94] Belle [95] and CDF [96] whilethe very latest results from LHCb [97] are shown in Fig 12 The world average for theparameter RADS which is the ratio of decay rates to the suppressed states compared tothose for the favoured channels including all these new results and illustrated in Fig 11(right) shows that the suppressed decay is now clearly established though no single mea-surement exceeds 5σ significance This is very promising for future γ determinations
Although the analyses withBplusmn rarr DKplusmn decays give the most precise results differentB decays have also been studied The use of both possible decays Dlowast rarr Dπ0 andDlowast rarr Dγ provides an extra handle on the extraction of γ fromBplusmn rarr DlowastKplusmn [98] that isbecoming visible in the most recent results [91 94] In addition theB0
d rarr DKlowast0 channel
10
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
References
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5 At Lepton Photon 2011 the author compared the long wait to discover effects beyond the SM to that forIndian batting hero Sachin Tendulkar to achieve his 100th century in international cricket Sadly at the time ofwriting these proceedings and despite some close calls we are still waiting for both historic achievements
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Overview of the CKM Matrix
[24] JS Nico J Phys G36 104001 (2009)[25] S Paul NuclInstrumMeth A611 157 (2009) 09020169[26] M Antonelli et al EurPhysJ C69 399 (2010) 10052323[27] V Cirigliano G Ecker H Neufeld A Pich and J Portoles (2011) 11076001[28] M Veltri (2011) 11015031[29] PA Boyle et al EurPhysJ C69 159 (2010) 10040886[30] V Cirigliano and H Neufeld PhysLett B700 7 (2011) 11020563[31] M Davier A Hocker and Z Zhang RevModPhys 78 1043 (2006) hep-ph0507078[32] A Pich NuclPhysProcSuppl 218 89 (2011) 11012107[33] B Aubert et al (BABAR) Phys Rev Lett 100 011801 (2008) 07072981[34] MJ Lee et al (Belle) Phys Rev D81 113007 (2010) 10010083[35] D Besson et al (CLEO) PhysRev D80 032005 (2009) 09062983[36] H Na CTH Davies E Follana GP Lepage and J Shigemitsu PhysRev D82 114506
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[48] B Aubert et al (BABAR) PhysRevLett 100 021801 (2008) 07091698[49] B Aubert et al (BABAR) PhysRev D79 092002 (2009) 09022660[50] A Matyja et al (Belle) PhysRevLett 99 191807 (2007) 07064429[51] A Bozek et al (Belle) PhysRev D82 072005 (2010) 10052302[52] YJ Kwon (2011) these proceeedings[53] P del Amo Sanchez et al (BABAR) PhysRev D83 052011 (2011) 10100987[54] P del Amo Sanchez et al (BABAR) PhysRev D83 032007 (2011) 10053288[55] H Ha et al (Belle) PhysRev D83 071101 (2011) 10120090[56] P Urquijo (2011) Preliminary results presented at EPS2011 URL http
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[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
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[65] B Aubert et al (BABAR) Phys Rev D79 052003 (2009) 08091174[66] K-F Chen et al (Belle) Phys Rev Lett 98 031802 (2007) hep-ex0608039[67] B Aubert et al (BABAR) PhysRevLett 99 021603 (2007) hep-ex0703016[68] H Ishino et al (Belle) Phys Rev Lett 98 211801 (2007) hep-ex0608035
15
Tim Gershon
[69] P Chang (Belle) (2011) Preliminary results presented at EPS 2011 URLhttpindicoin2p3frmaterialDisplaypycontribId=1019ampsessionId=2ampmaterialId=slidesampconfId=5116
[70] LHCb collaboration (2011) LHCb-CONF-2011-042[71] BR Ko et al (Belle) PhysRevLett 104 181602 (2010) 10013202[72] P del Amo Sanchez et al (BABAR) PhysRev D83 071103 (2011) 10115477[73] P del Amo Sanchez et al (BABAR) PhysRev D81 111103 (2010) 10033397[74] JP Lees et al (BABAR) PhysRev D84 031103 (2011) 11054410[75] R Aaij et al (LHCb) (2011) 11103970[76] Y Grossman and Y Nir (2011) 11103790[77] R Aaij et al (LHCb) (2011) 11120938[78] T Aaltonen et al (CDF) PhysRevD (2011) 11115023[79] LHCb collaboration (2011) LHCb-CONF-2011-004[80] T Aaltonen et al (CDF) PhysRev D83 052012 (2011) 11021961[81] LHCb collaboration (2011) LHCb-CONF-2011-048[82] T Higuchi (Belle) (2011) Preliminary results presented at EPS 2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=1017ampsessionId=2ampmaterialId=slidesampconfId=5116
[83] M Gronau and D London PhysRevLett 65 3381 (1990)[84] AE Snyder and HR Quinn PhysRev D48 2139 (1993)[85] B Aubert et al (BABAR) Phys Rev Lett 102 141802 (2009) 09013522[86] M Gronau and D London PhysLett B253 483 (1991)[87] M Gronau and D Wyler PhysLett B265 172 (1991)[88] P del Amo Sanchez et al (BABAR) Phys Rev D82 072004 (2010) 10070504[89] T Aaltonen et al (CDF) Phys Rev D81 031105 (2010) 09110425[90] LHCb collaboration (2011) LHCb-CONF-2011-031[91] Belle collaboration (2011) Preliminary results presented at Lepton Photon 2011
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[92] D Atwood I Dunietz and A Soni PhysRevLett 78 3257 (1997) hep-ph9612433[93] D Atwood I Dunietz and A Soni PhysRev D63 036005 (2001) hep-ph0008090[94] P del Amo Sanchez et al (BABAR) Phys Rev D82 072006 (2010) 10064241[95] Y Horii et al (Belle) Phys Rev Lett 106 231803 (2011) 11035951[96] T Aaltonen et al (CDF) PhysRevD (2011) 11085765[97] LHCb collaboration (2011) LHCb-CONF-2011-044[98] A Bondar and T Gershon PhysRev D70 091503 (2004) hep-ph0409281[99] I Dunietz PhysLett B270 75 (1991)
[100] M Gronau PhysLett B557 198 (2003) hep-ph0211282[101] T Gershon PhysRev D79 051301 (2009) 08102706[102] T Gershon and M Williams PhysRev D80 092002 (2009) 09091495[103] A Giri Y Grossman A Soffer and J Zupan PhysRev D68 054018 (2003) hep-ph
0303187[104] P del Amo Sanchez et al (BABAR) Phys Rev Lett 105 121801 (2010) 10051096[105] A Poluektov et al (Belle) Phys Rev D81 112002 (2010) 10033360[106] A Bondar and A Poluektov EurPhysJ C47 347 (2006) hep-ph0510246[107] A Bondar and A Poluektov EurPhysJ C55 51 (2008) 08010840[108] J Libby et al (CLEO) PhysRev D82 112006 (2010) 10102817[109] I Adachi K Adamczyk and H Aihara (Belle) (2011) 11064046[110] R Aleksan I Dunietz and B Kayser ZPhys C54 653 (1992)[111] T Aaltonen et al (CDF) PhysRevLett 103 191802 (2009) 08090080[112] LHCb collaboration (2011) LHCb-CONF-2011-057[113] J Dalseno et al (Belle) Phys Rev D79 072004 (2009) 08113665[114] B Aubert et al (BABAR) Phys Rev D80 112001 (2009) 09053615
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Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Overview of the CKM Matrix
Figure 10 Signals for Bplusmn rarr DCPKplusmn decays from Belle [91] (Top two plots)
D decays to CP -even final states (K+Kminus π+πminus) (Bottom two plots) D decays toCP -odd final states (K0
Sπ0 K0
Sη) In each pair of plots the left (right) figure is forBminus (B+) decays The plotted variable ∆E peaks at zero for signal decays whilebackground from Bplusmn rarr Dπplusmn appears as a satellite peak at positive values
may provide excellent sensitivity to γ once sufficient statistics become available [99ndash102]
Until now the strongest constraints on γ from Bplusmn rarr DKplusmn decays have come fromanalyses based on multibody D decays particularly D rarr K0
Sπ+πminus the so-called GGSZ
method [103] The most recent results3 are [104 105]
γ(BaBar) =(68 +15minus14 plusmn 4plusmn 3
) γ(Belle) =
(78 +11minus12 plusmn 4plusmn 9
) (21)
where the sources of uncertainty are statistical systematic and due to imperfect knowl-edge of the amplitude model to describe D rarr K0
Sπ+πminus decays The last source can be
eliminated by binning the Dalitz plot [103 106 107] using information on the averagestrong phase difference between D0 and D0 decays in each bin that can be determinedusing quantum correlated ψ(3770) rarr DD data samples The necessary measurementsfrom ψ(3770) data have recently been published by CLEO-c [108] and used by Belle toobtain a model-independent result [109]
γ = (77plusmn 15plusmn 4plusmn 4) (22)
where the last uncertainty is due to the statistical precision of the CLEO-c results (Notethat there is a strong statistical overlap in the data samples used for this result and themodel-dependent Belle result reported above4)
Combining all available information on tree-level processes sensitive to γ a worldaverage can be obtained The values obtained by two different fitting groups are [10 11]
γ(CKMfitter) =(68 +10minus11
) γ(UTfit) = (76plusmn 9)
(23)
3 The BaBar measurement includes Bplusmn decays to DKplusmn DlowastKplusmn and DKlowastplusmn and D decays to bothK0Sπ
+πminus and K0SK
+Kminus while the Belle results uses DKplusmn and DlowastKplusmn with D rarr K0Sπ
+πminus4 The Belle model-independent result uses only Bplusmn rarr DKplusmn with D rarr K0
Sπ+πminus
11
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
References
[1] N Cabibbo PhysRevLett 10 531 (1963)[2] M Kobayashi and T Maskawa ProgTheorPhys 49 652 (1973)[3] L Wolfenstein PhysRevLett 51 1945 (1983)[4] AJ Buras ME Lautenbacher and G Ostermaier PhysRev D50 3433 (1994) hep-ph
9403384[5] A Dighe (2011) these proceeedings[6] V Lubicz (2011) these proceeedings[7] K Nakamura et al (Particle Data Group) J Phys G37 075021 (2010)[8] D Asner et al (Heavy Flavor Averaging Group) (2010) 10101589 URL http
wwwslacstanfordeduxorghfag[9] M Antonelli et al PhysRept 494 197 (2010) 09075386
[10] J Charles et al (CKMfitter) EurPhysJ C41 1 (2005) hep-ph0406184 URL httpckmfitterin2p3fr
[11] M Bona et al (UTfit) JHEP 0507 028 (2005) hep-ph0501199 URL httpwwwutfitorgUTfit
[12] T Spadaro and A Young (2011) 11120238[13] J Laiho BD Pecjak and C Schwanda (2011) 11073934[14] M Gorbahn M Patel and S Robertson (2011) 11040826[15] M Kreps A Lenz and O Leroy (2011) 11034962[16] R Fleischer and S Ricciardi (2011) 11044029[17] MT Graham D Tonelli and J Zupan (2011) 11050179[18] DM Webber et al (MuLan) PhysRevLett 106 041803 (2011) 10100991[19] PJ Mohr BN Taylor and DB Newell RevModPhys 80 633 (2008) 08010028[20] WJ Marciano PhysRev D60 093006 (1999) hep-ph9903451[21] A Pak and A Czarnecki PhysRevLett 100 241807 (2008) 08030960[22] JC Hardy and IS Towner PhysRev C79 055502 (2009) 08121202[23] A Pichlmaier V Varlamov K Schreckenbach and P Geltenbort PhysLett B693 221
(2010)
5 At Lepton Photon 2011 the author compared the long wait to discover effects beyond the SM to that forIndian batting hero Sachin Tendulkar to achieve his 100th century in international cricket Sadly at the time ofwriting these proceedings and despite some close calls we are still waiting for both historic achievements
14
Overview of the CKM Matrix
[24] JS Nico J Phys G36 104001 (2009)[25] S Paul NuclInstrumMeth A611 157 (2009) 09020169[26] M Antonelli et al EurPhysJ C69 399 (2010) 10052323[27] V Cirigliano G Ecker H Neufeld A Pich and J Portoles (2011) 11076001[28] M Veltri (2011) 11015031[29] PA Boyle et al EurPhysJ C69 159 (2010) 10040886[30] V Cirigliano and H Neufeld PhysLett B700 7 (2011) 11020563[31] M Davier A Hocker and Z Zhang RevModPhys 78 1043 (2006) hep-ph0507078[32] A Pich NuclPhysProcSuppl 218 89 (2011) 11012107[33] B Aubert et al (BABAR) Phys Rev Lett 100 011801 (2008) 07072981[34] MJ Lee et al (Belle) Phys Rev D81 113007 (2010) 10010083[35] D Besson et al (CLEO) PhysRev D80 032005 (2009) 09062983[36] H Na CTH Davies E Follana GP Lepage and J Shigemitsu PhysRev D82 114506
(2010) 10084562[37] C Aubin et al (Fermilab Lattice MILC and HPQCD Collaborations) PhysRevLett 94
011601 (2005) hep-ph0408306[38] H Na et al (2011) 11091501[39] P del Amo Sanchez et al (BABAR) PhysRev D82 091103 (2010) 10084080[40] L Widhalm et al (Belle) PhysRevLett 100 241801 (2008) 07091340[41] P Naik et al (CLEO) PhysRev D80 112004 (2009) 09103602[42] J Laiho E Lunghi and RS Van de Water PhysRev D81 034503 (2010) 09102928[43] BA Dobrescu and AS Kronfeld PhysRevLett 100 241802 (2008) 08030512[44] VG Luth Annual Review of Nuclear and Particle Science 61 1 119 (2011)[45] W Dungel et al (Belle) PhysRev D82 112007 (2010) 10105620[46] JA Bailey et al (Fermilab Lattice and MILC Collaborations) PoS LATTICE2010 311
(2010) 10112166[47] BABAR collaboration (2011) Preliminary results presented at EPS2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=30ampsessionId=2ampmaterialId=slidesampconfId=5116
[48] B Aubert et al (BABAR) PhysRevLett 100 021801 (2008) 07091698[49] B Aubert et al (BABAR) PhysRev D79 092002 (2009) 09022660[50] A Matyja et al (Belle) PhysRevLett 99 191807 (2007) 07064429[51] A Bozek et al (Belle) PhysRev D82 072005 (2010) 10052302[52] YJ Kwon (2011) these proceeedings[53] P del Amo Sanchez et al (BABAR) PhysRev D83 052011 (2011) 10100987[54] P del Amo Sanchez et al (BABAR) PhysRev D83 032007 (2011) 10053288[55] H Ha et al (Belle) PhysRev D83 071101 (2011) 10120090[56] P Urquijo (2011) Preliminary results presented at EPS2011 URL http
indicoin2p3frmaterialDisplaypycontribId=1016ampsessionId=2ampmaterialId=slidesampconfId=5116
[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
httpindicoin2p3frgetFilepyaccesscontribId=114ampsessionId=7ampresId=0ampmaterialId=slidesampconfId=4403
[65] B Aubert et al (BABAR) Phys Rev D79 052003 (2009) 08091174[66] K-F Chen et al (Belle) Phys Rev Lett 98 031802 (2007) hep-ex0608039[67] B Aubert et al (BABAR) PhysRevLett 99 021603 (2007) hep-ex0703016[68] H Ishino et al (Belle) Phys Rev Lett 98 211801 (2007) hep-ex0608035
15
Tim Gershon
[69] P Chang (Belle) (2011) Preliminary results presented at EPS 2011 URLhttpindicoin2p3frmaterialDisplaypycontribId=1019ampsessionId=2ampmaterialId=slidesampconfId=5116
[70] LHCb collaboration (2011) LHCb-CONF-2011-042[71] BR Ko et al (Belle) PhysRevLett 104 181602 (2010) 10013202[72] P del Amo Sanchez et al (BABAR) PhysRev D83 071103 (2011) 10115477[73] P del Amo Sanchez et al (BABAR) PhysRev D81 111103 (2010) 10033397[74] JP Lees et al (BABAR) PhysRev D84 031103 (2011) 11054410[75] R Aaij et al (LHCb) (2011) 11103970[76] Y Grossman and Y Nir (2011) 11103790[77] R Aaij et al (LHCb) (2011) 11120938[78] T Aaltonen et al (CDF) PhysRevD (2011) 11115023[79] LHCb collaboration (2011) LHCb-CONF-2011-004[80] T Aaltonen et al (CDF) PhysRev D83 052012 (2011) 11021961[81] LHCb collaboration (2011) LHCb-CONF-2011-048[82] T Higuchi (Belle) (2011) Preliminary results presented at EPS 2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=1017ampsessionId=2ampmaterialId=slidesampconfId=5116
[83] M Gronau and D London PhysRevLett 65 3381 (1990)[84] AE Snyder and HR Quinn PhysRev D48 2139 (1993)[85] B Aubert et al (BABAR) Phys Rev Lett 102 141802 (2009) 09013522[86] M Gronau and D London PhysLett B253 483 (1991)[87] M Gronau and D Wyler PhysLett B265 172 (1991)[88] P del Amo Sanchez et al (BABAR) Phys Rev D82 072004 (2010) 10070504[89] T Aaltonen et al (CDF) Phys Rev D81 031105 (2010) 09110425[90] LHCb collaboration (2011) LHCb-CONF-2011-031[91] Belle collaboration (2011) Preliminary results presented at Lepton Photon 2011
(BELLE-CONF-1112) URL httpwwwinotifrresinMaKaCgetFilepyaccesscontribId=150ampsessionId=21ampresId=1ampmaterialId=slidesampconfId=79
[92] D Atwood I Dunietz and A Soni PhysRevLett 78 3257 (1997) hep-ph9612433[93] D Atwood I Dunietz and A Soni PhysRev D63 036005 (2001) hep-ph0008090[94] P del Amo Sanchez et al (BABAR) Phys Rev D82 072006 (2010) 10064241[95] Y Horii et al (Belle) Phys Rev Lett 106 231803 (2011) 11035951[96] T Aaltonen et al (CDF) PhysRevD (2011) 11085765[97] LHCb collaboration (2011) LHCb-CONF-2011-044[98] A Bondar and T Gershon PhysRev D70 091503 (2004) hep-ph0409281[99] I Dunietz PhysLett B270 75 (1991)
[100] M Gronau PhysLett B557 198 (2003) hep-ph0211282[101] T Gershon PhysRev D79 051301 (2009) 08102706[102] T Gershon and M Williams PhysRev D80 092002 (2009) 09091495[103] A Giri Y Grossman A Soffer and J Zupan PhysRev D68 054018 (2003) hep-ph
0303187[104] P del Amo Sanchez et al (BABAR) Phys Rev Lett 105 121801 (2010) 10051096[105] A Poluektov et al (Belle) Phys Rev D81 112002 (2010) 10033360[106] A Bondar and A Poluektov EurPhysJ C47 347 (2006) hep-ph0510246[107] A Bondar and A Poluektov EurPhysJ C55 51 (2008) 08010840[108] J Libby et al (CLEO) PhysRev D82 112006 (2010) 10102817[109] I Adachi K Adamczyk and H Aihara (Belle) (2011) 11064046[110] R Aleksan I Dunietz and B Kayser ZPhys C54 653 (1992)[111] T Aaltonen et al (CDF) PhysRevLett 103 191802 (2009) 08090080[112] LHCb collaboration (2011) LHCb-CONF-2011-057[113] J Dalseno et al (Belle) Phys Rev D79 072004 (2009) 08113665[114] B Aubert et al (BABAR) Phys Rev D80 112001 (2009) 09053615
16
Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Tim Gershon
DCP
K ACP+
HF
AG
LP
2011
-02 0 02 04 06 08
BaBarPRD 82 (2010) 072004
025 plusmn 006 plusmn 002
BelleLP 2011 preliminary
029 plusmn 006 plusmn 002
CDFPRD 81 031105(R) (2010)
039 plusmn 017 plusmn 004
LHCbLHCb-CONF-2011-031
007 plusmn 018 plusmn 007
AverageHFAG
027 plusmn 004
H F A GH F A GLP 2011
PRELIMINARY
D_Kπ K RADS
HF
AG
LP
2011
-0 001 002 003
BaBarPRD 82 (2010) 072006
00110 plusmn 00060 plusmn 00020
BellePRL 106 (2011) 231803
00163 +-00
00
00
44
41
+-00
00
00
01
73
CDFarXiv11085765
00220 plusmn 00086 plusmn 00026
LHCbLHCb-CONF-2011-044
00166 plusmn 00039 plusmn 00024
AverageHFAG
00160 plusmn 00027
H F A GH F A GLP 2011
PRELIMINARY
Figure 11 Compilations of results with world averages for Bplusmn rarr DKplusmn decays in(left) GLW and (right) ADS modes [8]
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K
DLL-KD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
5
10
15
gt 4 K DLL+KD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K
DLL-πD
K)π(rarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
10
20
lt 4 K DLL+πD
K)π(rarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K
DLL-KD
)π(Krarr-BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
100
200
gt 4 K DLL+KD
)π(Krarr+BLHCb Preliminary
-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4
K DLL-π
D)π(Krarr-B
LHCb Preliminary-1343 pb
)2m(B) (MeVc5200 5400 5600
)2Ev
ents
( 6
5 M
eVc
0
1000
2000
3000lt 4 K DLL+π
D)π(Krarr+B
LHCb Preliminary-1343 pbFigure 12 Signals for Bplusmn rarr DKplusmn D rarr Kplusmnπ∓ decays from LHCb [97] (Top
two plots) suppressed final states (Bottom two plots) favoured final states In each pairof plots the left (right) figure is for Bminus (B+) decays The plotted variable m(DK)peaks at the B mass for signal decays while background from Bplusmn rarr Dπplusmn appears asa satellite peak at positive values
The precision of the results is now reaching a level that the details of the statistical ap-proach used to obtain the average value no longer has a strong influence on the uncertaintybut some difference in the central values is apparent
An alternative approach to measuring γ still using tree-level B decays is based onthe time-dependent decay rates of Bs rarr Dplusmns K
∓ processes [110] This decay was previ-ously observed by CDF [111] and LHCb have recently reported clean signals [112] thatindicate that this mode can indeed be used to provide a competitive measurement of γ
It is also interesting to compare to the value of γ obtained from processes that involveloop diagrams since these may be affected by contributions from virtual non-standardparticles Recent results in charmless two-body B decays are discussed in Refs [5261] An interesting development in the last few years has been increased activity in thestudy of Dalitz plot distributions of charmless three-bodyB decays which can yield moreinformation about the contributing amplitudes and hence can yield determinations of γthat rely less strongly on theoretical input Results on B0
d rarr K0Sπ
+πminus [113 114] and
12
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
References
[1] N Cabibbo PhysRevLett 10 531 (1963)[2] M Kobayashi and T Maskawa ProgTheorPhys 49 652 (1973)[3] L Wolfenstein PhysRevLett 51 1945 (1983)[4] AJ Buras ME Lautenbacher and G Ostermaier PhysRev D50 3433 (1994) hep-ph
9403384[5] A Dighe (2011) these proceeedings[6] V Lubicz (2011) these proceeedings[7] K Nakamura et al (Particle Data Group) J Phys G37 075021 (2010)[8] D Asner et al (Heavy Flavor Averaging Group) (2010) 10101589 URL http
wwwslacstanfordeduxorghfag[9] M Antonelli et al PhysRept 494 197 (2010) 09075386
[10] J Charles et al (CKMfitter) EurPhysJ C41 1 (2005) hep-ph0406184 URL httpckmfitterin2p3fr
[11] M Bona et al (UTfit) JHEP 0507 028 (2005) hep-ph0501199 URL httpwwwutfitorgUTfit
[12] T Spadaro and A Young (2011) 11120238[13] J Laiho BD Pecjak and C Schwanda (2011) 11073934[14] M Gorbahn M Patel and S Robertson (2011) 11040826[15] M Kreps A Lenz and O Leroy (2011) 11034962[16] R Fleischer and S Ricciardi (2011) 11044029[17] MT Graham D Tonelli and J Zupan (2011) 11050179[18] DM Webber et al (MuLan) PhysRevLett 106 041803 (2011) 10100991[19] PJ Mohr BN Taylor and DB Newell RevModPhys 80 633 (2008) 08010028[20] WJ Marciano PhysRev D60 093006 (1999) hep-ph9903451[21] A Pak and A Czarnecki PhysRevLett 100 241807 (2008) 08030960[22] JC Hardy and IS Towner PhysRev C79 055502 (2009) 08121202[23] A Pichlmaier V Varlamov K Schreckenbach and P Geltenbort PhysLett B693 221
(2010)
5 At Lepton Photon 2011 the author compared the long wait to discover effects beyond the SM to that forIndian batting hero Sachin Tendulkar to achieve his 100th century in international cricket Sadly at the time ofwriting these proceedings and despite some close calls we are still waiting for both historic achievements
14
Overview of the CKM Matrix
[24] JS Nico J Phys G36 104001 (2009)[25] S Paul NuclInstrumMeth A611 157 (2009) 09020169[26] M Antonelli et al EurPhysJ C69 399 (2010) 10052323[27] V Cirigliano G Ecker H Neufeld A Pich and J Portoles (2011) 11076001[28] M Veltri (2011) 11015031[29] PA Boyle et al EurPhysJ C69 159 (2010) 10040886[30] V Cirigliano and H Neufeld PhysLett B700 7 (2011) 11020563[31] M Davier A Hocker and Z Zhang RevModPhys 78 1043 (2006) hep-ph0507078[32] A Pich NuclPhysProcSuppl 218 89 (2011) 11012107[33] B Aubert et al (BABAR) Phys Rev Lett 100 011801 (2008) 07072981[34] MJ Lee et al (Belle) Phys Rev D81 113007 (2010) 10010083[35] D Besson et al (CLEO) PhysRev D80 032005 (2009) 09062983[36] H Na CTH Davies E Follana GP Lepage and J Shigemitsu PhysRev D82 114506
(2010) 10084562[37] C Aubin et al (Fermilab Lattice MILC and HPQCD Collaborations) PhysRevLett 94
011601 (2005) hep-ph0408306[38] H Na et al (2011) 11091501[39] P del Amo Sanchez et al (BABAR) PhysRev D82 091103 (2010) 10084080[40] L Widhalm et al (Belle) PhysRevLett 100 241801 (2008) 07091340[41] P Naik et al (CLEO) PhysRev D80 112004 (2009) 09103602[42] J Laiho E Lunghi and RS Van de Water PhysRev D81 034503 (2010) 09102928[43] BA Dobrescu and AS Kronfeld PhysRevLett 100 241802 (2008) 08030512[44] VG Luth Annual Review of Nuclear and Particle Science 61 1 119 (2011)[45] W Dungel et al (Belle) PhysRev D82 112007 (2010) 10105620[46] JA Bailey et al (Fermilab Lattice and MILC Collaborations) PoS LATTICE2010 311
(2010) 10112166[47] BABAR collaboration (2011) Preliminary results presented at EPS2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=30ampsessionId=2ampmaterialId=slidesampconfId=5116
[48] B Aubert et al (BABAR) PhysRevLett 100 021801 (2008) 07091698[49] B Aubert et al (BABAR) PhysRev D79 092002 (2009) 09022660[50] A Matyja et al (Belle) PhysRevLett 99 191807 (2007) 07064429[51] A Bozek et al (Belle) PhysRev D82 072005 (2010) 10052302[52] YJ Kwon (2011) these proceeedings[53] P del Amo Sanchez et al (BABAR) PhysRev D83 052011 (2011) 10100987[54] P del Amo Sanchez et al (BABAR) PhysRev D83 032007 (2011) 10053288[55] H Ha et al (Belle) PhysRev D83 071101 (2011) 10120090[56] P Urquijo (2011) Preliminary results presented at EPS2011 URL http
indicoin2p3frmaterialDisplaypycontribId=1016ampsessionId=2ampmaterialId=slidesampconfId=5116
[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
httpindicoin2p3frgetFilepyaccesscontribId=114ampsessionId=7ampresId=0ampmaterialId=slidesampconfId=4403
[65] B Aubert et al (BABAR) Phys Rev D79 052003 (2009) 08091174[66] K-F Chen et al (Belle) Phys Rev Lett 98 031802 (2007) hep-ex0608039[67] B Aubert et al (BABAR) PhysRevLett 99 021603 (2007) hep-ex0703016[68] H Ishino et al (Belle) Phys Rev Lett 98 211801 (2007) hep-ex0608035
15
Tim Gershon
[69] P Chang (Belle) (2011) Preliminary results presented at EPS 2011 URLhttpindicoin2p3frmaterialDisplaypycontribId=1019ampsessionId=2ampmaterialId=slidesampconfId=5116
[70] LHCb collaboration (2011) LHCb-CONF-2011-042[71] BR Ko et al (Belle) PhysRevLett 104 181602 (2010) 10013202[72] P del Amo Sanchez et al (BABAR) PhysRev D83 071103 (2011) 10115477[73] P del Amo Sanchez et al (BABAR) PhysRev D81 111103 (2010) 10033397[74] JP Lees et al (BABAR) PhysRev D84 031103 (2011) 11054410[75] R Aaij et al (LHCb) (2011) 11103970[76] Y Grossman and Y Nir (2011) 11103790[77] R Aaij et al (LHCb) (2011) 11120938[78] T Aaltonen et al (CDF) PhysRevD (2011) 11115023[79] LHCb collaboration (2011) LHCb-CONF-2011-004[80] T Aaltonen et al (CDF) PhysRev D83 052012 (2011) 11021961[81] LHCb collaboration (2011) LHCb-CONF-2011-048[82] T Higuchi (Belle) (2011) Preliminary results presented at EPS 2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=1017ampsessionId=2ampmaterialId=slidesampconfId=5116
[83] M Gronau and D London PhysRevLett 65 3381 (1990)[84] AE Snyder and HR Quinn PhysRev D48 2139 (1993)[85] B Aubert et al (BABAR) Phys Rev Lett 102 141802 (2009) 09013522[86] M Gronau and D London PhysLett B253 483 (1991)[87] M Gronau and D Wyler PhysLett B265 172 (1991)[88] P del Amo Sanchez et al (BABAR) Phys Rev D82 072004 (2010) 10070504[89] T Aaltonen et al (CDF) Phys Rev D81 031105 (2010) 09110425[90] LHCb collaboration (2011) LHCb-CONF-2011-031[91] Belle collaboration (2011) Preliminary results presented at Lepton Photon 2011
(BELLE-CONF-1112) URL httpwwwinotifrresinMaKaCgetFilepyaccesscontribId=150ampsessionId=21ampresId=1ampmaterialId=slidesampconfId=79
[92] D Atwood I Dunietz and A Soni PhysRevLett 78 3257 (1997) hep-ph9612433[93] D Atwood I Dunietz and A Soni PhysRev D63 036005 (2001) hep-ph0008090[94] P del Amo Sanchez et al (BABAR) Phys Rev D82 072006 (2010) 10064241[95] Y Horii et al (Belle) Phys Rev Lett 106 231803 (2011) 11035951[96] T Aaltonen et al (CDF) PhysRevD (2011) 11085765[97] LHCb collaboration (2011) LHCb-CONF-2011-044[98] A Bondar and T Gershon PhysRev D70 091503 (2004) hep-ph0409281[99] I Dunietz PhysLett B270 75 (1991)
[100] M Gronau PhysLett B557 198 (2003) hep-ph0211282[101] T Gershon PhysRev D79 051301 (2009) 08102706[102] T Gershon and M Williams PhysRev D80 092002 (2009) 09091495[103] A Giri Y Grossman A Soffer and J Zupan PhysRev D68 054018 (2003) hep-ph
0303187[104] P del Amo Sanchez et al (BABAR) Phys Rev Lett 105 121801 (2010) 10051096[105] A Poluektov et al (Belle) Phys Rev D81 112002 (2010) 10033360[106] A Bondar and A Poluektov EurPhysJ C47 347 (2006) hep-ph0510246[107] A Bondar and A Poluektov EurPhysJ C55 51 (2008) 08010840[108] J Libby et al (CLEO) PhysRev D82 112006 (2010) 10102817[109] I Adachi K Adamczyk and H Aihara (Belle) (2011) 11064046[110] R Aleksan I Dunietz and B Kayser ZPhys C54 653 (1992)[111] T Aaltonen et al (CDF) PhysRevLett 103 191802 (2009) 08090080[112] LHCb collaboration (2011) LHCb-CONF-2011-057[113] J Dalseno et al (Belle) Phys Rev D79 072004 (2009) 08113665[114] B Aubert et al (BABAR) Phys Rev D80 112001 (2009) 09053615
16
Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Overview of the CKM Matrix
B0d rarr K+πminusπ0 [115] decays can be combined to provide a constraint on γ [116 117]
The current data do not however provide a competitive result
35 Global CKM fits
The results of global fits to the CKM Unitarity Triangle parameters from the two mainfitting groups CKMfitter [10] and UTfit [11] are shown in Fig 13 The results are
ρ = 0144 +0027minus0018 (CKMfitter) = 0132plusmn 0020 (UTfit) (24)
η = 0343plusmn 0014 (CKMfitter) = 0353plusmn 0014 (UTfit) (25)
In spite of the different statistical approaches used consistent results are obtained Theoverall consistency of the different constraints on the (ρndashη) plane is good though sometension exists (see for example Ref [118])
γ
γ
α
α
dm∆
Kε
Kε
sm∆ amp dm∆
ubV
βsin 2
(excl at CL gt 095)
lt 0βsol w cos 2
exc
luded a
t CL gt
09
5α
βγ
ρ
shy10 shy05 00 05 10 15 20
η
shy15
shy10
shy05
00
05
10
15
excluded area has CL gt 095
Summer 11
CKMf i t t e r
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
γ
β
α
)γ+βsin(2
sm∆d
m∆
dm∆
Kε
cbV
ubV
)ντrarrBR(B
postLP11
SM fit
ρ-1 -05 0 05 1
η
-1
-05
0
05
1
Figure 13 Results of global fits to the CKM Unitarity Triangle parameters from (left)CKMfitter [10] and (right) UTfit [11]
4 Future prospects and conclusions
The current time is certainly one of a changing era in quark flavour physics The previousgeneration of experiments is completing their analyses on their final data sets while thenext generation are commencing their programmes Looking further ahead there areexciting prospects for this field of research as new experiments are planned There isa future programme for kaon physics in the USA [119] and new experiments studyingdifferent aspects of kaon decays are also planned in Europe and Asia among which theKLOE-2 experiment [120] has notable prospects to improve the measurement of |Vus|
A new generation of high luminosity e+eminus machines operating as B factories or atlower energies is planned [121 122] Another important step forward will occur with theupgrade of the LHCb detector [123] which will allow to exploit fully the flavour physicscapability of the LHC The progress in theory must of course be matched by improvedtheoretical understanding While such advances are in general hard to predict there isvery good reason to be optimistic that lattice calculations will continue to become moreprecise [6]
13
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
References
[1] N Cabibbo PhysRevLett 10 531 (1963)[2] M Kobayashi and T Maskawa ProgTheorPhys 49 652 (1973)[3] L Wolfenstein PhysRevLett 51 1945 (1983)[4] AJ Buras ME Lautenbacher and G Ostermaier PhysRev D50 3433 (1994) hep-ph
9403384[5] A Dighe (2011) these proceeedings[6] V Lubicz (2011) these proceeedings[7] K Nakamura et al (Particle Data Group) J Phys G37 075021 (2010)[8] D Asner et al (Heavy Flavor Averaging Group) (2010) 10101589 URL http
wwwslacstanfordeduxorghfag[9] M Antonelli et al PhysRept 494 197 (2010) 09075386
[10] J Charles et al (CKMfitter) EurPhysJ C41 1 (2005) hep-ph0406184 URL httpckmfitterin2p3fr
[11] M Bona et al (UTfit) JHEP 0507 028 (2005) hep-ph0501199 URL httpwwwutfitorgUTfit
[12] T Spadaro and A Young (2011) 11120238[13] J Laiho BD Pecjak and C Schwanda (2011) 11073934[14] M Gorbahn M Patel and S Robertson (2011) 11040826[15] M Kreps A Lenz and O Leroy (2011) 11034962[16] R Fleischer and S Ricciardi (2011) 11044029[17] MT Graham D Tonelli and J Zupan (2011) 11050179[18] DM Webber et al (MuLan) PhysRevLett 106 041803 (2011) 10100991[19] PJ Mohr BN Taylor and DB Newell RevModPhys 80 633 (2008) 08010028[20] WJ Marciano PhysRev D60 093006 (1999) hep-ph9903451[21] A Pak and A Czarnecki PhysRevLett 100 241807 (2008) 08030960[22] JC Hardy and IS Towner PhysRev C79 055502 (2009) 08121202[23] A Pichlmaier V Varlamov K Schreckenbach and P Geltenbort PhysLett B693 221
(2010)
5 At Lepton Photon 2011 the author compared the long wait to discover effects beyond the SM to that forIndian batting hero Sachin Tendulkar to achieve his 100th century in international cricket Sadly at the time ofwriting these proceedings and despite some close calls we are still waiting for both historic achievements
14
Overview of the CKM Matrix
[24] JS Nico J Phys G36 104001 (2009)[25] S Paul NuclInstrumMeth A611 157 (2009) 09020169[26] M Antonelli et al EurPhysJ C69 399 (2010) 10052323[27] V Cirigliano G Ecker H Neufeld A Pich and J Portoles (2011) 11076001[28] M Veltri (2011) 11015031[29] PA Boyle et al EurPhysJ C69 159 (2010) 10040886[30] V Cirigliano and H Neufeld PhysLett B700 7 (2011) 11020563[31] M Davier A Hocker and Z Zhang RevModPhys 78 1043 (2006) hep-ph0507078[32] A Pich NuclPhysProcSuppl 218 89 (2011) 11012107[33] B Aubert et al (BABAR) Phys Rev Lett 100 011801 (2008) 07072981[34] MJ Lee et al (Belle) Phys Rev D81 113007 (2010) 10010083[35] D Besson et al (CLEO) PhysRev D80 032005 (2009) 09062983[36] H Na CTH Davies E Follana GP Lepage and J Shigemitsu PhysRev D82 114506
(2010) 10084562[37] C Aubin et al (Fermilab Lattice MILC and HPQCD Collaborations) PhysRevLett 94
011601 (2005) hep-ph0408306[38] H Na et al (2011) 11091501[39] P del Amo Sanchez et al (BABAR) PhysRev D82 091103 (2010) 10084080[40] L Widhalm et al (Belle) PhysRevLett 100 241801 (2008) 07091340[41] P Naik et al (CLEO) PhysRev D80 112004 (2009) 09103602[42] J Laiho E Lunghi and RS Van de Water PhysRev D81 034503 (2010) 09102928[43] BA Dobrescu and AS Kronfeld PhysRevLett 100 241802 (2008) 08030512[44] VG Luth Annual Review of Nuclear and Particle Science 61 1 119 (2011)[45] W Dungel et al (Belle) PhysRev D82 112007 (2010) 10105620[46] JA Bailey et al (Fermilab Lattice and MILC Collaborations) PoS LATTICE2010 311
(2010) 10112166[47] BABAR collaboration (2011) Preliminary results presented at EPS2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=30ampsessionId=2ampmaterialId=slidesampconfId=5116
[48] B Aubert et al (BABAR) PhysRevLett 100 021801 (2008) 07091698[49] B Aubert et al (BABAR) PhysRev D79 092002 (2009) 09022660[50] A Matyja et al (Belle) PhysRevLett 99 191807 (2007) 07064429[51] A Bozek et al (Belle) PhysRev D82 072005 (2010) 10052302[52] YJ Kwon (2011) these proceeedings[53] P del Amo Sanchez et al (BABAR) PhysRev D83 052011 (2011) 10100987[54] P del Amo Sanchez et al (BABAR) PhysRev D83 032007 (2011) 10053288[55] H Ha et al (Belle) PhysRev D83 071101 (2011) 10120090[56] P Urquijo (2011) Preliminary results presented at EPS2011 URL http
indicoin2p3frmaterialDisplaypycontribId=1016ampsessionId=2ampmaterialId=slidesampconfId=5116
[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
httpindicoin2p3frgetFilepyaccesscontribId=114ampsessionId=7ampresId=0ampmaterialId=slidesampconfId=4403
[65] B Aubert et al (BABAR) Phys Rev D79 052003 (2009) 08091174[66] K-F Chen et al (Belle) Phys Rev Lett 98 031802 (2007) hep-ex0608039[67] B Aubert et al (BABAR) PhysRevLett 99 021603 (2007) hep-ex0703016[68] H Ishino et al (Belle) Phys Rev Lett 98 211801 (2007) hep-ex0608035
15
Tim Gershon
[69] P Chang (Belle) (2011) Preliminary results presented at EPS 2011 URLhttpindicoin2p3frmaterialDisplaypycontribId=1019ampsessionId=2ampmaterialId=slidesampconfId=5116
[70] LHCb collaboration (2011) LHCb-CONF-2011-042[71] BR Ko et al (Belle) PhysRevLett 104 181602 (2010) 10013202[72] P del Amo Sanchez et al (BABAR) PhysRev D83 071103 (2011) 10115477[73] P del Amo Sanchez et al (BABAR) PhysRev D81 111103 (2010) 10033397[74] JP Lees et al (BABAR) PhysRev D84 031103 (2011) 11054410[75] R Aaij et al (LHCb) (2011) 11103970[76] Y Grossman and Y Nir (2011) 11103790[77] R Aaij et al (LHCb) (2011) 11120938[78] T Aaltonen et al (CDF) PhysRevD (2011) 11115023[79] LHCb collaboration (2011) LHCb-CONF-2011-004[80] T Aaltonen et al (CDF) PhysRev D83 052012 (2011) 11021961[81] LHCb collaboration (2011) LHCb-CONF-2011-048[82] T Higuchi (Belle) (2011) Preliminary results presented at EPS 2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=1017ampsessionId=2ampmaterialId=slidesampconfId=5116
[83] M Gronau and D London PhysRevLett 65 3381 (1990)[84] AE Snyder and HR Quinn PhysRev D48 2139 (1993)[85] B Aubert et al (BABAR) Phys Rev Lett 102 141802 (2009) 09013522[86] M Gronau and D London PhysLett B253 483 (1991)[87] M Gronau and D Wyler PhysLett B265 172 (1991)[88] P del Amo Sanchez et al (BABAR) Phys Rev D82 072004 (2010) 10070504[89] T Aaltonen et al (CDF) Phys Rev D81 031105 (2010) 09110425[90] LHCb collaboration (2011) LHCb-CONF-2011-031[91] Belle collaboration (2011) Preliminary results presented at Lepton Photon 2011
(BELLE-CONF-1112) URL httpwwwinotifrresinMaKaCgetFilepyaccesscontribId=150ampsessionId=21ampresId=1ampmaterialId=slidesampconfId=79
[92] D Atwood I Dunietz and A Soni PhysRevLett 78 3257 (1997) hep-ph9612433[93] D Atwood I Dunietz and A Soni PhysRev D63 036005 (2001) hep-ph0008090[94] P del Amo Sanchez et al (BABAR) Phys Rev D82 072006 (2010) 10064241[95] Y Horii et al (Belle) Phys Rev Lett 106 231803 (2011) 11035951[96] T Aaltonen et al (CDF) PhysRevD (2011) 11085765[97] LHCb collaboration (2011) LHCb-CONF-2011-044[98] A Bondar and T Gershon PhysRev D70 091503 (2004) hep-ph0409281[99] I Dunietz PhysLett B270 75 (1991)
[100] M Gronau PhysLett B557 198 (2003) hep-ph0211282[101] T Gershon PhysRev D79 051301 (2009) 08102706[102] T Gershon and M Williams PhysRev D80 092002 (2009) 09091495[103] A Giri Y Grossman A Soffer and J Zupan PhysRev D68 054018 (2003) hep-ph
0303187[104] P del Amo Sanchez et al (BABAR) Phys Rev Lett 105 121801 (2010) 10051096[105] A Poluektov et al (Belle) Phys Rev D81 112002 (2010) 10033360[106] A Bondar and A Poluektov EurPhysJ C47 347 (2006) hep-ph0510246[107] A Bondar and A Poluektov EurPhysJ C55 51 (2008) 08010840[108] J Libby et al (CLEO) PhysRev D82 112006 (2010) 10102817[109] I Adachi K Adamczyk and H Aihara (Belle) (2011) 11064046[110] R Aleksan I Dunietz and B Kayser ZPhys C54 653 (1992)[111] T Aaltonen et al (CDF) PhysRevLett 103 191802 (2009) 08090080[112] LHCb collaboration (2011) LHCb-CONF-2011-057[113] J Dalseno et al (Belle) Phys Rev D79 072004 (2009) 08113665[114] B Aubert et al (BABAR) Phys Rev D80 112001 (2009) 09053615
16
Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Tim Gershon
In conclusion the CKM paradigm continues its unreasonable success and despite somenotable tensions with the SM there is no discrepancy that can be considered proof ofnon-standard contributions5 Nonetheless there is reason for optimism since current andfuture projects promise significant improvements In the short term the BESIII and LHCbexperiments together with improved lattice calculations will at the very least advanceour knowledge and may provide a breakthrough In the certainty that new sources ofCP violation exist somewhere and with various other reasons to expect non-SM physicsaround the TeV scale (or higher) to cause observable effects in flavour-changing interac-tions in the quark sector continued study of the elements of the CKM matrix remains akey cornerstone of the global particle physics programme
Acknowledgments
I am grateful to help from individuals from the BaBar Belle CLEO-c KLOE LHCb andNA62 experiments the working group conveners from CKM2010 and the other speakersin the Flavour Physics sessions at Lepton Photon 2011 I would particularly like to thankMarcella Bona Erika De Lucia Vera Luth Karim Trabelsi and Guy Wilkinson Thiswork was supported by the EU under FP7
References
[1] N Cabibbo PhysRevLett 10 531 (1963)[2] M Kobayashi and T Maskawa ProgTheorPhys 49 652 (1973)[3] L Wolfenstein PhysRevLett 51 1945 (1983)[4] AJ Buras ME Lautenbacher and G Ostermaier PhysRev D50 3433 (1994) hep-ph
9403384[5] A Dighe (2011) these proceeedings[6] V Lubicz (2011) these proceeedings[7] K Nakamura et al (Particle Data Group) J Phys G37 075021 (2010)[8] D Asner et al (Heavy Flavor Averaging Group) (2010) 10101589 URL http
wwwslacstanfordeduxorghfag[9] M Antonelli et al PhysRept 494 197 (2010) 09075386
[10] J Charles et al (CKMfitter) EurPhysJ C41 1 (2005) hep-ph0406184 URL httpckmfitterin2p3fr
[11] M Bona et al (UTfit) JHEP 0507 028 (2005) hep-ph0501199 URL httpwwwutfitorgUTfit
[12] T Spadaro and A Young (2011) 11120238[13] J Laiho BD Pecjak and C Schwanda (2011) 11073934[14] M Gorbahn M Patel and S Robertson (2011) 11040826[15] M Kreps A Lenz and O Leroy (2011) 11034962[16] R Fleischer and S Ricciardi (2011) 11044029[17] MT Graham D Tonelli and J Zupan (2011) 11050179[18] DM Webber et al (MuLan) PhysRevLett 106 041803 (2011) 10100991[19] PJ Mohr BN Taylor and DB Newell RevModPhys 80 633 (2008) 08010028[20] WJ Marciano PhysRev D60 093006 (1999) hep-ph9903451[21] A Pak and A Czarnecki PhysRevLett 100 241807 (2008) 08030960[22] JC Hardy and IS Towner PhysRev C79 055502 (2009) 08121202[23] A Pichlmaier V Varlamov K Schreckenbach and P Geltenbort PhysLett B693 221
(2010)
5 At Lepton Photon 2011 the author compared the long wait to discover effects beyond the SM to that forIndian batting hero Sachin Tendulkar to achieve his 100th century in international cricket Sadly at the time ofwriting these proceedings and despite some close calls we are still waiting for both historic achievements
14
Overview of the CKM Matrix
[24] JS Nico J Phys G36 104001 (2009)[25] S Paul NuclInstrumMeth A611 157 (2009) 09020169[26] M Antonelli et al EurPhysJ C69 399 (2010) 10052323[27] V Cirigliano G Ecker H Neufeld A Pich and J Portoles (2011) 11076001[28] M Veltri (2011) 11015031[29] PA Boyle et al EurPhysJ C69 159 (2010) 10040886[30] V Cirigliano and H Neufeld PhysLett B700 7 (2011) 11020563[31] M Davier A Hocker and Z Zhang RevModPhys 78 1043 (2006) hep-ph0507078[32] A Pich NuclPhysProcSuppl 218 89 (2011) 11012107[33] B Aubert et al (BABAR) Phys Rev Lett 100 011801 (2008) 07072981[34] MJ Lee et al (Belle) Phys Rev D81 113007 (2010) 10010083[35] D Besson et al (CLEO) PhysRev D80 032005 (2009) 09062983[36] H Na CTH Davies E Follana GP Lepage and J Shigemitsu PhysRev D82 114506
(2010) 10084562[37] C Aubin et al (Fermilab Lattice MILC and HPQCD Collaborations) PhysRevLett 94
011601 (2005) hep-ph0408306[38] H Na et al (2011) 11091501[39] P del Amo Sanchez et al (BABAR) PhysRev D82 091103 (2010) 10084080[40] L Widhalm et al (Belle) PhysRevLett 100 241801 (2008) 07091340[41] P Naik et al (CLEO) PhysRev D80 112004 (2009) 09103602[42] J Laiho E Lunghi and RS Van de Water PhysRev D81 034503 (2010) 09102928[43] BA Dobrescu and AS Kronfeld PhysRevLett 100 241802 (2008) 08030512[44] VG Luth Annual Review of Nuclear and Particle Science 61 1 119 (2011)[45] W Dungel et al (Belle) PhysRev D82 112007 (2010) 10105620[46] JA Bailey et al (Fermilab Lattice and MILC Collaborations) PoS LATTICE2010 311
(2010) 10112166[47] BABAR collaboration (2011) Preliminary results presented at EPS2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=30ampsessionId=2ampmaterialId=slidesampconfId=5116
[48] B Aubert et al (BABAR) PhysRevLett 100 021801 (2008) 07091698[49] B Aubert et al (BABAR) PhysRev D79 092002 (2009) 09022660[50] A Matyja et al (Belle) PhysRevLett 99 191807 (2007) 07064429[51] A Bozek et al (Belle) PhysRev D82 072005 (2010) 10052302[52] YJ Kwon (2011) these proceeedings[53] P del Amo Sanchez et al (BABAR) PhysRev D83 052011 (2011) 10100987[54] P del Amo Sanchez et al (BABAR) PhysRev D83 032007 (2011) 10053288[55] H Ha et al (Belle) PhysRev D83 071101 (2011) 10120090[56] P Urquijo (2011) Preliminary results presented at EPS2011 URL http
indicoin2p3frmaterialDisplaypycontribId=1016ampsessionId=2ampmaterialId=slidesampconfId=5116
[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
httpindicoin2p3frgetFilepyaccesscontribId=114ampsessionId=7ampresId=0ampmaterialId=slidesampconfId=4403
[65] B Aubert et al (BABAR) Phys Rev D79 052003 (2009) 08091174[66] K-F Chen et al (Belle) Phys Rev Lett 98 031802 (2007) hep-ex0608039[67] B Aubert et al (BABAR) PhysRevLett 99 021603 (2007) hep-ex0703016[68] H Ishino et al (Belle) Phys Rev Lett 98 211801 (2007) hep-ex0608035
15
Tim Gershon
[69] P Chang (Belle) (2011) Preliminary results presented at EPS 2011 URLhttpindicoin2p3frmaterialDisplaypycontribId=1019ampsessionId=2ampmaterialId=slidesampconfId=5116
[70] LHCb collaboration (2011) LHCb-CONF-2011-042[71] BR Ko et al (Belle) PhysRevLett 104 181602 (2010) 10013202[72] P del Amo Sanchez et al (BABAR) PhysRev D83 071103 (2011) 10115477[73] P del Amo Sanchez et al (BABAR) PhysRev D81 111103 (2010) 10033397[74] JP Lees et al (BABAR) PhysRev D84 031103 (2011) 11054410[75] R Aaij et al (LHCb) (2011) 11103970[76] Y Grossman and Y Nir (2011) 11103790[77] R Aaij et al (LHCb) (2011) 11120938[78] T Aaltonen et al (CDF) PhysRevD (2011) 11115023[79] LHCb collaboration (2011) LHCb-CONF-2011-004[80] T Aaltonen et al (CDF) PhysRev D83 052012 (2011) 11021961[81] LHCb collaboration (2011) LHCb-CONF-2011-048[82] T Higuchi (Belle) (2011) Preliminary results presented at EPS 2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=1017ampsessionId=2ampmaterialId=slidesampconfId=5116
[83] M Gronau and D London PhysRevLett 65 3381 (1990)[84] AE Snyder and HR Quinn PhysRev D48 2139 (1993)[85] B Aubert et al (BABAR) Phys Rev Lett 102 141802 (2009) 09013522[86] M Gronau and D London PhysLett B253 483 (1991)[87] M Gronau and D Wyler PhysLett B265 172 (1991)[88] P del Amo Sanchez et al (BABAR) Phys Rev D82 072004 (2010) 10070504[89] T Aaltonen et al (CDF) Phys Rev D81 031105 (2010) 09110425[90] LHCb collaboration (2011) LHCb-CONF-2011-031[91] Belle collaboration (2011) Preliminary results presented at Lepton Photon 2011
(BELLE-CONF-1112) URL httpwwwinotifrresinMaKaCgetFilepyaccesscontribId=150ampsessionId=21ampresId=1ampmaterialId=slidesampconfId=79
[92] D Atwood I Dunietz and A Soni PhysRevLett 78 3257 (1997) hep-ph9612433[93] D Atwood I Dunietz and A Soni PhysRev D63 036005 (2001) hep-ph0008090[94] P del Amo Sanchez et al (BABAR) Phys Rev D82 072006 (2010) 10064241[95] Y Horii et al (Belle) Phys Rev Lett 106 231803 (2011) 11035951[96] T Aaltonen et al (CDF) PhysRevD (2011) 11085765[97] LHCb collaboration (2011) LHCb-CONF-2011-044[98] A Bondar and T Gershon PhysRev D70 091503 (2004) hep-ph0409281[99] I Dunietz PhysLett B270 75 (1991)
[100] M Gronau PhysLett B557 198 (2003) hep-ph0211282[101] T Gershon PhysRev D79 051301 (2009) 08102706[102] T Gershon and M Williams PhysRev D80 092002 (2009) 09091495[103] A Giri Y Grossman A Soffer and J Zupan PhysRev D68 054018 (2003) hep-ph
0303187[104] P del Amo Sanchez et al (BABAR) Phys Rev Lett 105 121801 (2010) 10051096[105] A Poluektov et al (Belle) Phys Rev D81 112002 (2010) 10033360[106] A Bondar and A Poluektov EurPhysJ C47 347 (2006) hep-ph0510246[107] A Bondar and A Poluektov EurPhysJ C55 51 (2008) 08010840[108] J Libby et al (CLEO) PhysRev D82 112006 (2010) 10102817[109] I Adachi K Adamczyk and H Aihara (Belle) (2011) 11064046[110] R Aleksan I Dunietz and B Kayser ZPhys C54 653 (1992)[111] T Aaltonen et al (CDF) PhysRevLett 103 191802 (2009) 08090080[112] LHCb collaboration (2011) LHCb-CONF-2011-057[113] J Dalseno et al (Belle) Phys Rev D79 072004 (2009) 08113665[114] B Aubert et al (BABAR) Phys Rev D80 112001 (2009) 09053615
16
Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Overview of the CKM Matrix
[24] JS Nico J Phys G36 104001 (2009)[25] S Paul NuclInstrumMeth A611 157 (2009) 09020169[26] M Antonelli et al EurPhysJ C69 399 (2010) 10052323[27] V Cirigliano G Ecker H Neufeld A Pich and J Portoles (2011) 11076001[28] M Veltri (2011) 11015031[29] PA Boyle et al EurPhysJ C69 159 (2010) 10040886[30] V Cirigliano and H Neufeld PhysLett B700 7 (2011) 11020563[31] M Davier A Hocker and Z Zhang RevModPhys 78 1043 (2006) hep-ph0507078[32] A Pich NuclPhysProcSuppl 218 89 (2011) 11012107[33] B Aubert et al (BABAR) Phys Rev Lett 100 011801 (2008) 07072981[34] MJ Lee et al (Belle) Phys Rev D81 113007 (2010) 10010083[35] D Besson et al (CLEO) PhysRev D80 032005 (2009) 09062983[36] H Na CTH Davies E Follana GP Lepage and J Shigemitsu PhysRev D82 114506
(2010) 10084562[37] C Aubin et al (Fermilab Lattice MILC and HPQCD Collaborations) PhysRevLett 94
011601 (2005) hep-ph0408306[38] H Na et al (2011) 11091501[39] P del Amo Sanchez et al (BABAR) PhysRev D82 091103 (2010) 10084080[40] L Widhalm et al (Belle) PhysRevLett 100 241801 (2008) 07091340[41] P Naik et al (CLEO) PhysRev D80 112004 (2009) 09103602[42] J Laiho E Lunghi and RS Van de Water PhysRev D81 034503 (2010) 09102928[43] BA Dobrescu and AS Kronfeld PhysRevLett 100 241802 (2008) 08030512[44] VG Luth Annual Review of Nuclear and Particle Science 61 1 119 (2011)[45] W Dungel et al (Belle) PhysRev D82 112007 (2010) 10105620[46] JA Bailey et al (Fermilab Lattice and MILC Collaborations) PoS LATTICE2010 311
(2010) 10112166[47] BABAR collaboration (2011) Preliminary results presented at EPS2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=30ampsessionId=2ampmaterialId=slidesampconfId=5116
[48] B Aubert et al (BABAR) PhysRevLett 100 021801 (2008) 07091698[49] B Aubert et al (BABAR) PhysRev D79 092002 (2009) 09022660[50] A Matyja et al (Belle) PhysRevLett 99 191807 (2007) 07064429[51] A Bozek et al (Belle) PhysRev D82 072005 (2010) 10052302[52] YJ Kwon (2011) these proceeedings[53] P del Amo Sanchez et al (BABAR) PhysRev D83 052011 (2011) 10100987[54] P del Amo Sanchez et al (BABAR) PhysRev D83 032007 (2011) 10053288[55] H Ha et al (Belle) PhysRev D83 071101 (2011) 10120090[56] P Urquijo (2011) Preliminary results presented at EPS2011 URL http
indicoin2p3frmaterialDisplaypycontribId=1016ampsessionId=2ampmaterialId=slidesampconfId=5116
[57] C Bernard et al PhysRev D80 034026 (2009) 09062498[58] G Altarelli (2011) 11083514[59] FU Bernlochner et al (2011) 11013310[60] AD Sakharov Pisma ZhEkspTeorFiz 5 32 (1967)[61] G Raven (2011) these proceeedings[62] R van Kooten (2011) these proceeedings[63] B Aubert et al (BABAR) PhysRev D79 072009 (2009) 09021708[64] A Poluektov (Belle) (2011) Preliminary results presented at Moriond EW 2011 URL
httpindicoin2p3frgetFilepyaccesscontribId=114ampsessionId=7ampresId=0ampmaterialId=slidesampconfId=4403
[65] B Aubert et al (BABAR) Phys Rev D79 052003 (2009) 08091174[66] K-F Chen et al (Belle) Phys Rev Lett 98 031802 (2007) hep-ex0608039[67] B Aubert et al (BABAR) PhysRevLett 99 021603 (2007) hep-ex0703016[68] H Ishino et al (Belle) Phys Rev Lett 98 211801 (2007) hep-ex0608035
15
Tim Gershon
[69] P Chang (Belle) (2011) Preliminary results presented at EPS 2011 URLhttpindicoin2p3frmaterialDisplaypycontribId=1019ampsessionId=2ampmaterialId=slidesampconfId=5116
[70] LHCb collaboration (2011) LHCb-CONF-2011-042[71] BR Ko et al (Belle) PhysRevLett 104 181602 (2010) 10013202[72] P del Amo Sanchez et al (BABAR) PhysRev D83 071103 (2011) 10115477[73] P del Amo Sanchez et al (BABAR) PhysRev D81 111103 (2010) 10033397[74] JP Lees et al (BABAR) PhysRev D84 031103 (2011) 11054410[75] R Aaij et al (LHCb) (2011) 11103970[76] Y Grossman and Y Nir (2011) 11103790[77] R Aaij et al (LHCb) (2011) 11120938[78] T Aaltonen et al (CDF) PhysRevD (2011) 11115023[79] LHCb collaboration (2011) LHCb-CONF-2011-004[80] T Aaltonen et al (CDF) PhysRev D83 052012 (2011) 11021961[81] LHCb collaboration (2011) LHCb-CONF-2011-048[82] T Higuchi (Belle) (2011) Preliminary results presented at EPS 2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=1017ampsessionId=2ampmaterialId=slidesampconfId=5116
[83] M Gronau and D London PhysRevLett 65 3381 (1990)[84] AE Snyder and HR Quinn PhysRev D48 2139 (1993)[85] B Aubert et al (BABAR) Phys Rev Lett 102 141802 (2009) 09013522[86] M Gronau and D London PhysLett B253 483 (1991)[87] M Gronau and D Wyler PhysLett B265 172 (1991)[88] P del Amo Sanchez et al (BABAR) Phys Rev D82 072004 (2010) 10070504[89] T Aaltonen et al (CDF) Phys Rev D81 031105 (2010) 09110425[90] LHCb collaboration (2011) LHCb-CONF-2011-031[91] Belle collaboration (2011) Preliminary results presented at Lepton Photon 2011
(BELLE-CONF-1112) URL httpwwwinotifrresinMaKaCgetFilepyaccesscontribId=150ampsessionId=21ampresId=1ampmaterialId=slidesampconfId=79
[92] D Atwood I Dunietz and A Soni PhysRevLett 78 3257 (1997) hep-ph9612433[93] D Atwood I Dunietz and A Soni PhysRev D63 036005 (2001) hep-ph0008090[94] P del Amo Sanchez et al (BABAR) Phys Rev D82 072006 (2010) 10064241[95] Y Horii et al (Belle) Phys Rev Lett 106 231803 (2011) 11035951[96] T Aaltonen et al (CDF) PhysRevD (2011) 11085765[97] LHCb collaboration (2011) LHCb-CONF-2011-044[98] A Bondar and T Gershon PhysRev D70 091503 (2004) hep-ph0409281[99] I Dunietz PhysLett B270 75 (1991)
[100] M Gronau PhysLett B557 198 (2003) hep-ph0211282[101] T Gershon PhysRev D79 051301 (2009) 08102706[102] T Gershon and M Williams PhysRev D80 092002 (2009) 09091495[103] A Giri Y Grossman A Soffer and J Zupan PhysRev D68 054018 (2003) hep-ph
0303187[104] P del Amo Sanchez et al (BABAR) Phys Rev Lett 105 121801 (2010) 10051096[105] A Poluektov et al (Belle) Phys Rev D81 112002 (2010) 10033360[106] A Bondar and A Poluektov EurPhysJ C47 347 (2006) hep-ph0510246[107] A Bondar and A Poluektov EurPhysJ C55 51 (2008) 08010840[108] J Libby et al (CLEO) PhysRev D82 112006 (2010) 10102817[109] I Adachi K Adamczyk and H Aihara (Belle) (2011) 11064046[110] R Aleksan I Dunietz and B Kayser ZPhys C54 653 (1992)[111] T Aaltonen et al (CDF) PhysRevLett 103 191802 (2009) 08090080[112] LHCb collaboration (2011) LHCb-CONF-2011-057[113] J Dalseno et al (Belle) Phys Rev D79 072004 (2009) 08113665[114] B Aubert et al (BABAR) Phys Rev D80 112001 (2009) 09053615
16
Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Tim Gershon
[69] P Chang (Belle) (2011) Preliminary results presented at EPS 2011 URLhttpindicoin2p3frmaterialDisplaypycontribId=1019ampsessionId=2ampmaterialId=slidesampconfId=5116
[70] LHCb collaboration (2011) LHCb-CONF-2011-042[71] BR Ko et al (Belle) PhysRevLett 104 181602 (2010) 10013202[72] P del Amo Sanchez et al (BABAR) PhysRev D83 071103 (2011) 10115477[73] P del Amo Sanchez et al (BABAR) PhysRev D81 111103 (2010) 10033397[74] JP Lees et al (BABAR) PhysRev D84 031103 (2011) 11054410[75] R Aaij et al (LHCb) (2011) 11103970[76] Y Grossman and Y Nir (2011) 11103790[77] R Aaij et al (LHCb) (2011) 11120938[78] T Aaltonen et al (CDF) PhysRevD (2011) 11115023[79] LHCb collaboration (2011) LHCb-CONF-2011-004[80] T Aaltonen et al (CDF) PhysRev D83 052012 (2011) 11021961[81] LHCb collaboration (2011) LHCb-CONF-2011-048[82] T Higuchi (Belle) (2011) Preliminary results presented at EPS 2011 URL
httpindicoin2p3frmaterialDisplaypycontribId=1017ampsessionId=2ampmaterialId=slidesampconfId=5116
[83] M Gronau and D London PhysRevLett 65 3381 (1990)[84] AE Snyder and HR Quinn PhysRev D48 2139 (1993)[85] B Aubert et al (BABAR) Phys Rev Lett 102 141802 (2009) 09013522[86] M Gronau and D London PhysLett B253 483 (1991)[87] M Gronau and D Wyler PhysLett B265 172 (1991)[88] P del Amo Sanchez et al (BABAR) Phys Rev D82 072004 (2010) 10070504[89] T Aaltonen et al (CDF) Phys Rev D81 031105 (2010) 09110425[90] LHCb collaboration (2011) LHCb-CONF-2011-031[91] Belle collaboration (2011) Preliminary results presented at Lepton Photon 2011
(BELLE-CONF-1112) URL httpwwwinotifrresinMaKaCgetFilepyaccesscontribId=150ampsessionId=21ampresId=1ampmaterialId=slidesampconfId=79
[92] D Atwood I Dunietz and A Soni PhysRevLett 78 3257 (1997) hep-ph9612433[93] D Atwood I Dunietz and A Soni PhysRev D63 036005 (2001) hep-ph0008090[94] P del Amo Sanchez et al (BABAR) Phys Rev D82 072006 (2010) 10064241[95] Y Horii et al (Belle) Phys Rev Lett 106 231803 (2011) 11035951[96] T Aaltonen et al (CDF) PhysRevD (2011) 11085765[97] LHCb collaboration (2011) LHCb-CONF-2011-044[98] A Bondar and T Gershon PhysRev D70 091503 (2004) hep-ph0409281[99] I Dunietz PhysLett B270 75 (1991)
[100] M Gronau PhysLett B557 198 (2003) hep-ph0211282[101] T Gershon PhysRev D79 051301 (2009) 08102706[102] T Gershon and M Williams PhysRev D80 092002 (2009) 09091495[103] A Giri Y Grossman A Soffer and J Zupan PhysRev D68 054018 (2003) hep-ph
0303187[104] P del Amo Sanchez et al (BABAR) Phys Rev Lett 105 121801 (2010) 10051096[105] A Poluektov et al (Belle) Phys Rev D81 112002 (2010) 10033360[106] A Bondar and A Poluektov EurPhysJ C47 347 (2006) hep-ph0510246[107] A Bondar and A Poluektov EurPhysJ C55 51 (2008) 08010840[108] J Libby et al (CLEO) PhysRev D82 112006 (2010) 10102817[109] I Adachi K Adamczyk and H Aihara (Belle) (2011) 11064046[110] R Aleksan I Dunietz and B Kayser ZPhys C54 653 (1992)[111] T Aaltonen et al (CDF) PhysRevLett 103 191802 (2009) 08090080[112] LHCb collaboration (2011) LHCb-CONF-2011-057[113] J Dalseno et al (Belle) Phys Rev D79 072004 (2009) 08113665[114] B Aubert et al (BABAR) Phys Rev D80 112001 (2009) 09053615
16
Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
Overview of the CKM Matrix
[115] JP Lees (BABAR) PhysRev D83 112010 (2011) 11050125[116] M Ciuchini M Pierini and L Silvestrini PhysRev D74 051301 (2006) hep-ph
0601233[117] M Gronau D Pirjol A Soni and J Zupan PhysRev D77 057504 (2008) 07123751[118] E Lunghi and A Soni PhysLett B697 323 (2011) 10106069[119] P Oddone (2011) these proceeedings[120] G Amelino-Camelia et al EurPhysJ C68 619 (2010) 10033868[121] H Aihara (2011) these proceeedings[122] TE Browder T Gershon D Pirjol A Soni and J Zupan RevModPhys 81 1887 (2009)
08023201[123] LHCb collaboration Letter of Intent for the LHCb Upgrade (2011) CERN-LHCC-2011-
001 LHCC-I-018
17
- 1 Introduction
- 2 CP conserving parameters ndash magnitudes of CKM matrix elements
-
- 21 The Fermi constant
- 22 Determination of | Vud |
- 23 Determination of | Vus |
- 24 Determination of | Vcd | and | Vcs |
- 25 Determination of | Vcb | and | Vub |
-
- 3 CP violating parameters ndash angles of the Unitarity Triangle and other phases
-
- 31 Searches for CP violation in the charm sector
- 32 Measurement of sin(2)
- 33 Measurement of
- 34 Measurement of
- 35 Global CKM fits
-
- 4 Future prospects and conclusions
-
