Flavour Physics: Theoretical Status and Prospects · 2018-09-18 · SSTC (Belarus); FNRS and FWO...

Flavour Physics: Theoretical Statusand Prospects

Robert Fleischer

Nikhef & Vrije Universiteit Amsterdam

25th International Workshop on Weak Interactions and Neutrinos – WIN2015MPIK Heidelberg, Germany, 8–13 June 2015

• Setting the Stage

• Theoretical Framework

• Studies of CP Violation

• Studies of Rare Decays

• Concluding Remarks

Setting the Stage

Status @ LHC High-Energy Frontier

• Examples of New Physics searches @ ATLAS: → no signals (CMS similar)

– SUSY:

– Exotics:

... but “Higgs-like” particle @ ATLAS and CMS

• Combined ATLAS and CMS measurement of the Higgs mass:

Slightly more complex fit models are used, as describedbelow, to perform additional compatibility tests betweenthe different decay channels and between the results fromATLAS and CMS.Combining the ATLAS and CMS data for the H → γγ

and H → ZZ → 4l channels according to the aboveprocedure, the mass of the Higgs boson is determined to be

mH ¼ 125.09" 0.24 GeV

¼ 125.09" 0.21 ðstatÞ " 0.11 ðsystÞ GeV; ð3Þ

where the total uncertainty is obtained from the width ofa negative log-likelihood ratio scan with all parametersprofiled. The statistical uncertainty is determined by fixingall nuisance parameters to their best-fit values, except forthe three signal-strength scale factors and the H → γγbackground function parameters, which are profiled. Thesystematic uncertainty is determined by subtracting inquadrature the statistical uncertainty from the total uncer-tainty. Equation (3) shows that the uncertainties in the mHmeasurement are dominated by the statistical term, evenwhen the Run 1 data sets of ATLAS and CMS arecombined. Figure 1 shows the negative log-likelihood ratioscans as a function of mH, with all nuisance parametersprofiled (solid curves), and with the nuisance parametersfixed to their best-fit values (dashed curves).The signal strengths at the measured value of mH are

found to be μγγggFþttH ¼ 1.15þ0.28−0.25 , μγγVBFþVH ¼ 1.17þ0.58

−0.53 ,and μ4l ¼ 1.40þ0.30

−0.25 . The combined overall signal strength

μ (with μγγggFþttH ¼ μγγVBFþVH ¼ μ4l ≡ μ) is μ ¼ 1.24þ0.18−0.16 .

The results reported here for the signal strengths are notexpected to have the same sensitivity, nor exactly the samevalues, as those that would be extracted from a combinedanalysis optimized for the coupling measurements.The combined ATLAS and CMS results for mH in the

separate H → γγ and H → ZZ → 4l channels are

mγγH ¼ 125.07" 0.29 GeV

¼ 125.07" 0.25 ðstatÞ " 0.14 ðsystÞ GeV ð4Þ

and

m4lH ¼ 125.15" 0.40 GeV

¼ 125.15" 0.37 ðstatÞ " 0.15 ðsystÞ GeV: ð5Þ

The corresponding likelihood ratio scans are shown inFig. 1. For the H → ZZ → 4l channel, the systematicuncertainty is dominated by the absolute scale uncertaintyin the momentum measurement for the muons and in themomentum and energy measurements for the electrons.Large samples (> 107 events) of dilepton decays of theJ=ψ , ϒðnSÞ, and Z resonances are used by both experi-ments to evaluate the absolute scales and to correct forresidual misalignments in the inner tracker systems [14,16].The systematic uncertainty in the ATLAS mH result fromH → ZZ → 4l decays was conservatively set to 60 MeV inRef. [14] to account for the limited numerical precision inits estimate. A more precise procedure, resulting in areduced systematic uncertainty of 40 MeV, is used here.For CMS, conservative systematic uncertainties of 0.1% forthe H → ZZ → 4μ and 2μ2e channels, and 0.3% for theH → ZZ → 4e channel, were obtained in Ref. [16] and areused here.A summary of the results from the individual analyses

and their combination is presented in Fig. 2.The observed uncertainties in the combined measure-

ment can be compared with expectations. The latter areevaluated by generating two Asimov data sets [26], wherean Asimov data set is a representative event sample thatprovides both the median expectation for an experimentalresult and its expected statistical variation, in the asymp-totic approximation, without the need for an extensiveMC-based calculation. The first Asimov data set is a“prefit” sample, generated using mH ¼ 125.0 GeV andthe SM predictions for the couplings, with all nuisanceparameters fixed to their nominal values. The secondAsimov data set is a “postfit” sample, in which mH, thethree signal strengths μγγggFþttH, μ

γγVBFþVH, and μ4l, and all

nuisance parameters are fixed to their best-fit estimatesfrom the data. The expected uncertainties for the combinedmass are

δmHprefit ¼ "0.24 GeV

¼ "0.22 ðstatÞ " 0.10 ðsystÞ GeV ð6Þ

(GeV)Hm124 124.5 125 125.5 126

)H

m(Λ

2ln

−

0

1

2

3

4

5

6

7CMS and ATLAS

Run 1LHC

γγ→Hl4→ZZ→H

l+4γγCombinedStat only uncert.

FIG. 1 (color online). Scans of twice the negative log-likelihood ratio −2 lnΛðmHÞ as functions of the Higgs bosonmass mH for the ATLAS and CMS combination of the H → γγ(red), H → ZZ → 4l (blue), and combined (black) channels.The dashed curves show the results accounting for statisticaluncertainties only, with all nuisance parameters associated withsystematic uncertainties fixed to their best-fit values. The 1 and 2standard deviation limits are indicated by the intersections of thehorizontal lines at 1 and 4, respectively, with the log-likelihoodscan curves.

PRL 114, 191803 (2015) P HY S I CA L R EV I EW LE T T ER S week ending15 MAY 2015

191803-3

for the prefit case and

δmHpostfit ¼ "0.22 GeV

¼ "0.19 ðstatÞ " 0.10 ðsystÞ GeV ð7Þ

for the postfit case, which are both very similar to theobserved uncertainties reported in Eq. (3).Constraining all signal yields to their SM predictions

results in an mH value that is about 70 MeV larger than thenominal result with a comparable uncertainty. The increasein the central value reflects the combined effect of thehigher-than-expected H → ZZ → 4l measured signalstrength and the increase of theH → ZZ branching fractionwith mH. Thus, the fit assuming SM couplings forces themass to a higher value in order to accommodate the valueμ ¼ 1 expected in the SM.Since the discovery, both experiments have improved

their understanding of the electron, photon, and muonmeasurements [16,30–34], leading to a significant reduc-tion of the systematic uncertainties in the mass measure-ment. Nevertheless, the treatment and understanding ofsystematic uncertainties is an important aspect of theindividual measurements and their combination. The com-bined analysis incorporates approximately 300 nuisanceparameters. Among these, approximately 100 are fittedparameters describing the shapes and normalizations of thebackground models in the H → γγ channel, including anumber of discrete parameters that allow the functionalform in each of the CMS H → γγ analysis categories tobe changed [35]. Of the remaining almost 200 nuisanceparameters, most correspond to experimental or theoreticalsystematic uncertainties.Based on the results from the individual experiments, the

dominant systematic uncertainties for the combined mHresult are expected to be those associated with the energy or

momentum scale and its resolution: for the photons in theH → γγ channel and for the electrons and muons in theH → ZZ → 4l channel [14–16]. These uncertainties areassumed to be uncorrelated between the two experimentssince they are related to the specific characteristics of thedetectors as well as to the calibration procedures, whichare fully independent except for negligible effects due tothe use of the common Z boson mass [36] to specifythe absolute energy and momentum scales. Other exper-imental systematic uncertainties [14–16] are similarlyassumed to be uncorrelated between the two experiments.Uncertainties in the theoretical predictions and in themeasured integrated luminosities are treated as fully andpartially correlated, respectively.To evaluate the relative importance of the different

sources of systematic uncertainty, the nuisance parametersare grouped according to their correspondence to threebroad classes of systematic uncertainty: (1) uncertainties inthe energy or momentum scale and resolution for photons,electrons, and muons (“scale”), (2) theoretical uncertain-ties, e.g., uncertainties in the Higgs boson cross section andbranching fractions, and in the normalization of SMbackground processes (“theory”), (3) other experimentaluncertainties (“other”).First, the total uncertainty is obtained from the full profile-

likelihood scan, as explained above. Next, parametersassociated with the scale terms are fixed and a new scanis performed. Then, in addition to the scale terms, theparameters associated with the theory terms are fixed anda scan performed. Finally, in addition, the other parametersare fixed and a scan performed. Thus the fits are performediteratively, with the different classes of nuisance parameterscumulatively held fixed to their best-fit values. The uncer-tainties associated with the different classes of nuisanceparameters are defined by the difference in quadrature

(GeV)Hm123 124 125 126 127 128 129

Total Stat SystCMS and ATLAS Run 1LHC Total Syst Stat

l+4γγCMS+ATLAS 0.11) GeV± 0.21 ± 0.24 ( ±125.09

l 4CMS+ATLAS 0.15) GeV± 0.37 ± 0.40 ( ±125.15

γγCMS+ATLAS 0.14) GeV± 0.25 ± 0.29 ( ±125.07

l4→ZZ→HCMS 0.17) GeV± 0.42 ± 0.45 ( ±125.59

l4→ZZ→HATLAS 0.04) GeV± 0.52 ± 0.52 ( ±124.51

γγ→HCMS 0.15) GeV± 0.31 ± 0.34 ( ±124.70

γγ→HATLAS 0.27) GeV± 0.43 ± 0.51 ( ±126.02

FIG. 2 (color online). Summary of Higgs boson mass measurements from the individual analyses of ATLAS and CMS and from thecombined analysis presented here. The systematic (narrower, magenta-shaded bands), statistical (wider, yellow-shaded bands), and total(black error bars) uncertainties are indicated. The (red) vertical line and corresponding (gray) shaded column indicate the central valueand the total uncertainty of the combined measurement, respectively.


191803-4

predictions. Assuming that the negative log-likelihood ratio−2 lnΛðμ; mHÞ is distributed as a χ2 variable with twodegrees of freedom, the 68% confidence level (C.L.)confidence regions are shown in Fig. 4 for each individualmeasurement, as well as for the combined result.In summary, a combined measurement of the Higgs

boson mass is performed in theH→ γγ andH → ZZ → 4lchannels using the LHC Run 1 data sets of the ATLAS

and CMS experiments, with minimal reliance on theassumption that the Higgs boson behaves as predictedby the SM.The result is

mH ¼ 125.09$ 0.24 GeV

¼ 125.09$ 0.21 ðstatÞ $ 0.11 ðsystÞ GeV; ð9Þ

where the total uncertainty is dominated by the statisticalterm, with the systematic uncertainty dominated by effectsrelated to the photon, electron, and muon energy ormomentum scales and resolutions. Compatibility tests areperformed to ascertain whether the measurements areconsistent with each other, both between the different decaychannels and between the two experiments. All tests onthe combined results indicate consistency of the differentmeasurements within 1σ, while the four Higgs boson massmeasurements in the two channels of the two experimentsagree within 2σ. The combined measurement of the Higgsboson mass improves upon the results from the individualexperiments and is the most precise measurement to date ofthis fundamental parameter of the newly discovered particle.

We thank CERN for the very successful operation of theLHC, as well as the support staff from our institutionswithout whom ATLAS and CMS could not be operatedefficiently. We acknowledge the support of ANPCyT(Argentina); YerPhI (Armenia); ARC (Australia);BMWFW and FWF (Austria); ANAS (Azerbaijan);SSTC (Belarus); FNRS and FWO (Belgium); CNPq,CAPES, FAPERJ, and FAPESP (Brazil); MES

0 0.05 0.1

ATLASObservedExpected

combined resultUncertainty in ATLAS

0 0.05 0.1

(GeV)Hmδ

CMSObservedExpected

combined resultUncertainty in CMS

0 0.02 0.04 0.06

CombinedObservedExpected

combined resultUncertainty in LHC

Theory uncertainties

Additional experimentalsystematic uncertainties

Integrated luminosity

background modelingγγ→HATLAS

Muon momentum scale and resolution

CMS electron energy scale and resolution

calibration ee→Z

vertex and conversionγγ→HATLASreconstruction

Photon energy resolution

ECAL lateral shower shape

ECAL longitudinal response

Material in front of ECAL

ATLAS ECAL nonlinearity /photon nonlinearityCMS

CMS and ATLAS Run 1LHC

FIG. 3 (color online). The impacts δmH (see text) of the nuisance parameter groups in Table I on the ATLAS (left), CMS (center), andcombined (right) mass measurement uncertainty. The observed (expected) results are shown by the solid (empty) bars.

(GeV)Hm

124 124.5 125 125.5 126 126.5 127

) µS

igna

l str

engt

h (

0.5

1

1.5

2

2.5

3CMS and ATLAS

Run 1LHC

γγ→HATLASl4→ZZ→HATLAS

γγ→HCMSl4→ZZ→HCMS

All combined

Best fit68% C.L.

FIG. 4 (color online). Summary of likelihood scans in the 2Dplane of signal strength μ versus Higgs boson mass mH for theATLAS and CMS experiments. The 68% C.L. confidence regionsof the individual measurements are shown by the dashed curvesand of the overall combination by the solid curve. The markersindicate the respective best-fit values. The SM signal strength isindicated by the horizontal line at μ ¼ 1.


191803-7

mH = [(125.09± 0.21(stat)± 0.11(syst)] GeV

[ATLAS & CMS Collaborations, PRL 114 (2015) 191803]

• Key question: is the new particle really the SM Higgs particle?

Status @ LHC High-Precision Frontier

• Flavour Physics:

– Observables are globally consistent with the Standard Model.

– Some “tensions” with respect to the SM have recently emerged:

→ not (yet?) conclusive, but hot topics for this conference!

• Implications for the general structure of NP:

L = LSM + LNP(ϕNP, gNP,mNP, ...)

– Large characteristic NP scale ΛNP, i.e. not just ∼ TeV, which wouldbe bad news for the direct searches at ATLAS and CMS, or (and?) ...

– Symmetries prevent large NP effects in FCNCs and the flavour sector;most prominent example: Minimal Flavour Violation (MFV).

• Much more is yet to come: → LHC run II, Belle II, LHCb upgrade

... but prepare to deal with “smallish/challenging” NP effects!

The Quark-Flavour Code

• Quark flavour physics and CP violation in the Standard Model (SM):

flavour

eigen-

states

d′

s′

b′

=

Vud Vus VubVcd Vcs VcbVtd Vts Vtb

︸︷︷︸quark-mixing matrix, also known as the

Cabibbo–Kobayashi–Maskawa (CKM) matrix

→ unitary matrix; complex phase→ CP violation

·

dsb

mass

eigen-

states

• CKM matrix connects electroweak flavour states (d′, s′, b′)with their mass eigenstates (d, s, b):

0@ d′

s′

b′

1A =

0@ Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

1A ·

0@ d

sb

1A

LCCint = − g2√

2(uL, cL, tL) γµ VCKM

0@ dL

sL

bL

1A W †

µ + h.c.

• CKM matrix is unitary:

V †CKM · VCKM = 1 = VCKM · V †

CKM

• CP-conjugate transitions:

D DU U

VUD V ∗UD

W−

CP−→

W +

VUDCP−→ V ∗

UD

• New Physics (NP):→ typically new sources for flavour and CP violation.

⇒ encoded in weak decays of K, D and B mesons ...

→ before searching for NP, understand the SM picture ...

• The key problem:

– The theory is formulated in terms of quarks, while flavour-physicsexperiments use their QCD bound states, i.e. B, D and K mesons.

– Impact of strong interactions (QCD) → “hadronic” uncertainties

• The B-meson system is a particularly promising flavour probe:

– Simplifications through the large b-quark mass mb ∼ 5 GeV� ΛQCD.

– Offers various strategies to eliminate the hadronic uncertainties andto determine the hadronic parameters from the data.

– Tests of clean SM relations that could be spoiled by NP ...

• This feature led to the “rise of the B mesons”: → focus of this talk

... after K decays had dominated for 35 years!

→ very rich phenomenology, as complex as the Tokyo Subway Map:

⇒ have to make a selection: challenges, progress & hot topics

Theoretical Framework

... in a nutshell

Hierarchy of Scales

ΛNP ∼ 10(0...?) TeV � ΛEW ∼ 10−1 TeV︸︷︷︸(very) short distances

�� ΛQCD ∼ 10−4 TeV︸︷︷︸long distances

• Powerful theoretical concepts/techniques:

→ “Effective Field Theories”

– Heavy degrees of freedom (NP particles, top, Z, W ) are “integratedout” from appearing explicitly: → short-distance loop functions.

– Calculation of perturbative QCD corrections.

– Renormalization group allows the summation of large log(µSD/µLD).

• Applied to the SM and various NP scenarios, such as the following:

– MSSM, UED, WED, LH, LHT, Z ′ models, ...

Low-Energy Effective Hamiltonians

• Separation of short-distance from long-distance contributions (OPE):

〈f |Heff|B〉 = GF√2

∑j λ

jCKM

∑kCk(µ) 〈f |Qjk(µ)|B〉

[GF: Fermi’s constant, λjCKM: CKM factors, µ: renormalization scale]

• Short-distance physics: [Buras et al.; Martinelli et al. (’90s); ...]

→ Wilson coefficients Ck(µ) → perturbative quantities → known!

b bc c

s s

u

u

O2W

b bc c

s s

u

u

O2W

WO1,2

b bc c

s s

u

u WO1,2

b bc c

s s

u

u

• Long-distance physics:

→ matrix elements 〈f |Qjk(µ)|B〉 → non-perturbative → “unknown”!?

Theoretical Challenges ...

• Theoretical precision is generally limited by strong interactions:

→ hadronic matrix elements

– Non-perturbative methods of QCD needed: QCD rum rules, lattice ...

• Impressive recent progress in Lattice QCD:

⇒ BK parameter (kaon physics), decay constants, form factors, ...:

→ rare B0s,d → µ+µ− decays, semileptonic B decays.

– Flavour Lattice Averaging Group (FLAG):

http://itpwiki.unibe.ch/flag/

• However, still a big challenge for Lattice QCD:

→ non-leptonic B decays

Theoretical Framework for Non-Leptonic B Decays

|Aj|eiδj ∝∑k

Ck(µ)︸︷︷︸pert. QCD

× 〈f |Qjk(µ)|B〉

• QCD factorization (QCDF):

Beneke, Buchalla, Neubert & Sachrajda (99–01); Beneke & Jager (05); ... Bell & Huber (14)

• Perturbative Hard-Scattering (PQCD) Approach:

Li & Yu (’95); Cheng, Li & Yang (’99); Keum, Li & Sanda (’00); ...

• Soft Collinear Effective Theory (SCET):

Bauer, Pirjol & Stewart (2001); Bauer, Grinstein, Pirjol & Stewart (2003); ...

• QCD sum rules:

Khodjamirian (2001); Khodjamirian, Mannel & Melic (2003); ...

⇒ Lots of (technical) progress, still a theoretical challenge...

Studies of CP Violation

Circumvent 〈f |Qjk(µ)|B〉 in CP-B Studies:

• Amplitude relations allow us in fortunate cases to eliminate the hadronicmatrix elements (→ typically strategies to determine the UT angle γ):

– Exact relations: class of pure “tree” decays (e.g. B → DK).

– Approximate relations, which follow from the flavour symmetries ofstrong interactions, i.e. SU(2) isospin or SU(3)F:

B → ππ, B → πK, B(s) → KK.

• Decays of neutral Bd or Bs mesons:

Interference effects through B0q–B0

q mixing:

Two Main Strategies

• Amplitude relations allow us in several cases to eliminate thehadronic matrix elements (→ typically γ):

– Exact relations:

Class of pure “tree” decays (e.g. B → DK).

– Relations, which follow from the flavour symmetries ofstrong interactions, i.e. isospin or SU(3)F:

B → ππ, B → πK, B → KK.

• Decays of neutral Bd and Bs mesons:

Interference effects through B0q–B

0q mixing!

B0q

B0q

f

– “Mixing-induced” CP violation!

– If one CKM amplitude dominates (e.g. Bd → ψ KS):

⇒ hadronic matrix elements cancel →

– Otherwise amplitude relations ...

– Lead to “mixing-induced” CP violation S(f), in addition to “direct”CP violation C(f) (caused by interference between decay amplitudes).

– If one CKM amplitude dominates:

⇒ hadronic matrix elements cancel in S(f), while C(f) = 0.

A Brief Roadmap of Quark-Flavour Physics

• CP-B studies through various processes and strategies:

A Brief Roadmap of Quark-Flavour Physics

• CP-B studies through various processes & strategies:

γ β

α

Rb (b → u, c$ν$)Rt (B0

q–B0q mixing)

B → ππ (isospin), B → ρπ, B → ρρ

B → πK (penguins)

B±u → K±D

Bd → K∗0DB±

c → D±s D

9>=>; only trees

Bd → ψKS (Bs → ψφ : φs ≈ 0)

Bd → φKS (pure penguin)

Bd → π+π−Bs → K+K−

ff

Bd → D(∗)±π∓ : γ + 2βBs → D±

s K∓ : γ + φs

)only trees

• Moreover “rare” B- and K-meson decays:

B → K∗γ, Bd,s → µ+µ−, K → πνν, ...

– Originate from loop processes in the SM.

– Complementary to CP-B & interesting correlations.

New Physics ⇒ Discrepancies

• Moreover “rare” decays: B → Xsγ, Bd,s → µ+µ−, K → πνν, ...

– Originate from loop processes in the SM.

– Interesting correlations with CP-B studies.

New Physics (NP) ⇒ Discrepancies (!?)

Unitarity Triangle

• Status of global fits:

– CKMfitter Collaboration [http://ckmfitter.in2p3.fr/];

– UTfit Collaboration [http://www.utfit.org/UTfit/WebHome]:

⇒ continuously updated results:

a

a

_

_

dm6K¡

K¡

sm6 & dm6

ubV

`sin 2

(excl. at CL > 0.95) < 0`sol. w/ cos 2

excluded at CL > 0.95

_

`a

l-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

d

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5excluded area has CL > 0.95

Summer 14

CKMf i t t e r

ρ-1 -0.5 0 0.5 1

η

-1

-0.5

0

0.5

1γ

β

α

)γ+βsin(2

sm∆dm∆

dm∆

Kε

cbVubV

)ντ→BR(B

Summer14SM fit

⇒ γ has currently still sizeable errors ...

Prospects for Extracting γ

• Pure tree decays: B → D(∗)K(∗) and Bs → DsK

B+

K+

D0

W

b

u

c

s

u

u

∝ |Vub|eiγ W

b u

c

! ei!

D+s

s

s

B0s K−

– The corresponding determinations of γ are theoretically clean, i.e. thehadronic matrix elements cancel out (simply speaking).

– Decays are very robust with respect to New-Physics contributions:

⇒ reference for the “true” Standard Model value of γ.

– Excellent prospects for the era of Belle II and the LHCb upgrade:

⇒ uncertainty of ∆γexp ∼ 1◦ (!)

• Decays with loops, i.e. penguin contributions: B(s) → ππ, πK,KK

B0

d

b

u

d d

π−

W

s

u

K+

B0

d

W

b

d

d

u

u

u, c, t

G

π−

sK

+

∝ Aλ4Rb eiγ ∝ Aλ2

– Decay amplitude relations following from SU(3) flavour symmetry.[Hernandez, London, Gronau & Rosner (1994–...); R.F. (1995–...); R.F. and Mannel

(1997); Neubert and Rosner (1998); Buras & R.F. (1998); ... ]

– Complemented through QCD factorization/SCET/PQCD, calculationsof SU(3)-breaking corrections, etc., [Beneke and Neubert (2003); ...]

• Goal: extraction of (γ)loops and comparison with (γ)tree

⇒ will discrepancies show up?

→ particularly (most) promising method ...

The B0s → K+K−, B0

d → π+π− System

• B0s → K+K−: A(B0

s → K+K−) ∝ C′[eiγ +

(1−λ2

λ2

)d′eiθ

′]

b u

u

W

B0

s

s s

s

K+

K−

W

b

u

u

u, c, t

G

s

s

s

K+

K−

B0

s

• B0d → π+π−: A(B0

d → π+π−) ∝ C[eiγ − d eiθ

]

B0

d

b u

u

d

d d

π+

π−

W

B0

d

W

b

d

d

d

u

u

u, c, t

G

π+

π−

⇒ s↔ d

• The decays Bd → π+π− and Bs → K+K− are related to each otherthrough the interchange of all down and strange quarks:

U -spin symmetry ⇒ d′ = d, θ′ = θ

– Determination of γ and hadronic parameters d(= d′), θ and θ′.

– Internal consistency check of the U -spin symmetry: θ?= θ′.

[R.F. (1999, 2007)]

• Detailed studies show that this strategy is very promising for LHCb:

Roger Forty B Physics at Future Hadron Facilities 25

! (°)

d

! from B " h+h#

• Time-dependent CP asymmetries for B0 " $+$# and Bs " %+%#

ACP(t) = Adir cos(&mt) + Amix sin(&mt)

Adir and Amix depend on weak phases ! and 'd (or 's),

and on ratio of penguin to tree amplitudes = d ei!

• Under U-spin symmetry [Fleischer]

(interchange of d and s quarks)

d$$ = dKK and !$$ = !KK

" 4 measurements, 3 unknowns

(taking 's & 'd from other modes)

" can solve for !

• 26k B0 " $+$# events/year (LHCb)

37k Bs " %+%# " ((!) ~ 5°

• Uncertainty from U-spin assumptionSensitive to new physics in penguins

Bs " K+K#

B0" $+$#

→ experimental accuracyfor γ of a few degrees!

[LHCb Collaboration (B. Adeva et al.)

LHCb-PUB-2009-029, arXiv:0912.4179v2

]

Extraction of γ• Input data:

– Information on K ∝ BR(Bs → K+K−)/BR(Bd → π+π−);

– CP violation in B0d → π+π− and B0

d → π∓K±;

– U -spin-breaking corrections: ξ ≡ d′/d = 1±0.15, ∆θ ≡ θ′−θ = ±20◦:

0 20 40 60 80 100 120

γ [deg]

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

d

K ±∆KAmix

CP (Bd)

AdirCP(Bd)

AmixCP (Bd)

Central value39% CL68% CL

0 10 20 30 40 50 60 70 80 90 100 110 120γ [deg]

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

d

ξ = 0.85

ξ = 1.15|∆θ| = 20◦

⇒ γ = (67.7+4.5−5.0|input

+5.0−3.7|ξ+0.1

−0.2|∆θ)◦

(2-fold ambiguity can be resolved [R.F. (’07)])

• “Tree-level” results: γ = (73.2+6.3−7.0)◦ [CKMfitter], (68.3± 7.5)◦ [UTfit].

[R.F. (2007); R.F. & R. Knegjens (2010); numerics: R. Knegjens, PhD thesis (2014)]

Prospects: “Optimal” Determination of γ

• Measurement of the CP asymmetries of B0s → K+K−:

0 10 20 30 40 50 60 70 80 90 100 110 120γ [deg]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8d

(′)

KAmix

CP(Bd)

Adir

CP(Bd)

Amix

CP(Bd)

Adir

CP(Bs)

Amix

CP(Bs)

0 10 20 30 40 50 60 70 80 90 100 110 120γ [deg]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

d(′)

AdirCP(Bd), Amix

CP (Bd)

AdirCP(Bs), Amix

CP (Bs)

Green bands: current SM projection current LHCb result

• γ and the hadronic parameters d = d′ and θ, θ′ [→ U -spin test] can bedetermined through the intersection of two theoretically clean contours.

• Information on the branching ratios (form factors, etc.) is not needed,but rather provides valuable further insights into U -spin-breaking effects.

⇒ look forward to high-precision CPV measurements in B0s → K+K−

Interesting Variant of the Method

• Combines the Bs → K+K−, Bd → π+π− U -spin method (see above)with the Gronau–London isospin B → ππ analysis:

– Reduces the sensitivity to U -spin-breaking effects.– Provides a competitive determination of φs = −2βs.

[Ciuchini, Franco, Mishima & Silvestrini (2012)]

• Pioneering LHCb analysis: [κ parametrises U -spin-breaking effects]

Table 3: Ranges of flat priors used for the determination of � and �2�s from B0 ! ⇡+⇡� andB0

s ! K+K� decays using U-spin symmetry.

Quantity Prior ranged [0, 20]# [�180�, 180�]rD [0, ]#rD

[�180�, 180�]rG [0, ]#rG

[�180�, 180�]� (analysis A only) [�180�, 180�]

�2�s [rad] (analysis B only) [�⇡, ⇡]

00

204060

80100120140160

180

g

]$ [a (a)

0.2 0.4 0.6 0.8 1-1.5

-1

-0.5

0

0.5

1

s [ra

d]`

-2

(b)

0g

0.2 0.4 0.6 0.8 1

Figure 1: Dependences of the 68% (hatched areas) and 95% (filled areas) probability intervals onthe allowed amount of non-factorizable U-spin breaking, for (a) � from analysis A and (b) �2�s

from analysis B.

This fast transition is related to the non-linearity of the constraint equations. For �2�s

the dependence of the sensitivity on is mild, but for values of exceeding 0.6 a slightshift of the distribution towards more negative values is observed.

In Fig. 2 we show the PDFs for � obtained from analysis A and for �2�s obtainedfrom analysis B, corresponding to = 0.5. The numerical results from both analyses arereported in Table 4. The 68% probability interval for � is [56�, 70�], and that for �2�s is[�0.28, 0.02] rad.

8

Table 6: Ranges of flat priors used for the determination of � and �2�s from B0 ! ⇡+⇡�,B0 ! ⇡0⇡0, B+ ! ⇡+⇡0 and B0

s ! K+K� decays, using isospin and U-spin symmetries.

Quantity Prior ranged [0, 20]# [�180�, 180�]q [0, 20]#q [�180�, 180�]rD [0, ]#rD

[�180�, 180�]rG [0, ]#rG

[�180�, 180�]� (analysis C only) [�180�, 180�]

�2�s [rad] (analysis D only) [�⇡, ⇡]

00

204060

80100120140160

180

g

]$ [a

0.2 0.4 0.6 0.8 1

(a)

-1.5

-1

-0.5

0

0.5

1

s [ra

d]`

-2

0g

0.2 0.4 0.6 0.8 1

(b)

Figure 3: Dependences of the 68% (hatched areas) and 95% (filled areas) probability intervals onthe allowed amount of non-factorizable U-spin breaking, for (a) � from analysis C and (b) �2�s

from analysis D.

determined using Eqs. 29 and 30.The dependences on of the 68% and 95% probability intervals for � and �2�s are

shown in Fig. 3. Again, when the amount of U-spin breaking exceeds 60%, additionalmaxima appear in the posterior PDF for �. By contrast, for �2�s, the dependence of thesensitivity on is very weak. In Fig. 4 we show the PDFs for � obtained from analysis Cand for �2�s obtained from analysis D, corresponding to = 0.5. The numerical resultsfrom both analyses are reported in Table 7. The 68% probability interval for � is [57�, 71�],and that for �2�s is [�0.28, 0.02] rad.

It is worth emphasising that, although this study is similar to that presented in Ref. [12],there are two relevant di↵erences, in addition to the use of updated experimental inputs.

11

γ =(63.5+7.2

−6.7

)◦, φs ≡ −2βs = −

(6.9+9.2−8.0

)◦

[LHCb Collaboration, V. Vagnoni et al., arXiv:1408.4368 [hep-ex]]

Yet Another Variant ...

→ Application of the U -spin method to B → PPP decays:

• Utilises the following decays:

B0d,s → KSh

+h− (h = K,π)

• Time-dependent Dalitz plot analyses allow the measurement of thecorresponding branching ratios and CP asymmetries.

• The U -spin method – analogous to the B0s → K+K−, B0

d → π+π−

system – to extract γ can be applied to each point of the Dalitz plot.

• A potential advantage of using three-body decays is that the effects ofU-spin breaking may be reduced by averaging over the Dalitz plot.

[Bhattacharya & London, arXiv:1503.00737 [hep-ph]]

CP Violation in b → s Penguin-Dominated Modes

• Plenty of experimental data:

sin(2`eff) > sin(2qe1ff)

HFA

GM

orio

nd 2

014

HFA

GM

orio

nd 2

014

HFA

GM

orio

nd 2

014

HFA

G

Mor

iond

201

4

HFA

G

Mor

iond

201

4

HFA

G

Mor

iond

201

4H

FAG

Mor

iond

201

4

HFA

GM

orio

nd 2

014

HFA

GM

orio

nd 2

014

bAccs

q K0

dv K

0

K S K S

K S

/0 K0

l0 KS

t K

Sf 0 K

S

K+ K- K

0

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

World Average 0.68 ± 0.02BaBar 0.66 ± 0.17 ± 0.07Belle 0.90 +-0

0..01

99

Average 0.74 +-00

.

.11

13

BaBar 0.57 ± 0.08 ± 0.02Belle 0.68 ± 0.07 ± 0.03Average 0.63 ± 0.06BaBar 0.94 +-0

0..22

14 ± 0.06

Belle 0.30 ± 0.32 ± 0.08Average 0.72 ± 0.19BaBar 0.55 ± 0.20 ± 0.03Belle 0.67 ± 0.31 ± 0.08Average 0.57 ± 0.17BaBar 0.35 +-0

0..23

61 ± 0.06 ± 0.03

Belle 0.64 +-00

.

.12

95 ± 0.09 ± 0.10

Average 0.54 +-00

.

.12

81

BaBar 0.55 +-00

.

.22

69 ± 0.02

Belle 0.91 ± 0.32 ± 0.05Average 0.71 ± 0.21BaBar 0.74 +-0

0..11

25

Belle 0.63 +-00

.

.11

69

Average 0.69 +-00

.

.11

02

BaBar 0.65 ± 0.12 ± 0.03Belle 0.76 +-0

0..11

48

Average 0.68 +-00

.

.01

90

H F A GH F A GMoriond 2014PRELIMINARY

Cf = -Af

HFA

GM

orio

nd 2

014

HFA

GM

orio

nd 2

014

HFA

GM

orio

nd 2

014

HFA

GM

orio

nd 2

014

HFA

G

Mor

iond

201

4

HFA

G

Mor

iond

201

4H

FAG

Mor

iond

201

4

HFA

GM

orio

nd 2

014

q K0

dv K

0K S

K S K S

/0 K0

l0 KS

t K

S

f 0 KS

K+ K- K

0-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

BaBar 0.05 ± 0.18 ± 0.05Belle -0.04 ± 0.20 ± 0.10 ± 0.02Average 0.01 ± 0.14BaBar -0.08 ± 0.06 ± 0.02Belle -0.03 ± 0.05 ± 0.03Average -0.05 ± 0.04BaBar -0.17 ± 0.18 ± 0.04Belle -0.31 ± 0.20 ± 0.07Average -0.24 ± 0.14BaBar 0.13 ± 0.13 ± 0.03Belle -0.14 ± 0.13 ± 0.06Average 0.01 ± 0.10BaBar -0.05 ± 0.26 ± 0.10 ± 0.03Belle -0.03 +-0

0..22

43 ± 0.11 ± 0.10

Average -0.06 ± 0.20BaBar -0.52 +-0

0..22

20 ± 0.03

Belle 0.36 ± 0.19 ± 0.05Average -0.04 ± 0.14BaBar 0.15 ± 0.16Belle 0.13 ± 0.17Average 0.14 ± 0.12BaBar 0.02 ± 0.09 ± 0.03Belle 0.14 ± 0.11 ± 0.08 ± 0.03Average 0.06 ± 0.08

H F A GH F A GMoriond 2014PRELIMINARY

⇒ NP could be present, but still cannot be resolved!?

• Key problem: control hadronic uncertainties ...

Particularly Interesting Decay: B0 → π0K0

• Isospin relation between neutral B → πK amplitudes:

√2A(B0 → π0K0) +A(B0 → π−K+) = −

[(T + C)eiγ + Pew

]

︸︷︷︸(T + C)(eiγ − qeiω)

≡ 3A3/2

• Implies a correlation between the CP asymmetries:

Γ(B0(t)→ π0KS) − Γ(B0(t)→ π0KS)

Γ(B0(t)→ π0KS) + Γ(B0(t)→ π0KS)

= Aπ0KScos(∆Md t) + Sπ0KS

sin(∆Md t)

!0.4 !0.3 !0.2 !0.1 0.0 0.1 0.20.0

0.2

0.4

0.6

0.8

1.0

AKs "o

S Ks"

o

b

t

d

d

sW

Z

B0

d

K0

π0

u, d

u, d

Electroweak “penguin” contribution→ NP?

[R.F., S. Jager, D. Pirjol and J. Zupan (’08); confirmed by Gronau & Rosner (’08)]

� Hot Topic in view of B0d → K∗0µ+µ− @ LHCb:

[→ see below]

• Puts also other non-leptonic B-meson decays with sensitivity

to Electroweak Penguins (again...) into the spotlight:

B+→ π0K+, B0s → φφ, B0

s → π0φ, B0s → ρ0φ, ...

Precision Measurementsof the

B0q–B

0q Mixing Phases

Current Experimental Situation

a

a

_

_

dm6K¡

K¡

sm6 & dm6

ubV

`sin 2

(excl. at CL > 0.95) < 0`sol. w/ cos 2

excluded at CL > 0.95

_

`a

l-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

d

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5excluded area has CL > 0.95

Summer 14

CKMf i t t e r

0.4 0.2 0.0 0.2 0.4

0.06

0.08

0.10

0.12

0.14

LHCb3 fb 1

ATLAS 4.9 fb 1

CMS20 fb 1

CDF 9.6 fb 1

DØ 8 fb 1

CombinedSM

68% CL contours( )

• B0s–B0

s mixing phase: B0s B0

s

b

bs

s

W

W

u, c, t u, c, t B0s B0

s

b

bs

s

NP?

φccss ≡ φs = φSMs + φNP

s = −2λ2η + φNPs

• HFAG average of the current experimental data:

φs = −(0.86± 2.01)◦ vs. φSMs = −

(2.086+0.080

−0.069

)◦

CP Violation in B0d → J/ψKS

b

c

c

s

d

d

K0

J/ψ

B0

d W B0

d

b

c

c

s

d

d

J/ψ

K0

u, c, t

W

colour singletexchange

• SM corrections: → doubly Cabibbo-suppressed penguins

A(B0d → J/ψKS) =

(1− λ2/2

)A′[1 + εa′eiθ

′eiγ]

[ε ≡ λ2/(1− λ2) ∼ 0.05]

• Generalized expression for mixing-induced CP violation: [φd = 2β + φNPd ]

S(Bd → J/ψKS)√1− C(Bd → J/ψKS)2

= sin(φd + ∆φd)

sin ∆φd ∝ 2εa′ cos θ′ sin γ + ε2a′2 sin 2γ

cos ∆φd ∝ 1 + 2εa′ cos θ′ cos γ + ε2a′2 cos 2γ

[S. Faller, R.F., M. Jung & T. Mannel (2008)]

Towards High-Precision Analyses

• Era of Belle II and the LHCb upgrade

– Experimental precision requires the control of the penguin correctionsto reveal possible CP-violating NP contributions to B0

d–B0d mixing.

– The topic receives increasing interest in the theory community:

R.F., (99); Ciuchini, Pierini & Silvestrini (05, 11); Faller, R.F., Jung & Mannel (08);

Gronau & Rosner(08); De Bruyn, R.F. & Koppenburg; Jung (2012); De Bruyn &

R.F. (15); Frings, Nierste & Wiebusch (15); ...

• The hadronic phase shift ∆φd cannot be calculated in a reliable way:

⇒ use data for B0s → J/ψKS:

– Key feature: → “magnified” penguin parameters (no ε suppression)

A(B0s → J/ψKS) ∝

[1− aeiθeiγ

]

– U -spin flavour symmetry: aeiθ = a′eiθ′

Constraints on the Penguin Parameters: χ2 Fit

→ uses SU(3) and currently available data on B → J/ψX decays:

• Internal consistency checks look fine, i.e. not any “anomalous” feature.

• The global fit yields χ2min = 2.6 for four degrees of freedom (a, θ, φd, γ),

indicating good agreement between the different input quantities:

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50φd [deg]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7a

φeffd (Bd → J/ψK0)a = 0.19+0.15

−0.12

θ = (179.5± 4.0)◦

φd = (43.2± 1.8)◦

39 % C.L.

68 % C.L.

90 % C.L.

a = 0.19+0.15−0.12 , θ = (179.5± 4.0)

◦, φd =

(43.2+1.8

−1.7

)◦

[K. De Bruyn and R.F., JHEP 1503 (2015) 145 [arXiv:1412.6834 [hep-ph]]]

• Illustration through intersecting contours for the different observables:

90 110 130 150 170 190 210 230 250 270

θ [deg]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0a

AdirCP(Bd → J/ψπ0)

AmixCP (Bd → J/ψπ0)

H(B(u/d) → J/ψ(π/K))

AdirCP(B± → J/ψπ±)

AdirCP(Bd → J/ψK0)

AdirCP(B± → J/ψK±)

H(B(s/d) → J/ψK0S)

a = 0.19+0.15−0.12

θ = (179.5± 4.0)◦

φd = (43.2± 1.8)◦

39 % C.L.

68 % C.L.

90 % C.L.


Constraints on ∆φψK0

Sd

90 110 130 150 170 190 210 230 250 270

θ [deg]

−3.5

−3.0

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

∆φψK

0 S

d[d

eg]

a = 0.1

a = 0.2

a =0.3

a=

0.4

a=

0.5

a=

0.6

a = 0.19+0.15−0.12

θ = (179.5± 4.0)◦

∆φψK0

S

d = −(1.10+0.70−0.85)◦

39 % C.L.

68 % C.L.

90 % C.L.

∆φψK0

Sd = −

(1.10+0.70

−0.85

)◦

→ χ2 fit gives “guidance” for the importance of penguin effects.


Prospects: CP Violation in B0s → J/ψKS

b

c

c

J/!

W d

s

s

B0

s

KS

b

c

c

J/!

u, c, t

W


d

s

s

B0

s

KS

A(B0s → J/ψKS) = −λA

[1− aeiθeiγ

]

• CP asymmetries allow clean determination of a and θ.

• U -spin partner of the B0d → J/ψKS decay:

aeiθU spin

= a′eiθ′

[no further dynamical assumptions (E and PA)]

• Cleanest penguin control for determination of φd from B0d → J/ψKS.

[R.F. (1999); De Bruyn, R.F. & Koppenburg (2010); De Bruyn & R.F., (2015)]

• Confidence contours for the CP asymmetries of B0s → J/ψK0

S in the

Standard Model following from the global χ2 fit:

−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0Amix

CP (Bs→ J/ψK0S)

−0.10

−0.08

−0.06

−0.04

−0.02

0.00

0.02

0.04

0.06

0.08

0.10

Ad

irC

P(B

s→

J/ψK

0 S)

sin(φeffs (Bs → J/ψφ))

sin(φSMs )

39 % C.L.

68 % C.L.

90 % C.L.

AdirCP|SM = 0.003± 0.021Amix

CP |SM = −0.29 ± 0.20A∆Γ|SM = 0.957± 0.061

• Pioneering LHCb analysis: [LHCb, K. De Bruyn et al., arXiv:1503.07055 [hep-ex]]

→ first measurement of the CP asymmetries:

AdirCP(Bs → J/ψK0

S) = −0.28± 0.41(stat)± 0.08(syst)Amix

CP (Bs → J/ψK0S) = 0.08± 0.40(stat)± 0.08(syst)

A∆Γ(Bs → J/ψK0S) = 0.49+0.77

−0.65(stat)± 0.06(syst)

? LHCb Upgrade Era:

→ benchmark scenario for the B0d,s→ J/ψK0

S analysis:

• Assumes the following future measurements: [see also arXiv:1208.3355]

– Clean γ determination from tree decays B → D(∗)K(∗): γ = (70±1)◦

– φs measured from B0s → J/ψφ and penguin strategies (see below):

φs = − (2.1± 0.5|exp ± 0.3|theo)◦

= −(2.1± 0.6)◦ .

– CP violation in the Bs → J/ψK0S decay:1


S) = 0.00± 0.05Amix

CP (Bs → J/ψK0S) = −0.28± 0.05


1These uncertainties were extrapolated from the current LHCb measurements of the CP violation inB0s → D∓s K

± decays, corrected for the B0s → J/ψK0

S event yield (no official LHCb study).

Determination of Penguin Parameters

90 110 130 150 170 190 210 230 250 270

θ [deg]

0.0

0.1

0.2

0.3

0.4

0.5

a


S)

AmixCP (Bs → J/ψK0

S)

a = 0.19± 0.03

θ = (179.5± 9.4)◦

39 % C.L.

68 % C.L.

90 % C.L.

• Comments:

– This determination of a and θ is theoretically clean.

– Relation to a′, θ′ (enter Bd → J/ψKS) through U -spin symmetry.

... conversion into ∆φd

• U -spin relation between B0s → J/ψK0

S and B0d → J/ψK0

S:

a′ = ξa , θ′ = θ + δ

→ allow for U -spin breaking (non-fact.): ξ = 1.00± 0.20, δ = (0± 20)◦:

90 110 130 150 170 190 210 230 250 270

θ′ = θ + δ [deg]

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

∆φψK

0 S

d[d

eg]


S)

AmixCP (Bs → J/ψK0

S)

a′ = 0.19± 0.03 +0.04−0.03

θ′ = (179.5± 9.4± 20.2)◦

∆φψK0

S

d = −(1.09± 0.20 +0.20−0.24)◦

39 % C.L.

68 % C.L.

90 % C.L.

∆φψK0

Sd = −

[1.09± 0.20 (stat)+0.20

−0.24 (U spin)]◦

= − [1.09± 0.30]◦

Using Branching Ratio Information

It is important to emphasise that BRs are not required in this analysis:

• Knowing (a, θ) (→ clean!), the following quantitiy can be determined:

H =1− 2 a cos θ cos γ + a2

1 + 2εa′ cos θ′ cos γ + ε2a′2∝ B (Bs → J/ψKS)

B(Bd → J/ψKS)

⇒ H(a,θ) = 1.172± 0.037 (a, θ)± 0.0016 (ξ, δ)

• We may then extract the following amplitude ratio from the BRs:

∣∣∣∣A′A

∣∣∣∣ =

√εH(a,θ)

PhSp (Bs → J/ψK0S)

PhSp (Bd → J/ψK0S)

τBsτBd

B (Bd → J/ψK0S)theo

B (Bs → J/ψK0S)theo

• B(Bs → f) measurements @ LHCb limited by fs/fd = 0.259± 0.015:

→ assuming no improvement of fs/fd, which is conservative ⇒∣∣∣∣A′A

∣∣∣∣exp

= 1.160± 0.035 vs

∣∣∣∣A′A

∣∣∣∣LCSR

fact

= 1.16± 0.18 (!)

Control Channel for Belle II: B0d → J/ψπ0

b

c

c

J/ψ

W dB0

d

d

d

⇡0

b

c

c

J/ψ

u, c, t

W


dB0

d

d

d⇡0

? Replace s spectator of B0s → J/ψKS by d quark ⇒ B0

d → J/ψπ0

• CKM amplitude structure of B0d → J/ψπ0 is analogous to B0

s → J/ψKS:

⇒ shows also “magnified penguins”!

• Exchange and penguin annihilation amplitudes have to be neglected inB0d → J/ψπ0 as they have no counterpart in B0

d → J/ψKS:

– Expected to be tiny, but can be probed through B0s → J/ψπ0 and

B0s → J/ψρ0 [no evidence in the current LHCb data].

[R.F. (1999): B0d → J/ψρ0; Ciuchini, Pierini & Silvestrini (2005, 2011)]

Prospects for Measuring φd

35

40

45

50

55

φeff d,J/ψK

0 S[D

eg]

Current Future

BaBar

Belle

LHCb

Belle II

LHCbUpgrade

∆φd

2.6◦

2.1◦

3.4◦

0.8◦

0.4◦

0.3◦

Sources :BaBar − arXiv : 0902.1708Belle − arXiv : 1201.4643LHCb − arXiv : 1503.07089Belle II − Talk at KrakowLHCb Upgrade − arXiv : 1208.3355∆φd − arXiv : 1412.6834

[Compilation: Kristof De Bruyn]

B0s,d→ J/ψV Decays:

• B0s → J/ψφ: benchmark decay to extract φs

• B0d → J/ψρ0: penguin probe → CPV @ LHCb

• B0s → J/ψK∗0: yet another penguin probe

The B0s → J/ψφ Decay

b

c

c

s

J/ψ

WB0

s

φ

s

s

b

c

c

s

J/ψ

u, c, t

W


B0

s

s

s

φ

• Final state is mixture of CP-odd and CP-even states:

→ disentangle through J/ψ[→ µ+µ−]φ[→ K+K−] angular distribution

• Impact of SM penguin contributions: f ∈ {0, ‖,⊥}

A(B0s → (J/ψφ)f

)=

(1− λ

2

2

)A′f[1 + εa′fe

iθ′feiγ]

? CP-violating observables⇒ φeffs,(ψφ)f

= φs + ∆φ(ψφ)fs

• Smallish B0s–B0

s mixing phase φs (indicated by data ...):

⇒ ∆φfs at the 1◦ level would have a significant impact ...

[Faller, R.F. & Mannel (2008)]

News on B0s → J/ψφ

• Penguin parameters:

– (a′f , θ′f) are expected to differ for different final-state configurations f .

– Simplified arguments along the lines of factorisation:

⇒ a′f ≡ a′ψφ , θ′f ≡ θ′ψφ ∀f ∈ {0, ‖,⊥}

→ interesting to test through data! [R.F. (1999)]

• New LHCb results for Bs → J/ψφ: [LHCb, arXiv:1411.3104]

– First polarisation-dependent results for φeffs,f : → pioneering character:

φeffs,0 = −0.045± 0.053± 0.007 = −(2.58± 3.04± 0.40)◦

φeffs,‖| − φeff

s,0 = −0.018± 0.043± 0.009 = −(1.03± 2.46± 0.52)◦

φeffs,⊥ − φeff

s,0 = −0.014± 0.035± 0.006 = −(0.80± 2.01± 0.34)◦

– Assuming a universal value of φeffs :

φeffs = φs + ∆φs = −0.058± 0.049± 0.006 = −(3.32± 2.81± 0.34)◦

• Further polarisation-dependent LHCb results for B0s → J/ψφ:

|λf | ≡∣∣∣∣A(B0

s → (J/ψφ)fA(B0

s → (J/ψφ)f

∣∣∣∣ =

∣∣∣∣∣∣1 + εa′fe

iθ′fe−iγ

1 + εa′feiθ′fe+iγ

∣∣∣∣∣∣|λ0| = 1.012± 0.058± 0.013

|λ⊥/λ0| = 1.02± 0.12± 0.05|λ‖/λ0| = 0.97± 0.16± 0.01

? Assuming a universal |λf | ≡ |λψφ|: ⇒ |λψφ| = 0.964±0.019±0.007

• Constraints in the θ′ψφ–a′ψφ plane following from the “universal” LHCb

values of φeffs and |λψφ|, assuming the SM value of φs:

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360

θ′ψφ [deg]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

a′ ψφ

AdirCP(Bs → J/ψφ)

AmixCP (Bs → J/ψφ)

a′ψφ = 0.42+0.48−0.31

θ′ψφ = (239± 58)◦

39 % C.L.

68 % C.L.

90 % C.L.

? Controlling the Penguin

Effects in B0s → J/ψφ:

• Use the SU(3) flavour symmetry.

• Neglect certain E and PA topologies:

– Probed through B0d → J/ψφ and B0

s → J/ψρ0.

– No evidence for enhancement in LHCb data:

→ stronger bounds in the future ...

[R.F. (1999), Faller, R.F. & Mannel (2008), De Bruyn & R.F. (2015)]

The B0d → J/ψρ0 Decay

b

c

c

J/ψ

W d

⇢0

B0d

d

d

b

c

c

J/ψ

u, c, t

W


dB0

d

d

d⇢0

• Decay amplitude:

√2A(B0d → (J/ψρ0)f

)= −λAf

[1− afeiθfeiγ

]

• CKM structure similar to B0s → J/ψKS and B0

d → J/ψπ0:

→ “magnified penguin contributions”

– Hardonic parameters in B0s,d → J/ψK0

S and B0d → J/ψρ0 are generally

expected to differ from one another.

• CP violation: → φeffd,f ≡ 2βeff

f (in general polarisation dependent)

Extracting CKM phases from angular distributions of Bd ,s decays into admixturesof CP eigenstates

Robert FleischerTheory Division, CERN, CH-1211 Geneva 23, Switzerland

!Received 27 April 1999; published 8 September 1999"

The time-dependent angular distributions of certain Bd ,s decays into final states that are admixtures ofCP-even and CP-odd configurations provide valuable information about CKM phases and hadronic param-eters. We present the general formalism to accomplish this task, taking also into account penguin contributions,and illustrate it by considering a few specific decay modes. We give particular emphasis to the decay Bd

→J/#$0, which can be combined with Bs→J/#% to extract the Bd0-Bd

0 mixing phase and—if penguin effectsin the former mode should be sizeable—also the angle & of the unitarity triangle. As an interesting by-product,this strategy allows us to take into account also the penguin effects in the extraction of the Bs

0-Bs0 mixing phase

from Bs→J/#% . Moreover, a discrete ambiguity in the extraction of the CKM angle ' can be resolved, andvaluable insights into SU(3)-breaking effects can be obtained. Other interesting applications of the generalformalism presented in this paper, involving Bd→$$ and Bs ,d→K*K* decays, are also briefly noted.(S0556-2821!99"03619-X)

PACS number!s": 12.15.Hh, 13.25.Hw

PHYSICAL REVIEW D, VOLUME 60, 073008

• First experimental results for CP violation in the B0d → J/ψρ0 channel:

→ pioneering polarisation-dependent analysis:

φeffd,0 = +

(44.1± 10.2+3.0

−6.9

)◦

φeffd,‖ − φeff

d,0 = −(0.8± 6.5+1.9

−1.3

)◦

φeffd,⊥ − φeff

d,0 = −(3.6± 7.2+2.0

−1.4

)◦

[L. Zhang and S. Stone, arXiv:1212.6434; LHCb Collaboration, arXiv:1411.1634]

• Assuming polarisation-independent penguin parameters: ⇒

φeffd =

(41.7± 9.6+2.8

−6.3

)◦

AdirCP(Bd → J/ψρ) ≡ CJ/ψρ = −0.063± 0.056+0.019

−0.014

−AmixCP (Bd → J/ψρ) ≡ SJ/ψρ = −0.66+0.13+0.09

−0.12−0.03

• Using γ = (70.0+7.7−9.0)◦ [CKMfitter] and φd =

(43.2+1.8

−1.7

)◦determined

from our B → J/ψP analysis (see above), a χ2 fit to the data yields:

aψρ = 0.037+0.097−0.037 , θψρ = −

(67+181−141

)◦, ∆φ

J/ψρ0

d = −(1.5+12−10

)◦

• Illustration of the determination of af and θf from the χ2 fit through

intersecting contours derived from the CP observables in B0d → J/ψρ0:

−180−160−140−120−100 −80 −60 −40 −20 0 20 40 60 80 100 120 140 160 180

θψρ [deg]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

aψρ

AdirCP(Bd → J/ψρ0)

AmixCP (Bd → J/ψρ0)


aψρ = 0.04+0.10−0.04

θψρ = −(67+181−141)◦

39 % C.L.

68 % C.L.

90 % C.L.

−180−160−140−120−100 −80 −60 −40 −20 0 20 40 60 80 100 120 140 160 180

θ0 [deg]

0.0

0.1

0.2

0.3

0.4

0.5

a0

Adir,0CP (Bd → J/ψρ0)

Amix,0CP (Bd → J/ψρ0)

Adir,0CP (Bs → J/ψφ)

a0 = 0.05+0.14−0.04

θ0 = −(98+115−157)◦

39 % C.L.

68 % C.L.

90 % C.L.

−180−160−140−120−100 −80 −60 −40 −20 0 20 40 60 80 100 120 140 160 180

θ‖ [deg]

0.0

0.1

0.2

0.3

0.4

0.5

a‖

Adir,‖CP (Bd → J/ψρ0)

Amix,‖CP (Bd → J/ψρ0)

Adir,‖CP (Bs → J/ψφ)

a‖ = 0.06+0.12−0.06

θ‖ = −(89+145−102)◦

39 % C.L.

68 % C.L.

90 % C.L.

−180−160−140−120−100 −80 −60 −40 −20 0 20 40 60 80 100 120 140 160 180

θ⊥ [deg]

0.0

0.1

0.2

0.3

0.4

0.5

a⊥

Adir,⊥CP (Bd → J/ψρ0)

Amix,⊥CP (Bd → J/ψρ0)

Adir,⊥CP (Bs → J/ψφ)

a⊥ = 0.03+0.12−0.03

θ⊥ = (35+223−252)◦

39 % C.L.

68 % C.L.

90 % C.L.

[K. De Bruyn & R.F. (2015)]

? Further Implications of the B0d → J/ψρ0 Analysis:

• Conversion into the B0s → J/ψφ penguin parameters:

a′ψφ = ξaψρ θ′ψφ = θψρ + δ [ξ = 1.00± 0.20, δ = (0± 20)◦]

⇒ ∆φψφs =[0.08+0.56

−0.72 (stat)+0.15−0.13 (SU(3))

]◦(!)

... to be compared with φeffs = φs + ∆φψφs = −(3.32± 2.81± 0.34)◦.

[In agreement with LHCb Collaboration, S. Stone et al., arXiv:1411.1634]

• Extraction of hadronic amplitude ratios: [→ B0s,d → J/ψKS discussion]

∣∣∣ A′0(Bs→J/ψφ)

A0(Bd→J/ψρ0)

∣∣∣ = 1.06± 0.07 (stat)± 0.04 (a0, θ0)fact= 1.43± 0.42∣∣∣∣

A′||(Bs→J/ψφ)

A‖(Bd→J/ψρ0)

∣∣∣∣ = 1.08± 0.08 (stat)± 0.05 (a‖, θ‖)fact= 1.37± 0.20

∣∣∣ A′⊥(Bs→J/ψφ)

A⊥(Bd→J/ψρ0)

∣∣∣ = 1.24± 0.15 (stat)± 0.06 (a⊥, θ⊥)fact= 1.25± 0.15

[Naive “fact” refers to LCSR form factors [Ball & Zwicky (’05)];

recent PQCD calculation: X. Liu, W. Wang and Y. Xie (2014)]

]

A Penguin Roadmap

AdirCP(Bd → J/ψρ0)

AmixCP (Bd → J/ψρ0)


AmixCP (Bs → J/ψφ)

B(Bd → J/ψρ0) B(Bs → J/ψK∗0) AdirCP(Bs → J/ψK∗0)

QCD Calculations

af , θf

|A′f/Af | |A′

f/Af |

φs

New Link

∆φ(ψφ)fs

Minimal Fit

Test

Extended Fit

Old Input

[K. De Bruyn & R.F. (2015)]

Interplay Between the φd and φs Analyses

B0d → J/ψK0

S

B0d → J/ψρ0

B0s → J/ψφ

B0s → J/ψK0

S

∆φd φd

∆φsφs

[K. De Bruyn & R.F. (2015)]

Studies of Rare Decays

New Observables

→ LHCb Upgrade Era

General Features of B0s → µ+µ−

• Situation in the Standard Model (SM): → only loop contributions:

b

t

t

WZ

µ

µ

s

B0s

b

t

W

W

µ

µ

!µ

s

B0s

– Moreover: helicity suppression → BR ∝ m2µ

⇒ strongly suppressed decay

• Hadronic sector: → very simple, only the Bs decay constant FBs enters:

〈0|bγ5γµs|B0s(p)〉 = iFBspµ

⇒ B0s → µ+µ− belongs to the cleanest rare B decays

Highlight of LHC Run I: Observation of B0s → µ+µ−

• Combined analysis of CMS and LHCb:

In addition to the combinatorial background, specific b-hadrondecays, such as B0 R p2m1n where the neutrino cannot be detectedand the charged pion is misidentified as a muon, or B0 R p0m1m2,where the neutral pion in the decay is not reconstructed, can mimic thedimuon decay of the B0

(s) mesons. The invariant mass of the recon-structed dimuon candidate for these processes (semi-leptonic back-ground) is usually smaller than the mass of the B0

s or B0 meson becausethe neutrino or another particle is not detected. There is also a back-ground component from hadronic two-body B0

(s) decays (peakingbackground) as B0 R K1 p2, when both hadrons from the decay aremisidentified as muons. These misidentified decays can produce peaksin the dimuon invariant-mass spectrum near the expected signal,especially for the B0 R m1m2 decay. Particle identification algorithmsare used to minimize the probability that pions and kaons are mis-identified as muons, and thus suppress these background sources.Excellent mass resolution is mandatory for distinguishing betweenB0 and B0

s mesons with a mass difference of about 87 MeV/c2 andfor separating them from backgrounds. The mass resolution forB0

s?mzm{ decays in CMS ranges from 32 to 75 MeV/c2, dependingon the direction of the muons relative to the beam axis, while LHCbachieves a uniform mass resolution of about 25 MeV/c2.

The CMS and LHCb data are combined by fitting a common value foreach branching fraction to the data from both experiments. The branch-ing fractions are determined from the observed numbers, efficiency-corrected, of B0

(s) mesons that decay into two muons and the totalnumbers of B0

(s) mesons produced. Both experiments derive the latterfrom the number of observed B1 R J/y K1 decays, whose branchingfraction has been precisely measured elsewhere14. Assuming equal ratesfor B1 and B0 production, this gives the normalization for B0 R m1m2.To derive the number of B0

s mesons from this B1 decay mode, the ratioof b quarks that form (hadronize into) B1 mesons to those that form B0

smesons is also needed. Measurements of this ratio27,28, for which there isadditional discussion in Methods, and of the branching fractionB(B1 R J/y K1) are used to normalize both sets of data and are con-strained within Gaussian uncertainties in the fit. The use of these tworesults by both CMS and LHCb is the only significant source of correla-tion between their individual branching fraction measurements. Thecombined fit takes advantage of the larger data sample to increase theprecision while properly accounting for the correlation.

In the simultaneous fit to both the CMS and LHCb data, the branch-ing fractions of the two signal channels are common parameters ofinterest and are free to vary. Other parameters in the fit are consideredas nuisance parameters. Those for which additional knowledge isavailable are constrained to be near their estimated values by usingGaussian penalties with their estimated uncertainties while the othersare free to float in the fit. The ratio of the hadronization probabilityinto B1 and B0

s mesons and the branching fraction of the normaliza-tion channel B1 R J/y K1 are common, constrained parameters.Candidate decays are categorized according to whether they weredetected in CMS or LHCb and to the value of the relevant BDT dis-criminant. In the case of CMS, they are further categorized accordingto the data-taking period, and, because of the large variation in massresolution with angle, whether the muons are both produced at largeangles relative to the proton beams (central-region) or at least onemuon is emitted at small angle relative to the beams (forward-region).An unbinned extended maximum likelihood fit to the dimuon invari-ant-mass distribution, in a region of about 6500 MeV/c2 around theB0

s mass, is performed simultaneously in all categories (12 categoriesfrom CMS and eight from LHCb). Likelihood contours in the plane ofthe parameters of interest, B(B0 R m1m2) versus B(B0

s?mzm{), areobtained by constructing the test statistic 22DlnL from the differencein log-likelihood (lnL) values between fits with fixed values for theparameters of interest and the nominal fit. For each of the two branch-ing fractions, a one-dimensional profile likelihood scan is likewiseobtained by fixing only the single parameter of interest and allowingthe other to vary during the fits. Additional fits are performed wherethe parameters under consideration are the ratio of the branching

fractions relative to their SM predictions, SB0

(s)SM:B(B0

(s)?mzm{)=

B(B0(s)?mzm{)SM, or the ratioR of the two branching fractions.

The combined fit result is shown for all 20 categories in ExtendedData Fig. 1. To represent the result of the fit in a single dimuoninvariant-mass spectrum, the mass distributions of all categories,weighted according to values of S/(S 1 B), where S is the expectednumber of B0

s signals and B is the number of background events underthe B0

s peak in that category, are added together and shown in Fig. 2.The result of the simultaneous fit is overlaid. An alternative repres-entation of the fit to the dimuon invariant-mass distribution for the six

(MeV/c2)P+P–m5,000 5,200 5,400 5,600 5,800

Wei

ghte

d ca

ndid

ates

per

40

MeV

/c2

0

10

20

30

40

50

60 Data

Signal and background

P+P–→s0

P+P–→Combinatorial background

Semi-leptonic background

Peaking background

CMS and LHCb (LHC run I)

B0

B

Figure 2 | Weighted distribution of the dimuon invariant mass, mm1m2, forall categories. Superimposed on the data points in black are the combined fit(solid blue line) and its components: the B0

s (yellow shaded area) and B0 (light-blue shaded area) signal components; the combinatorial background (dash-dotted green line); the sum of the semi-leptonic backgrounds (dotted salmon

line); and the peaking backgrounds (dashed violet line). The horizontal bar oneach histogram point denotes the size of the binning, while the vertical bardenotes the 68% confidence interval. See main text for details on the weightingprocedure.

0 0 M O N T H 2 0 1 5 | V O L 0 0 0 | N A T U R E | 3

LETTER RESEARCH

G2015 Macmillan Publishers Limited. All rights reserved

B(B0s → µ+µ−) = (2.8+0.7

−0.6)× 10−9, B(B0d → µ+µ−) = (3.9+1.6

−1.4)× 10−10

[CMS and LHCb Collaborations, Nature, 13 May 2015]

• Most recent theoretical Standard Model analysis:

B(B0s → µ+µ−) = (3.66± 0.23)× 10−9,

B(B0d → µ+µ−) = (1.06± 0.09)× 10−10

[Bobeth, Gorbahn, Hermann, Misiak, Stamou & Steinhauser, Phys. Rev. Lett. 112 (14) 101801]

• Interesting situation to monitor:

categories with the highest S/(S 1 B) value for CMS and LHCb, as wellas displays of events with high probability to be genuine signal decays,are shown in Extended Data Figs 2–4.

The combined fit leads to the measurements B(B0s?mzm{)~

(2:8z0:7{0:6) |10{9 and B(B0?mzm{)~(3:9z1:6

{1:4)|10{10, where theuncertainties include both statistical and systematic sources, the lattercontributing 35% and 18% of the total uncertainty for the B0

s and B0

signals, respectively. Using Wilks’ theorem29, the statistical signifi-cance in unit of standard deviations, s, is computed to be 6.2 for theB0

s?mzm{ decay mode and 3.2 for the B0 R m1m2 mode. For eachsignal the null hypothesis that is used to compute the significanceincludes all background components predicted by the SM as well asthe other signal, whose branching fraction is allowed to vary freely. Themedian expected significances assuming the SM branching fractionsare 7.4s and 0.8s for the B0

s and B0 modes, respectively. Likelihoodcontours forB(B0 R m1m2) versusB(B0

s?mzm{) are shown in Fig. 3.One-dimensional likelihood scans for both decay modes are displayedin the same figure. In addition to the likelihood scan, the statisticalsignificance and confidence intervals for the B0 branching fraction aredetermined using simulated experiments. This determination yields asignificance of 3.0s for a B0 signal with respect to the same null hypo-thesis described above. Following the Feldman–Cousins30 procedure,

61s and 62s confidence intervals for B(B0 R m1m2) of [2.5, 5.6] 310210 and [1.4, 7.4] 3 10210 are obtained, respectively (see ExtendedData Fig. 5).

The fit for the ratios of the branching fractions relative to their SMpredictions yieldsSB0

sSM~0:76z0:20

{0:18 andSB0

SM~3:7z1:6{1:4. Associated like-

lihood contours and one-dimensional likelihood scans are shown inExtended Data Fig. 6. The measurements are compatible with the SMbranching fractions of the B0

s?mzm{ and B0 R m1m2 decays at the1.2s and 2.2s level, respectively, when computed from the one-dimensional hypothesis tests. Finally, the fit for the ratio of branchingfractions yieldsR~0:14z0:08

{0:06, which is compatible with the SM at the2.3s level. The one-dimensional likelihood scan for this parameter isshown in Fig. 4.

The combined analysis of data from CMS and LHCb, taking advant-age of their full statistical power, establishes conclusively the existenceof the B0

s?mzm{ decay and provides an improved measurement of itsbranching fraction. This concludes a search that started more thanthree decades ago (see Extended Data Fig. 7), and initiates a phase ofprecision measurements of the properties of this decay. It also pro-duces three standard deviation evidence for the B0 R m1m2 decay. Themeasured branching fractions of both decays are compatible with SMpredictions. This is the first time that the CMS and LHCb collabora-tions have performed a combined analysis of sets of their data in orderto obtain a statistically significant observation.

Online Content Methods, along with any additional Extended Data display itemsandSourceData, are available in the online version of the paper; references uniqueto these sections appear only in the online paper.

Received 12 November 2014; accepted 31 March 2015.Published online 13 May 2015.

1. Bobeth, C. et al. Bs,d R l1l2 in the Standard Model with reduced theoreticaluncertainty. Phys. Rev. Lett. 112, 101801 (2014).

2. Evans, L. & Bryant, P. LHC machine. J. Instrum. 3, S08001 (2008).3. Planck Collaboration, Ade P. A. R. et al. Planck 2013 results. XVI. Cosmological

parameters. Astron. Astrophys. 571, A16 (2014).4. Gavela, M., Lozano, M., Orloff, J. & Pene, O. Standard model CP-violation and

baryon asymmetry (I). Zero temperature. Nucl. Phys. B 430, 345–381 (1994).5. RBC–UKQCD Collaborations, Witzel, O. B-meson decay constants with domain-

wall light quarks and nonperturbatively tuned relativistic b-quarks. Preprint athttp://arXiv.org/abs/1311.0276 (2013).

6. HPQCD Collaboration, Na, H. et al. B and Bs meson decay constants from latticeQCD. Phys. Rev. D 86, 034506 (2012).

7. Fermilab Lattice and MILC Collaborations, Bazavov A. et al. B- and D-meson decayconstants from three-flavor lattice QCD. Phys. Rev. D 85, 114506 (2012).

8. Huang, C.-S., Liao, W. & Yan, Q.-S. The promising process to distinguish super-symmetric models with large tanb from the standard model: B R Xsm

1m2. Phys.Rev. D 59, 011701 (1998).

0 0.2 0.4 0.6 0.8

–2Δl

nL

0

2

4

6

8

10SM

0 2 4 6 8

–2Δl

nL

0

10

20

30

40SM

→s(B0

0 1 2 3 4 5 6 7 8 90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

68.27%

95.45%

99.73%

1 − 6.3×10 –5

1 − 5.7×10 –71 − 2×10 –9

SM

CMS and LHCb (LHC run I)a b

c

P+P–) (10−9)

→s(B0 P+P–) (10−9)

→(B0 P+P–) (10−9)

→(B

0P+ P

– ) (1

0−9)

Figure 3 | Likelihood contours in the B(B0 R m1m2) versusB(B0

s Rm1m2) plane. The (black) cross in a marks the best-fit central value.The SM expectation and its uncertainty is shown as the (red) marker. Eachcontour encloses a region approximately corresponding to the reportedconfidence level. b, c, Variations of the test statistic 22DlnL forB(B0

s ?mzm{)

(b) andB(B0 R m1m2) (c). The dark and light (cyan) areas define the 61s and62s confidence intervals for the branching fraction, respectively. The SMprediction and its uncertainty for each branching fraction is denoted with thevertical (red) band.

0 0.1 0.2 0.3 0.4 0.5

–2Δl

nL

0

2

4

6

8

10

SM and MFV

CMS and LHCb (LHC run I)

Figure 4 | Variation of the test statistic 22DlnL as a function of the ratio ofbranching fractionsR:B(B0 Rm1m2)/B(B0

s Rm1m2). The dark and light(cyan) areas define the 61s and 62s confidence intervals forR, respectively.The value and uncertainty forR predicted in the SM, which is the same in BSMtheories with the minimal flavour violation (MFV) property, is denoted withthe vertical (red) band.

4 | N A T U R E | V O L 0 0 0 | 0 0 M O N T H 2 0 1 5

RESEARCH LETTER

G2015 Macmillan Publishers Limited. All rights reserved[CMS and LHCb Collaborations, Nature, 13 May 2015]

LHCb Upgrade Era: B0s → µ+µ−

• Branching ratio measurement requires normalization:

BR(B0s → µ+µ−) = BR(Bq → X)

εXεµµ

NµµNX

fqfs

→ ratio of fragmentations functions fs/fd is the major limiting factor...

[R.F., Nicola Serra & Niels Tuning (2010)]

• Is there an observable beyond the branching ratio?: yes ...

– Exploit the sizeable Bs decay width difference ∆Γs:

ys ≡∆Γs2 Γs

≡ Γ(s)L − Γ

(s)H

2 Γs= 0.075± 0.012

– Provides access to another observable:

Aµµ∆Γ =|P |2 cos(2ϕP − φNP

s )− |S|2 cos(2ϕS − φNPs )

|P |2 + |S|2SM−→ 1

[De Bruyn, R.F., Knegjens, Koppenburg, Merk, Pellegrino & Tuning (2012)]

Comments on Aµµ∆Γ: theoretically clean

• Aµµ∆Γ involves the following New Physics parameters:

Heff = − GF√2πV ∗tsVtbα

[C10O10+CSOS+CPOP+C ′10O

′10+C ′SO

′S+C ′PO

′P

]

P ≡ |P |eiϕP ≡ C10 − C ′10

CSM10

+M2Bs

2mµ

(mb

mb +ms

)(CP − C ′PCSM

10

)SM−→ 1

S ≡ |S|eiϕS ≡√

1− 4m2µ

M2Bs

M2Bs

2mµ

(mb

mb +ms

)(CS − C ′SCSM

10

)SM−→ 0

• Aµµ∆Γ can be extracted from a time-dependent untagged analysis:

〈Γ(Bs(t)→ µ+µ−)〉 ≡ Γ(B0s(t)→ µ+µ−) + Γ(B0

s(t)→ µ+µ−)

∝ e−t/τBs[cosh(yst/τBs) +Aµµ∆Γ sinh(yst/τBs)

]

– Currently only time-integrated analyses → BR measurement.

– Need to correct for ∆Γs when comparing with theory BR calculation.

New Degree of Freedom to Probe New Physics

• Useful to introduce the following ratio:

R ≡ B(B0s → µ+µ−)exp

B(B0s → µ+µ−)SM

=

[1 +Aµµ∆Γ ys

1− y2s

](|P |2 + |S|2)

=

[1 + ys cos(2ϕP − φNP

s )

1− y2s

]|P |2 +

[1− ys cos(2ϕS − φNP

s )

1− y2s

]|S|2

– Current situation: R = 0.82± 0.21

– R does not allow a separation of the P and S contributions:

⇒ sizeable NP could be present ...

• Further information from the measurement of Aµµ∆Γ:

|S| = |P |√

cos(2ϕP − φNPs )−Aµµ∆Γ

cos(2ϕS − φNPs ) +Aµµ∆Γ

⇒ offers a new window for NP in Bs → µ+µ−

• Current constraints in the |P |–|S| plane and illustration of those following

from a future measurement of the Bs → µ+µ− obsevable Aµµ∆Γ:

0.2 0.4 0.6 0.8 1.0 1.2 1.4

|P |0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

|S|

A ∆Γ

=−0.9

0

A ∆Γ

=−0.5

0

A∆Γ=

+0.

00

A∆Γ= +0.5

0

A∆Γ = +0.90

SM

Ratio R = 0.82± 0.21Illustration for A∆Γ (ϕP,S = 0, π)

- Assumes no NP phases for the A∆Γ curves (e.g. MFV without flavour-blind phases).

[De Bruyn, R.F., Knegjens, Koppenburg, Merk, Pellegrino & Tuning (2012)]

• Detailed analysis within specific NP scenarios:

0.5 1.0 1.5 2.0R ≡ BR(Bs→ µ+µ−)/BRSM(Bs→ µ+µ−)

−1.0

−0.5

0.0

0.5

1.0

Aµµ

∆Γ

SM

H0 (LHS)

A0 (LHS)

Z ′ (LHS)

H0 + A0 (MFV)

R = 0.79+0.20−0.20

[Buras, R.F., Girrbach & Knegjens (2013)]

• Aµµ∆Γ is encoded in the effective B0s → µ+µ− lifetime:

τµ+µ− ≡∫∞

0t 〈Γ(Bs(t)→ µ+µ−)〉 dt∫∞

0〈Γ(Bs(t)→ µ+µ−)〉 dt =

τBs1− y2

s

[1 + 2Aµµ∆Γys + y2

s

1 +Aµµ∆Γys

]

→ promising observable for the LHCb upgrade era!

New Observables in B0s → φ`+`−

• In analogy to the B0s → µ+µ−, the decay width difference ∆Γs can also

be utilized in the rare decay B0s → φ`+`−:

– Angular analysis is required.

– Much more involved than B0s → µ+µ−: form factors, resonances, etc.,

– Interesting to complement the search for NP with B0d → K∗0µ+µ−.

• Discuss also the observables of the time-dependent analysis of the angulardistribution of the B0

d → K∗0(→ π0KS) decay.

→{

interesting to fully exploit the physics potential of semileptonicrare B(s) decays in the era of Belle II and the LHCb upgrade.

[S. Descotes-Genon and J. Virto, arXiv:1502.05509 [hep-ph]]

“Puzzles” inSemileptonic

Rare B Decays

Results from LHCb: B0 → K∗0µ+µ−

• “Optimised” observables of the angular distribution: → focus on P ′5

[Descotes-Genon, Matias & Virto (’13); Buras & Girrbach (’13); Jager & Martin

Camalich (’13); Hurth & Mahmoudi (’14); Lyon & Zwicky (’14); Hiller & Zwicky

(’14); Descotes-Genon, Hofer, Matias & Virto, ...]

• Detailed recent analysis: Altmannshofer & Straub, arXiv:1503.06199

→ guideline for the following discussion + results

• Many more observables provided by b→ s semileptonic rare decays:

Decay obs. q2 bin SM pred. measurement pull

B0 ! K⇤0µ+µ� FL [2, 4.3] 0.81 ± 0.02 0.26 ± 0.19 ATLAS +2.9

B0 ! K⇤0µ+µ� FL [4, 6] 0.74 ± 0.04 0.61 ± 0.06 LHCb +1.9

B0 ! K⇤0µ+µ� S5 [4, 6] �0.33 ± 0.03 �0.15 ± 0.08 LHCb �2.2

B0 ! K⇤0µ+µ� P 05 [1.1, 6] �0.44 ± 0.08 �0.05 ± 0.11 LHCb �2.9

B0 ! K⇤0µ+µ� P 05 [4, 6] �0.77 ± 0.06 �0.30 ± 0.16 LHCb �2.8

B� ! K⇤�µ+µ� 107 dBRdq2 [4, 6] 0.54 ± 0.08 0.26 ± 0.10 LHCb +2.1

B0 ! K0µ+µ� 108 dBRdq2 [0.1, 2] 2.71 ± 0.50 1.26 ± 0.56 LHCb +1.9

B0 ! K0µ+µ� 108 dBRdq2 [16, 23] 0.93 ± 0.12 0.37 ± 0.22 CDF +2.2

Bs ! �µ+µ� 107 dBRdq2 [1, 6] 0.48 ± 0.06 0.23 ± 0.05 LHCb +3.1

Table 1: Observables where a single measurement deviates from the SM by 1.9� or more (cf. 15 for the B !K⇤µ+µ� predictions at low q2).

one can construct a �2 function which quantifies, for a given value of the Wilson coe�cients,the compatibility of the hypothesis with the experimental data. It reads

�2( ~CNP) =h~Oexp � ~Oth( ~C

NP)iT

[Cexp + Cth]�1

h~Oexp � ~Oth( ~C

NP)i. (5)

where Oexp,th and Cexp,th are the experimental and theoretical central values and covariancematrices, respectively. All dependence on NP is encoded in the NP contributions to the Wilsoncoe�cients, CNP

i = Ci � CSMi . The NP dependence of Cth is neglected, but all correlations

between theoretical uncertainties are retained. Including the theoretical error correlations andalso the experimental ones, which have been provided for the new angular analysis by the LHCbcollaboration, the fit is independent of the basis of observables chosen (e.g. P 0

i vs. Si observables).In other words, the “optimization” 18 of observables is automatically built in.

In total, the �2 used for the fit contains 88 measurements of 76 di↵erent observables by 6experiments (see the original publication4 for references). The observables include B ! K⇤µ+µ�

angular observables and branching ratios as well as branching ratios of B ! Kµ+µ�, B !Xsµ

+µ�, Bs ! �µ+µ�, B ! K⇤�, B ! Xs�, and Bs ! µ+µ�.

2.2 Compatibility of the SM with the data

Setting the Wilson coe�cients to their SM values, we find �2SM ⌘ �2(~0) = 116.9 for 88 mea-

surements, corresponding to a p value of 2.1%. Including also b ! se+e� observablesc the �2

deteriorates to 125.8 for 91 measurements, corresponding to p = 0.91%. The observables withthe biggest individual tensions are listed in table 1. It should be noted that the observablesin this table are not independent. For instance, of the set (S5, FL, P 0

5), only the first two areincluded in the fit as the last one can be expressed as a function of them18,d.

cWe have not yet included the recent measurement 19 of B ! K⇤e+e� angular observables at very low q2.Although these observables are not sensitive to the violation of LFU, being dominated by the photon pole, theycan provide important constraints on the Wilson coe�cients C

(0)7 .

dIncluding the last two instead leads to equivalent results since we include correlations as mentioned above;this has been checked explicitly.

• Complemented by yet another puzzling LHCb measurement: [→ see below]

RK ≡B(B → Kµ+µ−)[1,6]

B(B → Ke+e−)[1,6]= 0.745+0.090

−0.074 ± 0.036

⇒ indication for lepton flavour non-universality (!?)

• Global fit to the b→ sµ+µ− and b→ se+e− data:

Global Fit: Individual Wilson Coefficients

b ! sµ+µ� data + b ! se+e� data

�2SM = 125.8 for 91 measurements (p = 0.92%)

Wolfgang Altmannshofer (PI) State of NP in Rare B Decays April 9, 2015 7 / 21[W. Altmannshofer @ Portoroz 2015]

• Constraints on Wilson coefficient functions:

-3 -2 -1 0 1 2

-2

-1

0

1

2

Re(C9NP)

Re(C10NP)

-3 -2 -1 0 1 2-2

-1

0

1

2

3

Re(C9NP)

Re(C9� )

Figure 1 – Allowed regions in the Re(CNP9 )-Re(CNP

10 ) plane (left) and the Re(CNP9 )-Re(C0

9) plane (right). The bluecontours correspond to the 1 and 2� best fit regions from the global fit. The green and red contours correspondto the 1 and 2� regions if only branching ratio data or only data on B ! K⇤µ+µ� angular observables is takeninto account.

(including braching ratios and non-LHCb measurements) into sets with data below 2.3 GeV2,between 2 and 4.3 GeV2, between 4 and 6 GeV2, and above 15 GeV2 (the slight overlap of thebins, caused by changing binning conventions over time, is of no concern as correlations aretreated consistently). The resulting 1� regions are shown in fig. 2 (the fit for the region between6 and 8 GeV2 is shown for completeness as well but only as a dashed box because we assumenon-perturbative charm e↵ects to be out of control in this region and thus do not include thisdata in our global fit). We make some qualitative observations, noting that these will have tobe made more robust by a dedicated numerical analysis.

• The NP hypothesis requires a q2 independent shift in C9. At roughly 1�, this hypothesisseems to be consistent with the data.

• If the tensions with the data were due to errors in the form factor determinations, naivelyone should expect the deviations to dominate at one end of the kinematical range whereone method of form factor calculation (lattice at high q2 and LCSR at low q2) dominates.Instead, if at all, the tensions seem to be more prominent at intermediate q2 values whereboth complementary methods are near their domain of validity and in fact give consistentpredictions15.

• There does seem to be a systematic increase of the preferred range for C9 at q2 belowthe J/ resonance, increasing as this resonance is approached. Qualitatively, this is thebehaviour expected from non-factorizable charm loop contributions. However, the centralvalue of this e↵ect would have to be significantly larger than expected on the basis ofexisting estimates 20,21,22,23,24, as conjectured earlier 23.

Concerning the last point, it is important to note that a charm loop e↵ect does not have tomodify the H� and H0 helicity amplitudese in the same way (as a shift in C9 induced by NPwould). Repeating the above exercise and allowing a q2-dependent shift of C9 only in one ofthese amplitudes, one finds that the resulting corrections would have to be huge and of the samesign. It thus seems that, if the tensions are due to a charm loop e↵ect, this must contribute toboth the H� and H0 helicity amplitude with the same sign as a negative NP contribution to C9.

eThe modification of the H+ amplitude is expected to be suppressed 22,24.

→ Z ′ boson could do the job ...

[Altmannshofer & Straub, arXiv:1503.06199 [hep-ph]]

Key question: → Standard Model or New Physics?

• Sources of hadronic uncertainties:

– Power corrections ΛQCD/mb affecting form-factor relations.

– Influences of hadronic resonances ...

– Complicated hadronic setting ...

• Important to have critical analyses: → example ... [S. Jager @ Portoroz 2015]

0 2 4 6 8-1.0

-0.5

0.0

0.5

1.0

Angular observable P5’

pink: full scan over all theory errors

light blue: “68% Gaussian” theory error(a la )

LHCb 2013 (1 fb-1)

LHCb Moriond 2015 (3 fb-1)

red line: heavy-quark limit, no power corrections

Pure heavy-quark limit (!) describes data surprisingly well.

Within errors there appears to be no significant discrepancy

Cannot support LHCb claim of 2.9 sigma effect in the 4..6 GeV2 bin

Descotes-Genon, Hofer, Matias, Virto

SJ, Martin Camalich, preliminary

yellow: add theory errors in quadrature

15Wednesday, 8 April 15

• Interesting experimental probe: → q2 dependence of CNP9

0 5 10 15

-3

-2

-1

0

1

q2 [GeV2]

C9NP

Figure 2 – Purple: ranges preferred at 1� for a new physics contribution to C9 from fits to all B ! K⇤µ+µ�

observables in di↵erent bins of q2. Blue: 1� range for CNP9 from the global fit (cf. tab. 2). Green: 1� range for

CNP9 from a fit to B ! K⇤µ+µ� observables only. The vertical gray lines indicate the location of the J/ and 0

resonances, respectively.

3 Summary and Outlook

The new LHCb measurement of angular observables in B ! K⇤µ+µ� is in significant tensionwith SM expectations. An explanation in terms of new physics is consistent with the data.Models with a negative shift of C9 or with CNP

9 = �CNP10 < 0 give the best fit to the data. These

findings are in very good agreement with preliminary results from a similar analysis presentedat this conference 25.

Arguments have been given why the tension being caused by underestimated form factoruncertainties, suggested 24 as an explanation of the original B ! K⇤µ+µ� anomaly 1, doesnot seem to be supported by the data. A detailed numerical analysis of this point, with thehelp of the new LCSR result 15 (and possibly the relations in the heavy quark limit 22,26,24 as across-check) would be interesting.

An important cross-check of the NP hypothesis is the q2 dependence of the preferred shift inC9 and it has been argued that also an unexpectedly large charm-loop contribution at low q2 nearthe J/ resonance could solve, or at least reduce, the observed tensions. A possible experimentalstrategy to resolve this ambiguity could contain, among others, the following steps.

• Testing LFU in the B ! K⇤µ+µ� vs. B ! K⇤e+e� branching ratios and angular observ-ables, where spectacular deviations from the SM universality prediction would occur if theRK anomaly is due to NP 12,27,24, which can be accomodated in various NP models witha Z 0 boson 28,29,30,31,32,12,33 f or leptoquarks 8,38,29,39,40,41;

• Searching for lepton flavour violating B decays like B ! K(⇤)e±µ⌥, because in leptoquarkmodels explaining the B ! K⇤µ+µ� anomaly, either RK(⇤) deviates from one or leptonflavour is violated 29,41 and also in Z 0 models these decays could arise 30.

• Measuring the T-odd CP asymmetries42,43 A7,8,9, which could be non-zero in the presenceof new sources of CP violation.

• Measuring BR(Bs ! µ+µ�) more precisely as a clean(er) probe of C10.

The first three items are null tests of the SM and could unambiguously prove the presence ofnew physics not spoiled by hadronic uncertainties; the last one is at least much cleaner thansemi-leptonic decays.

fSome Z0 models 34,35,36,37 predict LFU to hold but could still solve the B ! K⇤µ+µ� anomaly.

– Should CNP9 be found to be q2 independent: ⇒ support for NP

– Should CNP9 show q2 dependence: ⇒ support for hadronic effects...

⇒ stay tuned ...

[Altmannshofer & Straub, arXiv:1503.06199 [hep-ph]]

Closer Look @ Testing Lepton Flavour Universality

• Observable in the current spot light:

RK ≡B(B → Kµ+µ−)[1,6]

B(B → Ke+e−)[1,6]= 0.745+0.090

−0.074 ± 0.036

[Hiller & Kruger [hep-ph/0310219]; Data: LHCb [hep-ph/0310219]]

• Standard Model prediction: RK = 1 → excellent approximation

⇒ 2.6σ deviation from LHCb (!?)

[Bobeth, Hiller and Piranishvili [arXiv:0709.4174 [hep-ph]]]

• Differences with respect to the B0 → K∗0µ+µ− observables:

– Hadronic effects cannot explain the LHCb central value...

– Is it an experimental fluctuation?

– Is it New Physics? → Various studies in the literature:

leptoquarks, Z ′ models, composite Higgs models, ...

[Hiller & Schmaltz (2014); Gripaios & Nardecchia (2014); Niehoff, Stangl & Straub

(2015); Becirevic, Fajfer & Kosnik (2015); De Medeiros Varzielas & Hiller (2015);

Crivellin (2015); Celis et al. (2015); Alonso, Grinstein & Martin Camalich (’15); ...]

Concluding Remarks

Great Opportunities for Flavour Physics

→ many more interesting topics than covered in this talk: ...

• Leptonic and semileptonic B decays with τ leptons:

⇒ intriguing data for B → τ ντ , D(∗)τ ντ : extended Higgs sector (?)

– First LHCb B → D∗τ ν result and Belle update @ FPCP 2015:

⇒ (still) inconclusive situation ...

• Charm physics: → complementay to the B-meson system:

⇒ down-type quarks in FCNC loop processes

– Pattern of tiny CP violation in the SM model.– Difference ∆ACP of CP violation in D0 → K+K− and D0 → π+π−

has received a lot of attention some time ago: looks now SM-like ...– Hadronic uncertainties are challenging, SU(3) is a useful tool...

• Search for lepton-flavour-violating processes:

B → Kµe, B → Kµτ, Bs → µe, Bs → µτ, ...

– Would be unambiguous signals of New Physics.– Links to violation of lepton flavour universality?

• Kaon physics: → focus on rare kaon decays:

K+ → π+νν and KL → π0νν

– NA62 (CERN) and KOTO (J-PARC) aim to measure the BRs.

– Theoretically very clean and interesting probes for New Physics:3 CKM inputs from tree-level observables 13

0 5 10 15 20 25 30 35

BR(K+ ! ⇡+⌫⌫) [10�11]

0

5

10

15

20

25

BR

(KL

!⇡

0⌫⌫)

[10�

11]

Gro

ssm

an-N

irbo

und

SM

MFV relation � present constraints

|Vub|incl

/|Vcb|incl

central value

|Vub|excl

/|Vcb|excl

central value

95% CL using |Vub|avg

/|Vcb|avg

95% CL using S KS

' sin 2�

68% CL K+ ! ⇡+⌫⌫ measurement

0 5 10 15 20 25 30 35

BR(K+ ! ⇡+⌫⌫) [10�11]

0

5

10

15

20

25

BR

(KL

!⇡

0⌫⌫)

[10�

11]

Gro

ssm

an-N

irbo

und

SM

MFV relation � future constraints (c. 2025)

95% CL using central |Vub|avg

/|Vcb|avg

± 1%, � ± 1�

95% CL using central � ± 0.25�

Example measurement : 10% precision relative to SM

Example measurement : non-MFV NP scenario (same precision)

Figure 4: The MFV relation between K+ ! ⇡+⌫⌫ and KL ! ⇡0⌫⌫ using S KS' sin 2�

versus using the various tree-level inputs of |Vcb/Vub| and � (see text). In the left panel weshow situation from current constraints, and in the right panel the possible situation inthe following decade, including 10% precision on the two branching ratios, for illustration.

remarkable that within the SM all these uncertainties practically cancel out in thistriple correlation [63]. Moreover, this property turns out to be true for all modelswith constrained MFV [64].

We note that the main uncertainty in (33) resides in Pc, as the uncertainty in �is very small. We stress that this relation is practically immune to any variation ofthe function X(xt) within MFV models. This means that once B(K+ ! ⇡+⌫⌫) andS KS

will be precisely measured we will know the unique value of B(KL ! ⇡0⌫⌫)within CMFV models. This relation is analogous to the one between B(Bs,d !µ+µ�) and �Ms,d [66], where the present knowledge of �Ms,d together with thefuture precise value of B(Bs ! µ+µ�) will allow us to uniquely predict the branchingratio B(Bd ! µ+µ�) in CMFV models well ahead of its precise direct measurement.

In the right panel of Figure 3 we show the correlation between K+ ! ⇡+⌫⌫ andKL ! ⇡0⌫⌫ for di↵erent fixed values of � (S KS

). The dashed regions correspondto a 68% C.L. that results from including the uncertainties on all the other inputparameters, whereas the inner filled regions are a result of only including the un-certainties of |Vcb| (we use the average in (19)), � (as given in (20)) and |Vus| in(10). We observe that in the latter case the dependence on the remaining CKMparameters, for fixed �, is indeed minimal.

It is also possible to express the ratio in (32) as

Re�t

Im�t=

⇣1 � �2

2

⌘2

sin �

"cos � �

�

1 � �2

2

!��Vcb

Vub

��

#, (35)

i.e. in terms of the tree-level CKM inputs discussed in this section, which are gen-erally assumed to be free of NP e↵ects. We note that in MFV also S KS

is nota↵ected by NP and is more accurately determined than �. On the other hand,there is a class of models – e.g. models with a U(2)3 flavour symmetry [67] – wherethe correlation with S KS

is no longer true, while (31) and the generic relation (35)still hold.

[Recent update: Buras, Buttazzo, Girrbach-Noe & Knegjens [arXiv:1503.02693]]

Towards New Frontiers in Precision Flavour Physics

• Crucial for the full exploitation of flavour physics in the next ∼ 10 years:

� (continued) strong interaction theory ↔ experiment:

– Hadronic physics: factorization, SU(3)-breaking corrections, data...

– Think further about new observables to probe the SM/NP.

– Explore correlations/patterns between processes in specific NP models.

• Exciting times for (quark) flavour physics:

(2–3)σ deviations seem to accumulate: → first footprints of NP (?):

– First signals for B0d → µ+µ− (?)

– Anomalies in B0d → K∗0µ+µ− (?)

– RK = B(B+ → K+µ+µ−)/B(B+ → K+e+e−) (?)

– Data for B → τν decays, B → D(∗)τν decays (?)

⇒ hot topics for discussions @ WIN 2015

Flavour Physics: Theoretical Status and Prospects · 2018-09-18 · SSTC (Belarus); FNRS and FWO...

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