Post on 10-Jun-2020
Beautiful Physics at LHCLarge Hadron Colliderbeauty Experiment
b s
Content:MotivationTheoretical Introduction LHCb ExperimentLHCb Measurements and expected performance
Precision measurements of loop-dominated B decays as possible probes for New Physics
Ulrich Uwer
Physikalisches Institut Heidelberg
Motivation
Precision B Meson Physics as Probe for New Physics in Loop-Processes:
WNew
PhysicsW
New Physics
Box Diagrams (Oscillation) Penguin Decays
Popular New Physics Scenarios: SUSY, Little Higgs Models Deviations from Standard Model predictions
Complementary to direct New Physics searches by ATLAS and CMS
Examples from the past
910)5.02.7()(
)( −−+
⋅±=→
→allKBR
KBRL
L µµ
ccM θθ cossin~
0Kd
−µ
+µW
W
su
cθsin
cθcos
µν
GIM Mechanism
Observed branching ratio K0→µµ
In contradiction with theoretical expectation in the 3-Quark Model
Glashow, Iliopolus, Maiani (1970):
Prediction of a 2nd up-type quark, additional Feynman graph cancels the “u box graph”.
0Kd
−µ
+µW
W
sc
ccM θθ cossin~ −
cθcos
cθsin−
µν
More Examples
ARGUS Experiment, 1987:
Observation of B0-B0 Oscillation
0B 0Bb
d
dv
bt
t
uc
uc
tdV ∗tbV
tdV∗tbV
Precision electro-weak Physics at the Z
mH< 144 GeV (95% C.L)
mt > 50 GeV
LEWWG March 2007
Pros and Cons
1. Interpretation of precision measurements (CP asymmetries, charge asymmetries, branching ratios) requires good understanding of the “old physics” (Standard Model).
2. Nobel Prizes are generally not awarded for “dubious” conclusions from precision measurements.
Go to ATLAS and CMS ? But are all questions solvable ?
3. New particles / signatures found with ATLAS and CMS must interact with existing particles: What is the flavor structure of NP ? What are the coupling of NP ?
4. Particles at ~1 TeV scale are difficult to be directly observed
Wait for new collider ? Exploit the B Physics Potential of LHC !
Theoretical Introduction
• Quark Mixing and CKM matrix
• Mixing phenomenon
• C, P and CP Violation
• CP Violation in the Standard Model
• Standard Model and Baryon Asymmetry in the Universe
• Measurement of CP Violation
• CKM Metrology
• Rare (Penguin) decays
Quark Mixing in Standard ModelStandard Model Lagrangian:Yukawa coupling between fermions and the Higgs field
Spontaneous symmetry breaking Massive fermions mf ~Yf ⋅υ / √2
For quarks: mass eigenstates different from weak eigenstates
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛∝
bsd
)-(1 )t,c,u( 5 CKMVµγγ
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛⋅
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
′′′
bsd
VVVVVVVVV
bsd
tbtstd
cbcscd
ubusud
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
′′′
∝+
bsd
)-(1 )t,c,u(J 5 µµ γγ
weak massCKM matrix W
d uudV
Charged currents:
CKM Matrix
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
bsd
VVVVVVVVV
tbtstd
cbcscd
ubusud
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
'''
bsd
d s b
u
C
t
4 real Parameter = 3 Euler-angles und 1 Phase
complex, unitary 3x3 matrix:
( )4
23
22
32
1)1(2
1
)(2
1
λ
ληρλ
λλλ
ηρλλλ
O
AiA
A
iA
+
⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
−−−
−−
−−
=CKMV
WolfensteinParametrization
λ, A, ρ, η
λ = sinθc≈ 0.22
Quark Mixing and Flavor Oscillation
0B 0Bb
d
dv
bt
t
uc
uc
tdV ∗tbV
tdV∗tbV
⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
Γ−Γ−
Γ−Γ−=⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −=⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛0
0
22221212
*12
*121111
0
0
0
0
2212
21110
0
0
0
22
222 B
Bimim
imim
BBi
BB
HHHH
BB
BB
dtdi ΓMH
Diagonal elements:timt eet
Γ−− ⋅⋅= 21
0)( ψψ
Γ=Γ=Γ
==
==
2211
2211
2211
CPT mmmHHH
⇒M and Γ hermitian:
*1221
*1221
Γ=Γ
= mm
Off-diag elements: mixing
Mixing phase φ= arg(m12)
LH
00
B and B seigenstate Mass
B and B states Flavor≠
Mixing phenomenology decribed by
Flavor and Mass Eigenstates
HHH
LLL
mBqBpB
mBqBpB
Γ−=
Γ+=
,00
,00
with
with
122 =+ qp
2112
2112
2112,
2112,
Im4
Re2
Im2
Re
HH
HHmmm
HH
HHmm
LH
LH
LH
LH
−=Γ−Γ=∆Γ
=−=∆
Γ=Γ
±=
m
Γ∆Γ
≡Γ
∆≡
2und ymx
Mass eigenstates
complex coefficients
Parameters of the mass states
)(Moriond07 64.009.0/)%90(07.0/
(CDF) ps12.078.17
(PDG) ps007.0502.01
1
±=Γ∆Γ<Γ∆Γ
±=∆
±=∆−
−
ss
s
d
CLm
m
Neutral B mesons
)(21
)(21
0
0
HL
HL
BBq
B
BBp
B
−=
+=
⇒ Diagonalizing Hamitonian:
Flavor states
Mixing of neutral mesons
( )[ ]mteeeBBPBBP ttt HLHL ∆++=→=→Γ+Γ−Γ−Γ− cos2
41)()( 2/0000
( )[ ]( )[ ]mteee
qpBBP
mteeepqBBP
ttt
ttt
HLHL
HLHL
∆−+=→
∆−+=→
Γ+Γ−Γ−Γ−
Γ+Γ−Γ−Γ−
cos241)(
cos241)(
2/2
00
2/2
00
CPT
CP, T- violation in mixing: 1)()( 0000 ≠⇒→≠→pqBBPBBP
LH mmm −=∆
B0-B0 Mixing
0
0,2
0,4
0,6
0,8
1
1,2
0 2 4 6 8 10
)cos1(21)( 00 mteBBP t ∆−Γ=→ Γ−
( )mteBBP t ∆+Γ=→ Γ− cos121)( 00
-1,5
-1
-0,5
0
0,5
1
1,5
0 1 2 3 4 5 6 7 8 9 10B
tτ
)()()()(
0000
0000
BBPBBPBBPBBP
→+→
→−→
Bt τ/
LH mmm −=∆
) (mit ΓΓΓ LH ≈≈
m∆πOscillation Frequency
Standard Model Prediction
0B 0Bb
d
dv
bt
t
uc
uc
tdV ∗tbV
tdV∗tbV
⎟⎟⎠
⎞⎜⎜⎝
⎛=∆ ∗
2
2222
2
2
)(6 W
tBWtbtdBBB
Fd m
mFmVVBfmGm ηπ e.w. correction
222 )1233235( MeVBf BB ±±=
NLO QCD
01.055.0 ±=Bη
from lattice QCD
0sB 0
sBb
s
s
bt
t
tsV ∗tbV
tsV∗tbV
2)(~ tbtss VVm ∗∆
00dd BB −
00ss BB −
B0 Oscillation
-1ps004.0006.0506.0 ±±=∆ dmB
0.774τ
≈
dm∆π
(BABAR mean value March 2006)
-1ps)syst.(07.0)stat.(10.077.17 ±±=∆ smB
26τ
≈
(CDF Collaboration, September 2006)
00dd BB −
00ss BB −
Discrete Symmetries
+ −Charge conjugation CParticle ⇔ Anti-particle γγ →
→ +− ee
Parity P
LL
pprr
rr
rr
rr
→
−→−→
Time inversion Ttt −→
Weak Interaction: P, C and CP Symmetry
−π−τ
Lτν
While the weak interaction violates C and P maximally, CP was thought to be a good symmetry until 1964, when CPV was observed in K decays:
−π−τ
RτνP
C
+π+τ
Lτν P+π
+τRτν
C
Small (10-3) effect !
CP Violation in B Meson DecaysSummer 2001
CP Violation in B decays:
CP Asymmetry „70 % effect“
BABAR
Ere
igni
sse
Rel
at. A
ntei
l
CP violation is observed in many B decays with loop-contributions but also in tree-dominated decays.
))(())(())(())(()( 00
00
tfBtfBtfBtfBtACP →Γ+→Γ
→Γ−→Γ=
BR ~ 4x10-4
S00 KJ/)B(B ψ→
CP Violation in the Standard Model
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
bsd
VVVVVVVVV
bsd
tbtstd
cbcscd
ubusud
'''
Quarks:
Anti-quarks:
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
=⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
bsd
VVVVVVVVV
bsd
tbtstd
cbcscd
ubusud
***
***
***
'''
W
d ttdV
CP Violation ⇔ complex matrix elements
W
∗tdVd t
CP
Unitarity Triangle
Vud
Vcd
Vtd
Vus
Vcs
Vts
Vub
Vcb
Vtb
=100
010
001
Vud
Vus
Vub
Vcd
Vcs
Vcb
Vtd
Vts
Vtb
*
*
*
*
*
*
*
*
*
⇒ Vud Vub + Vcd Vcb + Vtd Vtb = 0***
Vud
Vus
Vub
Vcd
Vcs
Vcb
Vtd
Vts
Vtb
*
*
*
*
*
*
*
*
*
Vud
Vcd
Vtd
Vus
Vcs
Vts
Vub
Vcb
Vtb
=100
010
001
Unitarity triangle „bd“
β
-i
-i
γ1 11 1 1
1 1
e
e
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
b u
t d
CKM Phases
)( 4λO+CP Violation if Triangle has finite area !
Standard Model & Baryon-Asymmetry
Sacharow Conditions:
• Baryon number violation
• C und CP violation
• Deviation from thermal equilibrium
Explains the Standard Model the Baryon-Asymmetry of the Universe ?
NoNo
• CP Violation in quark sector by faktor ~1010 too small.• For MHiggs> 114 GeV: Symmetry breaking = 2nd order phase transition
Attractive: SUSY extensions of the Standard Model
• Additional CP Violation
• extended Higgs-Sector→ strong phase transition
Alternatives: Lepto-Baryogenesis
Measurement of CP violating Phases
1AfB
δφ ii eeA CP2
fB →
)cos(2 21
22
21
2
δφ ++
+=
CPAA
AAA
CP
1AfB
δφ ii eeA CP−2
fB →
)cos(2 21
22
21
2
δφ −+
+=
CPAA
AAA
„Golden“ Decay B0→J/ψKs
sKJB ψ/0 → sKJB ψ/0 →CP
0B
b
d
c
cs
cbV
csVs
0 KK →
ψ/J0B
b
d
c
cs
cbV
csV
s0 KK →
ψ/J
ηCP=-1
0B 0Bb
d
dv
bt
t
uc
uc
tdV tbV
tdVtbV
Mixing Phase:
βφ 2ii ee d =
„Golden“ Decay B0→J/ψKs
sKJB ψ/0 →
)sin( β2sin))(/())(/())(/())(/()( 00
00
mttKJBtKJBtKJBtKJBtA
ss
ssCP ∆=
→Γ+→Γ→Γ−→Γ
=ψψψψ
A
Aβ2ie
sKJ ψ/0B
0B
CP
))(/( 0 tKJB sψ→Γ ))(/( 0 tKJB sψ→Γ≠
ηCP=-1
sKJB ψ/0 →
CKM Phases from CPV in B Decays
β
α
γ
00 / :CPV SKJB ψ→
ρρρπππ ,, :CPV 0 →B
KKKDB
DKDKDKB
ss
s
,
,,,:CPV0
*0)(0
→
→ ∗ ππ
0 1
Im
Very rare decays → several 109 B mesons necessary
„Golden channel“
Over-constrain the Unitarity Triangle !
CKM Metrology
oo 0.13.21 ±=β %)4(026.0674.02sin ±±=β
With BABAR/BELLE difficult:o
oo 38
2460 ±=γ
β
α
γ
World Averageoo 1093 ±=α
CKM Metrology
CKM Mechanism is primary source of CP violation in quark sector.Test of New Physics needs high precision measurements of α,β γ.
Further New Physics Searches
W
b
dd
u
u
d
gtcu ,,
B0
Pinguin-Graphen
T. Hurth
CPV in Penguin suppressed decays:
sKBB φ→)( 00
φφ→)( 00ss BB
Bs mixing diagrams (non SM phases):
φψ/)( 00 JBB ss →
Rates of rare decays:
ll)(0 ∗→ KB
µµ→0)(sB
s
ss
φ
0K
910~ −BR
610~ −BR (visible)
5103~ −×BR (visible)
B Physics at the LHC
ATLAS
B Prodcution at LHC:
pp @ 14 TeV → σbb ≈ 500 µb
40% B0/B+, 10% Bs, 10% b-baryons
but 40 MHz IA rate, σinel ≈ 80 mb
B Physics Program
B Physics Program
Dedicated B Experiment
B Production at LHC
LHC
• pp collisions at √s = 14 TeV
• Forward production of bb, correlated
• for L ~ 2 x 1032 cm-2s-1
(defocused beams at LHCb IP)
~1012 b⎯b events/yr produced
LHCb
• Single arm forward spectrometer 12 mrad < θ < 300 mrad(1.8<η<4.9)
σinel ~ 80 mbσbb ~ 500 µb
bb production:(forward!)
θb θb
p
parton 1
b
b
Boost
p
parton 2
~ 35 %
B Physics & LHC Detectors
LHCb:• designed to maximize B acceptance• Forward, single arm spectrometer, 1.9 < η < 4.9
(bb pairs correlated, mainly forward)• Excellent vertexing and particle ID (K/π separation)• “lower” pT triggers, including purely hadronic
modes, very flexible• Luminosity tuneable by adjusting beam focus:
run at L ~ 2×1032 cm–2s–1 → n≈0.5
ATLAS/CMS:• optimized for high-pT discovery physics• central detectors, |η|<2.5• B physics using high-pT muon triggers,
Purely hadronic modes triggered by “opposite” tagging muon
• aim for highest possible luminosities: expect L<2×1033 cm–2s–1 for first 3 yr → n=5(afterwards L~ 1033 cm–2s–1 → n=25) 1
10
10 2
-2 0 2 4 6
eta of B-hadron
pT
of
B-h
adro
n
ATLAS/CMS
LHCb100 µb230 µb
Pythia production cross section
1
23
4
0
Luminosity [cm−2 s−1]1031 1032 1033
0.2
0.4
0.6
0.8
1.0
Prob
abili
ty
n = # of pp interactions/crossing
LHC
b
n=0
n=1
ATL
AS
/CM
S
Typical Event
b-hadron
π+
l −
Κ−
π+
π+
π−
B0
pp interaction(primary vertex)
L
• Decay length L typical ~ 7 mm • Decay products with p ~ 1–100 GeV• Trigger on “low pt” particles (similar to backgr)
Typical Event
b-hadron
π+
l −
Κ−
π+
π+
π−
B0
pp interaction(primary vertex)
L
all 25 ns
Simulated Event
LHCb DetectorAcceptance: 15-300 mrad (bending)
15-250 mrad (non-bending)
RICH1RICH2
Calorimeters
Muon System
VELO
Magnet
Tracking stations(inner and outer)
20 m
LHCb detector
p p
~ 300 mrad
10 mrad
Forward spectrometer (running in pp collider mode)Inner acceptance 10 mrad from conical beryllium beam pipe
LHCb detector
Vertex locator around the interaction regionSilicon strip detector with ~ 30 µm impact-parameter resolution
Vertex detector
• 21 stations w/ double sided silicon sensors •micro-strip sensors with rφ geometry, • approach to 8 mm from beam (inside complex secondary vacuum system)
Beam
Vertex Reconstruction
Bs → Ds(K K π ) π
K-Ds
±
π+
K+
π±
47µm144 µm
440 µmBs0( )
mm7=L Proper time resolution
+−→ πss DB0
σ ~ 42 fstcL βγ=
Life time information is used in the trigger !
LHCb detector
Tracking system and dipole magnet to measure angles and momenta∆p/p ~ 0.4 %, mass resolution ~ 14 MeV (for Bs → DsK)
Warm Magnet, 4.2 MW, 4 Tm,
T1 T2 T3
OuterTracker
264 Module
6 m
5 m
Main Tracking Stations
Inner Tracker: Silicon sensors
Cross to optimize occupancy for OT
6.3 %side6.6 %corner5.4 %top4.3 %average
OT occupancy
1.3% area 20% tracks
Outer Tracker
pitch 5.25 mm
5mm cellsTrack
e- e
-e-
Straw tube drift chamber modules
Straw tube winding:
Lamina Dielectrics Ltd.2.5 m
Cathode
Outer Tracker
LHCb detector
Two RICH detectors for charged hadron identification
RICH = Ring Imaging CHerenkov Detector
Cherenkov Radiation
nc
>β if
Ring Imaging
)(1cos c nβθ =
Ring radius → θc → β
RICH detectors are the specialized detectors to allow charged hadron(π, K, p) identification.
Important for B physics, as there are many hadronic decay modes e.g.: Bs → Ds
- K+ → (K+ K-π-) K+
Since ~7× more π than K are produced in pp events, making the mass combinations would give rise to large combinatorial background unless K and π tracks can be separated
θ C (
mra
d)
250
200
150
100
50
01 10 100
Momentum (GeV/c)
Aerogel
C4F10 gas
CF4 gas
eµ
p
K
π
242 mrad
53 mrad
32 mrad
θC max
Kπ
3 radiators to coverfull momentum range
Particle Identification
RICH 1 RICH 2
Radiator: AerogelC4F10
Radiator: CF4
60
40
20
0
-60 -40 -20 0 20 40 60x (cm)
y (
cm)
n=1.0005 n=1.03 n=1.0014
θ C (
mra
d)
250
200
150
100
50
01 10 100
Momentum (GeV/c)
Aerogel
C4F10 gas
CF4 gas
eµ
p
K
π
242 mrad
53 mrad
32 mrad
θC max
Kπ
3 radiators to coverfull momentum range
Particle Identification
RICH 1 RICH 2
Radiator: AerogelC4F10
Radiator: CF4
ε (K K) = 88%
ε (π K) = 3%
n=1.0005 n=1.03 n=1.0014
Background suppression with PID
purity 13%
purity 7%
purity 84% efficiency 79%
purity 67% efficiency 89%
Bs→ Ds K
Bs→ K K
No RICH With RICH
LHCb detector
Calorimeter system to identify electrons, hadrons and neutralsImportant for the first level (Level 0) of the trigger.
e
h
LHCb detector
Muon system to identify muons, also used in first level (L0) of the trigger
µ
LHCb Detector
Trigger Level-0
CalorimeterMuon system
Pile-up system
LevelLevel--0 Hardware0 Hardware: (4: (4µµs)s)High High ppTT µµ, , ee, , hh, , γγ signatures signatures
1.11.1, , 2.82.8, , 3.63.6, , 2.62.6 GeVGeV40 MHz 1 MHz
PC Farm:
Higher Level Trigger (full event info)
Higher Level Trigger
B (data mining)Trigger Inclusive b (e.g. b→µ)900 HzCharm (mixing & CPV)PIDD* candidates300 Hz
J/ψ, b→J/ψX (unbiased)TrackingHigh mass di-muons600 Hz
B (core program)TaggingExclusive B candidates200 HzPhysicsCalibrationEvent typeHLT rate
Storage (event size ~ 50 kB)
L0, HLT and L0×HLT efficiency
Higher Level Trigger (Software)
Stepwise event reconstruction:• Confirmation of trigger signature
using tracking chambers• Secondary vertex reconstruction• Full event reconstruction
1 MHz
2 KHz
Necessary Tool: B Flavor Tagging
~6~4Combined B0 (decay dependent:
Combined Bs trigger + select.)
2.13318Frag. kaon (Bs)1.04024Vertex Charge2.43117Kaon0.4365Electron1.03511Muon
εeff (%)w (%)εTag (%)Tag
B0
B0 D
π+
π−
K-
b
b
s
u
s
u
Bs
Κ+
Signal B (same side tagging)
Tagging B (opposite tagging)• lepton • kaon• Vertex charge
• Fragmentation kaon near Bs
Dilution form oscillation if B0+l
Mistag rate
Dilution D=(1-2w)Effective Tagging Power
εeff=εTagD2
LHCb - Expected Physics Performance
sin(2β) - the reference measurement
Bs – mixing
∆ms with Bs0 → Dsπ
φs and ∆Γs with B0s→ J/ψφ (η)
Measurement of γ
Rare decays
• Bs0 → µ+µ-
• Exclusive b → s µ+µ-
sin(2β) in B0→J/ψKs
• sin(2β) will be measured very precisely at e+e- B factories. Expect. for 2008: σ(sin2β)~0.02
• Not a primary goal for LHCb. Measurement will serve as reference:
0 1 2 3 4 5 6 7 8 9 10-0.8
-0.6
-0.4
-0.2
0
0.2
ACP
Proper time (ps)
(background subtracted)
2 fb-1 (1 yr)
245k events
⇒ σstat(sin2β) ~ 0.02
(for 2 fb-1, 1 yr))sin( β2sin
)sin( )(sin
))(/())(/())(/())(/(
)(
KJ/d
00
00
mt
mt
tKJBNtKJBNtKJBNtKJBN
tA
ss
ss
CP
∆=
∆+=
→+→→−→
=
ψφφ
ψψψψ
sin(2β) in Penguin Decays
000 K)B(B φ→
b
dg
t
d
s
s
s0B
φ
0K
)sin( β2sin)( mttACP ∆=
g~
q~
d g
s0B
φ
0K
Standard Model SUSY contributions
)sin(β2sin)( eff mttACP ∆=
)Kβ(J/2sin sψ= ≠ effβ2sin
LHCb Measurement of Penguin Decays
LHCb:
Experimental status (2006)• sin(2β) in penguin decays always
lower than sin(2β) in B0→J/ψKs
• Statistics ? Need more data !
σstat(sin2β) =0.12…0.18 (10 fb-1, 5 yr) ~4000 evts
Similar:
04.0:)(
stat ±≈
→
σφφsCP BA
Second triangle accessible at LHCb
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
tbtstd
cbcscd
ubusud
VVVVVVVVV
V
„bd“
0)1()( 333 =−−+−+ ηρλληρλ iAAiA
0=++ ∗∗∗tbtdcbcdubud VVVVVV
„tu“
0)()1( 333 =++−−− ηρλληρλ iAAiA
0=++ ∗∗∗tbubtsustdud VVVVVV
)( 3λO
Same triangle !
Different in O(λ5)
„bd“
0)1()( 333 =−−+−+ ηρλληρλ iAAiA0=++ ∗∗∗
tbtdcbcdubud VVVVVV
)(21)(
21 55 ηρληρλ iAiA +++−
)( 7λO+
β
α
γ
*
*
cbcd
ubud
VVVV
*
*
cbcd
tbtd
VVVVη
0 1
Im
ρ Re
„tu“
0)()1( 333 =++−−− ηρλληρλ iAAiA
0=++ ∗∗∗tbubtsustdud VVVVVV
))(21())(
21( 55 ηρληρλ iAiA +−++−−
β′
α
γ′
η
0 1
Im
ρ Re
22
21 ρλλ
+−
2ηλ∆γ
02.0≈−′=′−=∆ ββγγγ 3λAVV tsus
∗
)2
1(2λρρ −⋅=)
21(
2ληη −⋅=
)( 7λO+
Very small in SM
Bs Mixing
siepq
pq φ−== or 1
LH
LH mmmΓ−Γ=∆Γ
−=∆
⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
Γ−Γ−
Γ−Γ−=⎟⎟
⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛0
0
22221212
*12
*121111
0
0
0
0
22
22s
s
s
s
s
s
BB
imim
imim
BB
BB
dtdi H
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
Γ−∆Γ−∆
−
∆Γ−∆−Γ−
=−
+
222/
22/
2imime
imeim
s
s
i
i
φ
φ
H
φs,d
O(0.1)·ΓsO(0.01)·Γd∆Γ=ΓH-ΓL
17.8 ps-10.5 ps-1∆m=mH-mL
BsBd
β2)arg( =∗tdtbVV γ∆=∗ 2)arg( tstbVV
0sB 0
sBb
s
s
bt
t
tsV ∗tbV
tsV∗tbV
(if CPV in mixing is ignored)
In SM small: 0.04
Measurement of Bs Mixing
LHCb expects 80k Bs→Dsπ events in 1 yr
5σ measurement w/ less than 1 month of good data possible !
Proper time (ps)E
vent
s
1000
800
600
400
200
0 1 2 3 4 5
Perfect reconstruction
0
Proper time (ps)E
vent
s
1000
800
600
400
200
0 1 2 3 4 5
Perfect reconstruction+ flavour tagging
0
Proper time (ps)E
vent
s
1000
800
600
400
200
0 1 2 3 4 5
Perfect reconstruction+ flavour tagging+ proper time resolution
0
Proper time (ps)
Eve
nts
1000
800
600
400
200
0 1 2 3 4 5
Perfect reconstruction+ flavour tagging+ proper time resolution+ background
0
Proper time (ps)E
vent
s
1000
800
600
400
200
0 1 2 3 4 5
Perfect reconstruction+ flavour tagging+ proper time resolution+ background+ acceptance
0
Bs→Dsπ
2 fb-1 (1 yr) of data ∆ms=20 ps-1
Bs oscillates about 26 times until it decays: need excellent proper time resolution to resolve the mixing. LHCb: 44 fs
Bs mixing has been observed at Tevatro
Observation of Bs mixing is basis for time dependent CP asymmetry measurements.
∆Γs and Bs→J/ψφ
As φs is small in the SM (0.04):
Mass eigenstates are CP eigenstates
)even CP(B)B(CP
)odd CP(B)B(CP
LL
HH
+=
−=
evenL
oddH
Γ=Γ
Γ=Γ
ψφ/)B(B ss J→
−−= 1PCJ
−−= 1PCJ
LJJ )1)((CP)/(CP)/(CP −= φψψφL=0,2 → CP even L=1 → CP odd
Final state is mixture of CP even/odd.
Interference between Mixing and Decay
sst
trtr
st
trtr
stt
trtr
ttrtr
ttrtr
tme
tme
ee
e
eJ
L
L
LH
H
L
φθφθ
θφθ
φθφθ
θφθ
θφθψφ
φ
φ
φ
φ
φ
sin)sin(),,(f
)sin(),,(f
sin)(),,(f
),,(f
),,(f)/B/B(
5
4
3
2
1ss
∆⋅⋅±
∆⋅⋅±
⋅−⋅+
⋅+
⋅=→Γ
Γ−
Γ−
Γ−Γ−
Γ−
Γ−
Simultaneous determination of ∆Γ and φs
Measurement possible as tagged and untagged analysis!
Expected Constraints for φs
Expect 130k recon. Bs→J/ψφ events/yrεtot=1.6%, B/S<0.1, σct=37 fs, εD2=5.5%
Expectation:%2)/(
06.002.0)(sin
stat
stat
=Γ∆Γ
−=
σφσ s
Constraints on new physics
W New Physics
SMssss mihm ∆+=∆ ))2exp(1( σ
sσ
Measurement of γ with B→DK decays
γiubub eVV −= ||
cbV
comf
CKM +Color suppressed
Interference ⇒ direct CPV (i.e. in decay) ⇒ γ
In lowest order, there is no loop diagram !!
Gronau and Wyler
ADS Method (Atwood,Dunietz,Soni)B±→D0K± w/ D0→[K+π-] & D0→[K-π+]
Dalitz Method (Giri,Grossman,Soffer,Zupan)B±→D0K± w/ D0→[K0
sπ+π-]
Dunietz+GW Method (Gronau,Wyler,Dunietz)B0→D0
CP K*0 w/ D0CP →K+K- σ(γ)≈8o
σ(γ)≈5o
LHCb (2fb-1)
Studies ongoing: 2007
σ(γ)≈20oσ(γ)≈8o ?
σ(γ)≈5o
Measurements of γ with Bs decays
Measure γ + φs from 4 time-dependent rates: Bs→Ds
− K+ and Bs→Ds+K−
(+ CP-conjugates) → strong phase difference δUse φs from Bs→J/ψφ
Time dependent CP asymmetries in Bs→DsK
5 yrs of data, ∆ms=20 ps-1
t [ps]
Asy
m (
Ds +
K− )
−0.5
−0.25
0
0.25
0.5
0 0.5 1 1.5 2 2.5 3 3.5 4
Bs→Ds+K−
σ(γ) ~ 13o (2fb-1 1yr)
Feynman tree diagrams
γδ−iesie φ−
γδ+ie
−+KDs
+−KDs)(0 tBs
)(0 tBs
)0(0sB
s
su
cbs
0sB
+K−sD
s
sc
ubs
0sB −K
+sD
Interference between direct decayand decay after oscillation
LHCb Measurement of CKM Angle γ
γ from B→DK at LHCb (10 fb–1)
Two possible scenarios
γloops (2006)
CKM Metrology and LHCb
%7.4/)(%17/)(
==
ηησρρσ
Summer 2006
ρ-1 -0.5 0 0.5 1
η
-1
-0.5
0
0.5
1γ
β
α
sm∆dm∆ dm∆
KεcbVubV
ρ-1 -0.5 0 0.5 1
η
-1
-0.5
0
0.5
1
%7.1/)(%5.3/)(
=ηησ=ρρσ
LHCb at L=10fb-1
Rare B Decays Bs,d→µµ
2 fb–1 ⇒ 3σ evidence of SM signal10 fb–1 ⇒ >5σ observation of SM signal
W
Wb
s µ +
tµ−
ν
SM Branching ratio: BR(Bs→µ+µ-) = (3.5 ± 0.9) ×10–9
BR(Bd→µ+µ-) = (1.0 ± 0.5) ×10–10
Large contribution from SUSY
Limits from CDF+D0: BR ~ 1×10–7 LHCb Sensitivity(signal+bkg is observed)
Integrated Luminosity (fb-1)
5σ
3σ
SM prediction
BR
(x10
–9)
1
2
3
4
5
6
7
89
10
0 1 2 3 4 5 6 7 8 9 10
LHCb Mass resolution ∆mµµ≈18 MeV
b s
d
0B 0∗KW
Z/γµ
µ
Rare B0 → K*0µ+µ− decays
s = (mµµ)2 [GeV2]
AFB(s), theory AFB(s), fast MC, 2 fb–1
s = (mµµ)2 [GeV2]
µ+
µ– Κ∗
Β0 θ
In Standard Model: Suppressed by loop decay: BR ~1.2×10–6
Forward-backward asymmetry AFB(s) In the µµ rest-frame is sensitive probe of New Physics
b s
d
0B 0∗KW
Z/γµ
µ
New Physics
LHCb - Conclusion
b s
LHCb is a dedicated experiment to exploit the enormous B production rate at LHC: excellent vertexing and PID, good tracking, flexible trigger.
Precision measurement of loop-suppressed B decays at LHC opens a window to look for New Physics.
This approach is complementary to the direct searches of New Physics at ATLAS and CMS.
Numbers