B meson key measurements at the LHC 85 LHCb Key Measurements B s - - PDF document
B meson key measurements at the LHC 85 LHCb Key Measurements B s mixing phase s b s penguins Very rare FCNC proc. + B B s s B d, s 0 0 B K A CP (B s J/ ) B d,s B d K*
1
85
Bs mixing phase φs b → s γ penguins Very rare FCNC proc.
s
s
∗
K μ μ
s d,
B
+
−
ACP (Bs → J/ψ φ) Bd → K*γ Bd,s → μμ
86 d
γ Bd → K* μμ → In addition: Measurement of the CKM angle γ in tree level decays.
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To proof the understanding of the detector a set of reference measurements is necessary:
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Bu, Bd→ J/ψ (μμ) X
To reduce backgrounds from prompt g p p J/ψ production exploit lifetime of “B” by applying impact parameter cut: B
PV SV
μ μ J/ψ
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PV = Primary Vertex SV = Secondary Vertex impact parameter
→ Lifetime dependent acceptance!
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) (t ACP =
Time dependent CP asymmetry: for 2 fb-1, 1 yr
) sin( β 2 sin ) sin( ) ( sin ) )( / ( ) )( / ( ) )( / ( ) )( / (
K J/ d
mt mt t K J B N t K J B N t K J B N t K J B N
s s s s
Δ = Δ + = → + → → − →
ψ
φ φ ψ ψ ψ ψ
e+e- B-factories:
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sin2β = 0.670 ± 0.023 (±0.020stat-only) LHCb expectation for 2 fb-1: ~ 200k events, B/S~0.6 Δ(sin2β)stat=0.20 … 0.23
Bs – mixing Bs mixing frequency (reference) Bs mixing frequency (reference) φs and ΔΓs with B0
s→ J/ψφ
Measurement of γ Radiative (penguin) decays
0 → μ+μ-
90
4
A h 2 d
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Access to the 2nd Unitarity Triangle
cb cs cd ub us ud
tb ts td
„bd“ ) 1 ( ) (
3 3 3
= − − + − + η ρ λ λ η ρ λ i A A i A
∗ ∗ ∗ tb td cb cd ub ud
3
„tu“ ) ( ) 1 (
3 3 3
= + + − − − η ρ λ λ η ρ λ i A A i A
∗ ∗ ∗ tb ub ts us td ud
Same triangle !
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„bd“ ) 1 ( ) (
3 3 3
= − − + − + η ρ λ λ η ρ λ i A A i A
= + +
∗ ∗ ∗ tb td cb cd ub ud
V V V V V V
„tu“ ) ( ) 1 (
3 3 3
= + + − − − η ρ λ λ η ρ λ i A A i A
= + +
∗ ∗ ∗ tb ub ts us td ud
V V V V V V
) ( ) ( η ρ η ρ ) ( 2 1 ) ( 2 1
5 5
η ρ λ η ρ λ i A i A + + + − ) (
7
λ O +
α
* * cb cd ub ud
V V V V
* * tb td
V V V V η
Im
) ( ) 1 ( + + η ρ λ λ η ρ λ i A A i A
)) ( 2 1 ( )) ( 2 1 (
5 5
η ρ λ η ρ λ i A i A + − + + − −
α
η
Im
2 2
2 1 ρλ λ + − ) (
7
λ O +
β α γ
cb cdV
V
1
ρ
Re
β′
α γ′
1
ρ
Re 2 ρ
2
ηλ
Δγ 02 0. ≈ − ′ = ′ − = β β γ γ βs
3
λ A V V
ts us ∗
) 2 1 (
2
λ ρ ρ − ⋅ = ) 2 1 (
2
λ η η − ⋅ = Very small in SM
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⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎟ ⎞ ⎜ ⎜ ⎜ ⎜ ⎛ Γ Γ Γ − Γ − = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛
12 12 11 11
2 2
s s s
B B i i i m i m B B B B dt d i
* *
H
s
B
s
B b s s b t t
ts
V
∗ tb
V
s
i
e p q p q
φ −
= =
1
L H L H
m m m Γ − Γ = ΔΓ − = Δ ⎠ ⎝ ⎟ ⎟ ⎠ ⎜ ⎜ ⎝ Γ − Γ − ⎠ ⎝ ⎠ ⎝
22 22 12 12
2 2
s s s
B m m B B dt ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ Γ − ΔΓ − Δ − ΔΓ − Δ − Γ − =
− +
2 2 2 / 2 2 / 2 i m i m e i m e i m
s s
i i φ φ
H b s t
ts
V
∗ tb
V Bd Bs Δm=mH-mL 0.5 ps-1 17.8 ps-1 ΔΓ=ΓH-ΓL O(0.01)·Γd O(0.1)·Γs φs,d β 2 ) arg( =
∗ td tbV
V
s ts tbV
V β 2 =
∗)
arg( (if CPV in mixing is ignored) In SM small: 0.04
94
K- K+
Signal B (flavor specific decay)
Bs → Ds
Bs → Ds
+ π-
Bs
PV
π+ Ds
B
flavor tagging B
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t m t B N t B N t B N t B N t A
s mixed unmixed mixed unmixed mix
Δ + − = sin ~ ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (
B0 B0
D π+ π−
Signal B (same side tagging) Tagging B (opposite tagging)
l t
Dilution Tag εTag (%) w (%) εeff (%)
Muon 11 35 1.0 K-
b b s s u
Bs
Κ+
form
if B0 +
Mistag rate Muon 11 35 1.0 Electron 5 36 0.4 Kaon 17 31 2.4 Vertex Charge 24 40 1.0
18 33 2.1 Combined B0 (decay dependent: Combined Bs trigger + select.) ~4 ~6
u
Dilution D=(1-2w) Effective Tagging Power εeff=εTagD2
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) )( ( ) )( ( ) )( ( ) )( ( ) ( t B N t B N t B N t B N t A + − = ω
Observed asymmetry w/ wrong tag fraction
B t B = = ) (
) )( ( ) )( ( ) )( ( ) 1 )( )( ( ) )( ( ) 1 )( )( ( ) )( ( ) 1 )( )( ( ) )( ( ) 1 )( )( ( ) )( ( ) )( ( ) )( ( ) )( ( ) ( t B N t B N t B N t B N t B N t B N t B N t B N t B N t B N t B N t B N t B N t B N t Ameas + − + + − − − − + − = ′ + ′ ′ − ′ = ω ω ω ω ω ω ω ω ω
Observed asymmetry w/ wrong tag fraction
) ( ) ( ) 2 1 ( ) )( ( ) )( ( ) )( ( ) )( ( ) 2 1 ( t A D t A t B N t B N t B N t B N = − = − − − = ω ω ) ( ), ( B N B N ′ ′ ) 2 1 ( ω − = D
Observed number of events of given flavor Tagging “dilution”: ω=50% → D=0 no measurement possible
ω ×(1-2ω)
Statistical error of asymmetry
) ( ) ( B N B N N +
T t l t b fixed
) ( ) ( ) ( ) ( B N B N B N B N A + − =
N N q pN N q N qN N
B B B
) 1 ( , = = − = =
) ( ) ( B N B N N + =
Total event number fixed Statistical error calculated according binominal distribution (A or notA):
2 / 1 2)
1 ( 1 A N A − = Δ
Tagging efficiency:
N N N ε = ′ →
2 / 1 2)
) ( 1 ( 1
meas meas
A N A − = Δ ε
q q N qN ) 1 ( ) (
2
− = σ
Tagging efficiency:
N N N ε = →
Wrong tag fraction:
A D Ameas =
We are interested in A and therefore also in the error of A
meas
A D A Δ = Δ 1 N D Astat
2
1 ~ ε Δ
= effective tagging power
1000 800 Perfect reconstruction 1000 800 Perfect reconstruction + flavour tagging 1000 800 Perfect reconstruction + flavour tagging + proper time resolution 1000 800 Perfect reconstruction + flavour tagging + proper time resolution + background 1000 800 Perfect reconstruction + flavour tagging + proper time resolution + background + acceptance
Bs→Dsπ Bs oscillates about 26 times until it decays: need excellent proper time resolution to resolve the mixing (LHCb ~40 fs) Events
600 400 200
Events
600 400 200
Events
600 400 200
Events
600 400 200
Events
800 600 400 200 + acceptance 2 fb-1 (1 yr) of data Δms=20 ps-1
Observation of Bs mixing is basis for time dependent CP asymmetry measurements. LHCb expects 80k Bs→Dsπ events in 1 yr Proper time (ps)
1 2 3 4 5
Proper time (ps)
1 2 3 4 5
Proper time (ps)
1 2 3 4 5
Proper time (ps)
1 2 3 4 5
Proper time (ps)
1 2 3 4 5
100
CDF:
ps ) syst. ( . ) stat. ( . 07 10 ± ±
As φs is small in the SM (0.04): Mass eigenstates are CP eigenstates Significant lifetime difference between mass eigenstates ) even CP ( B ) B ( CP )
CP ( B ) B ( CP
L L H H
+ = − =
even L
H
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2 π i
CP
s
2
s
i
β 2
s
) )( / ( t J B
CP s
ψφ → Γ
) )( / ( t J B
CP s
ψφ → Γ
102
[ ] [ ] [ ] [ ]
) sin( β sin ~ ) )( / ( ) )( / ( ) )( / ( ) )( / ( ) (
s
t m t J B t J B t J B t J B t A
s CP s CP s CP s CP s CP
Δ → Γ + → Γ → Γ − → Γ = 2 ψφ ψφ ψφ ψφ
ψφ / ) B ( B
s s
J → Problem: is not a pure CP state
ψφ / ) B ( B
s s
J →
− −
= 1
PC
J
L
J J ) 1 )( ( CP ) / ( CP ) / ( CP − = φ ψ ψφ L 0 2 CP +1
Problem: not a pure CP state
− −
= 1
PC
J
L=0,2 → CP = +1 L=1 → CP = -1 Final state is mixture of CP even/odd. Angular analysis of the decay
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Angular analysis of the decay products to distinguish between L=0,2 (CP=+1) and L=1 (CP=-1). Possible only in a statistical way – not for a single event. Transversity basis
ψ cos
Lifetime
background
t tr tr t tr tr
e e J
H L
θ φ θ θ φ θ ψφ
φ φ
) , , ( f ) , , ( f ) / B / B (
2 1 s s
⋅ + ⋅ = → Γ
Γ − Γ −
CP odd CP even
s s t tr tr s t tr tr s t t tr tr
t m e t m e e e
L L L H
φ θ φ θ θ φ θ φ θ φ θ
φ φ φ
sin ) sin( ) , , ( f ) sin( ) , , ( f sin ) ( ) , , ( f
5 4 3
Δ ⋅ ⋅ ± Δ ⋅ ⋅ ± ⋅ − ⋅ +
Γ − Γ − Γ − Γ −
Simultaneous determination of ΔΓ and φs Measurement possible as tagged and untagged analysis!
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EPS 2009 # Bs (CDF) ~ 3200 (2.8 fb-1)
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W
New Physics
s
B
s
B
A.Lenz, U.Nierste
) ) Im( ) Re( (
q q SM NP SM
i Δ + Δ × =
+
A A
There is room for NP in Bs mixing.
#Evts (2fb-1) B/S εtag(%) 117k 2.0 6.2
A Bi H id lb
04 . 2 − ≈ − =
s SM s
β φ
able point estimate?
2010 φs = -0.8 [CDF] Toy study with 3200 evts ~ 55 pb-1
No relia
Feldman-Cousin Contour: 40%, 68%, 95% CL
Indirect Direct
from B factories Direct measurement from B factories
from direct measurements yet
107
Precise determination of γ in tree and loop decays.
γ i ub ub
e V V
−
= | |
Tree decays: ⇒ fD ( ) ( )
B
i i B
A B D K A B D K
r e e
δ
γ
− − − −
−
→ = → ⇒ fD P i i l f th “ i t ” t
108
Principle of the “γ in trees” measurement: Cabibbo favored and suppressed decay amplitudes of the B- (B+) can interfere in case that the D0 and D0 decay into the same final state fD. Several methods are proposed and have already been explored at the B factories.
GLW (Gronau,London,Wyler) method: fD is a CP eigenstate, fD= K+K-, π+π- ADS (Atwood,Dunietz,Soni) method: Common flavour state fD= (K+ π –)
D
g
D D (
) Note: D0→K+π– doubly Cabibbo suppr. σγ = 11°… 13° (2 fb-1) σγ = 10°(13o) ampl.model/binned fit GGSZ (Giri,Grossman,Soffer,Zupan): Use Dalitz decays σγ = 11°… 13° (2 fb-1) δB° (°) 45 90 135 180 σ(γ) 4.6° 6.1° 5.7° 6.0° 4.3° Combined (2fb-1)
LHCb-2008-031
− +
→ π π ππ) ( K D / D
s
109
Combination: B±→D0K±
δB0 (o) 45 90 135 180 σγ for 0.5 fb-1 (o) 8.1 10.1 9.3 9.5 7.8
Tree Level Processes
LHCb-2008-031
B0→D0K*0 Time dependent:
Bs → DsΚ (B0 → Dπ) σγ for 2 fb-1 (o) 4.1 5.1 4.8 5.1 3.9 σγ for 10 fb-1 (o) 2.0 2.7 2.4 2.6 1.9 2o …3o reachable after 5 yr
110
Today
η
1 γ
η
1
LHCb at L=10fb-1
% 17 / ) (
0.5 β α
s
m ∆
d
m ∆
d
m ∆
K
ε
cb
V
ub
V
0.5
% 5 3 / ) ( ρ ρ % 7 . 4 / ) ( % 17 / ) ( = = η η σ ρ ρ σ
ρ
0.5 1
ρ
0.5 1
% 7 . 1 / ) ( % 5 . 3 / ) ( = = η η σ ρ ρ σ
111
γ from B→DK at LHCb (10 fb–1)
γ
loops (2006)
Two possible scenarios
112
113
A.Lenz
Challenge for any NP model
Probe photon polarization:
Constraints from observed BR on Type II 2-Higgs Doublett Models:
σ(Br)
Bs→φγ events: From time dependent decay rates: LHCb: 12k (2fb-1)
114
Br × 10-4 σ(Br)
= amount of wrong pol. photons
Test models w/ RH currents
LHCb: σ(ψ)≈0.11 Misiak et al. PRL (2007)
Standard Model
7
O
10 9 O
O
Effective Theory
115
Corresponding Wilson coefficients Ci describe short-range physics. New Physics in Wilson coefficients Ci = Ci
SM + Ci NP or new operators.
Operator Product Expansion
Observables: θl, θK, φ, m2
μμ
f d b k d t q2
SUSY
116
Angular observables offer a powerful test bench for any New Physics model
AFB(q2) ~ - Re { C10* [ C7
eff + β(q2) C9 eff ] }
→ μμ forward-backward asymmetry:
B0→ K*μμ events:
BELLE arXiv:0904.07770 657 M BB
(4.4 fb-1)
~450 evts
Poor agreement with SM. LHCb data will clarify.
384 M BB BABAR PR D79:031102
117
LHCb expectation for 2 fb-1 ~7000 events w/ B/S~0.25 700 events for 200 pb-1
Example: LHCb sensitivity for early data ( BELLE l f A ) 2 fb-1 100 pb-1 (assume BELLE values for AFB)
1) Simple Counting
10 fb-1
2
GeV 5 . ) ( ± = s σ
118
2) Full angular fit
s [GeV2]
2
GeV 28 . ) ( ± = s σ
AFB(s)
− +
s d
Constrained MSSM Buchmüller et al., 2009 SM: BR(Bs →μ+μ-)= (3.2±0.2)x10-9 BR(Bd →μ+μ-)= (1.0±0.1)x10-10 w/ non-universal Higgs mass (NUHM)
119
Large SUSY contributions possible
Experimental status: CDF 2009 BR(Bs → μ+ μ-) < 4.3×10-8 95% CL
Discovery (x10–9) For ~150 pb-1 LHCb expects to reach the final Tevatron sensitivity.
BR(Bs μ μ ) 4.3 10 95% CL BR(Bd → μ+ μ-) < 7.6×10-9 95% CL
120
2 2
~
td ts d s
V V ) (B ) (B R μμ μμ
μμ
→ → = B B
SM prediction 5σ observation 3σ evidence BR
Ratio is sensitive test for MFV
MFV SM
) (
1 −
fb L
5 10
TeV-scale physics must have a sophisticated flavor structure not to be excluded by existing data.
flavor structure of New Physics at the Tera-scale: 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
121
Physics at ATLAS and CMS. Flavor structure of new particles found by direct searches.
For some key observables early results (2010 data?) are possible.