1. LHCb prospects in flavour physics and CP violation
Stephan Eisenhardt, University of Edinburgh
On behalf of the LHCb experiment
Introduction – LHCb Physics Programme
fs: BS  J/Y f
g: B±  DK±
rare decays: BS  mm, B0K*0mm
Conclusions
EPS 2007, Manchester,

2. LHCb Physics Programme g
~Vub*
~Vtd
~Vts g b a
~Vub*
~Vtd
~Vcb
g-2 g
and g
Rare decays - very sensitive to NP
Radiative penguin e.g. Bd  K* g, Bs  f g
Electroweak penguin e.g. Bd  K*0 m+m-
Gluonic penguin e.g. Bs  ff, Bd  fKs
Rare loop diagram e.g. Bs m+m-
B production,
Bc, b-baryon physics
Charm decays
Tau Lepton flavour violation
EPS 2007, Manchester,
Stephan Eisenhardt

3. _ fS: BsJ/Yf bccs  fS = fSSM+fSNP
BS mixing phase is very small in SM: fS = ± rad (BsJ/Yf : fS=-2c)
not yet measured
could be much larger if New Physics adds to BS0-BS0 transitions
BS0f
BS0BS0f
+NP?
measure time-dependent asymmetry in decay rates:
need flavour tagging
need very good proper time resolution to resolve BS0-BS0 oscillations
need angular analysis to separate CP-even and CP-odd contributions 
fS = fSSM+fSNP
EPS 2007, Manchester,
Stephan Eisenhardt

4. fS: BsJ/Yf wtag, s(t) fS = 0.2 = 5SM full LHCb MC Flavour tagging:
Tagging efficiency: etag – probability that tagging procedure gives an answer
Wrong tag fraction: wtag – probability for the answer to be wrong
Dilution of the observed asymmetry: D = 1 – 2wtag
Effective tagging efficiency:
eeff = etagD2 = 7.08 ± 0.23 %
fS = 0.2 = 5SM
+ wrong tag fraction
+ proper-time resolution
+ acceptance
BS0 tag
full LHCb MC
Proper time resolution:
dependent on reconstruction errors of final states
LHCb:
most channels have proper-time resolution ~ 40fs
BsJ/Yf: s(t) = 36.0 fs
EPS 2007, Manchester,
Stephan Eisenhardt

5. fS: BsJ/Yf angular analysis
BSJ/Y(l+l-)f(K+K-): golden channel
theoretically clean
experimentally easy: mm trigger and 4 charged tracks
LHCb: yield in 2 fb-1: 131k, B/S=0.12
angular analysis:
disentangle mixture of CP-even (hf=-1, A0, A||) and CP odd (hf=+1, A)
1-angle analysis: qtr
wrong-tag fraction: wtag from control sample BSDSp
needs external DmS
gives: fS, DGS
3-angle analysis: qtr, ftr, qf
better separation power
indication: wtag and DmS can be measured as well
(to lower accuracy wrt. external measurements)
total
CP even
CP odd
flat background
EPS 2007, Manchester,
Stephan Eisenhardt

6. fS: BsJ/Yf sensitivity
BSJ/Y(l+l-)f(K+K-):
for 1-angle analysis: sensitivity for s(fS) = rad, s(DGS/GS) =
2 fb-1 = “1 yr of LHCb”:
Add other CP-even final states:
combined relative weight: only 13%
total sensitivity for 2 fb-1: s(fS) = rad
Constraining New Physics
in BS mixing from fS measurement:
Parameterise NP with mixing amplitude
ASNP/ASSM and phase fSNP
ASNP/ASSM
fSNP
hep-ph/
>90% CL
>32% CL
>5% CL
CDF: DmS 04/2006
included
ASNP/ASSM
fSNP
After LHCb measurement of fS
with s(fS)=±0.1 (~0.2 fb-1)
EPS 2007, Manchester,
Stephan Eisenhardt

7. g: B±D0K± ADS method Charged B decays to D0 or D0 and K:
D0 and D0 can both decay into K-p+ (and K+p-):
Four decay rates:
two favoured with small interferences (opposite-sign p)
two suppressed with large interferences (like-sign p)
Counting experiment: no flavour tagging, no proper time analysis
Only through D0 mixing sensitive to NP
3 relative decay rates vs. 5 parameters: rB, rD, dB, dD, g
rD well measured; but dD poorly constraint by CLEO-c (Dcos dD ~ 20%)
Atwood, Dunietz and Soni, Phys. Rev. Lett. 78, 3257 (1997).
rB = 0.075±0.030
colour favoured
colour suppressed
Amplitude ratio
rD = 0.060±0.003
doubly Cabibbo suppressed
Cabibbo favoured
EPS 2007, Manchester,
Stephan Eisenhardt

8. g: B±D0K± ADS+GLW method
Improvements:
add D0 decay mode: D0Kppp
adds: 3 observables, 1 unknown strong phase dK3p, 1 well measured rel. decay rate rDK3p
add D0 decay mode into CP eigenstates: D0KK/pp (GLW method)
adds: 1 observable, 0 unknown
Simultaneous fit to all B±D0K± decays (ADS+GLW)
LHCb performance:
Charged B decays:
Neutral B decays: (same method can be applied)
Gronau, London, Wyler, PLB. 253, 483 (1991), PLB 265, 172 (1991).
Expected event yield / 2fb-1
B/S
B-D0[Kp,K3p]K- + c.c k
B-D0[Kp,K3p]K- + c.c k
B-D0CP[KK,pp]K- + c.c. 7.6k
0.6 ~3 ~2
Sensitivity with 2 fb-1:
s(g) ~ 5°-15°
(depends on strong phase dD)
Expected event yield / 2fb-1
B/S
B0D0[K+p-]K*0 + c.c k
B0D0[K-p+]K*0 + c.c k
B0D0CP[KK,pp]K*0 + c.c. 0.6k
<0.3
<1.7
<1.4
Sensitivity with 2 fb-1:
s(g) ~ 7°-10°
(depends on strong phase dD)
EPS 2007, Manchester,
Stephan Eisenhardt

9. g: B±D0K± GGSZ method
When D0 decays into a 3- or 4-particle CP Eigenmode:
no significant CP violation in D decays
D decay model:
‘exclusive’ point-by-point in phase space or ‘inclusive’ (integrating)
measure magnitudes (rD) from Dflavour tags
phases (dD) from DCP tags
choice: D0KS0p+p- (or KS0K+K-)  phase space = Dalitz plot
invariant mass: m±= KS0p±
Dalitz amplitudes: A(D0KS0p+p-) = f(m+2,m-2)
A(D0KS0p-p+) = f(m-2,m+2)
B decay amplitudes:
A(B-(KSp+p-)DK-)  f(m-2,m+2) + f(m+2,m-2) rB ei(dB-g)
A(B+(KSp+p-)DK+)  f(m-2,m+2) + f(m-2,m+2) rB ei(dB+g)
With known f : fit simultaneously for: rB, dB, g
rB & dB depend on mode: B-DCPK- B-D*CPK- B-DCPK*-
Giri, Grossman, Soffer, Zupan, PRD 68, (2003).
many resonances needed
m+2 [GeV2/C4]
m-2 [GeV2/C4] D0
EPS 2007, Manchester,
Stephan Eisenhardt

10. current Dalitz uncertainty 11%
g: B±D0K± GGSZ method
Select B decays:
“Cartesian parameters”: to better disentangle parameters in fit
(x±, y±) = (rB cos (dB±g), rB sin (dB±g))
B± Dalitz plot distribution depends on x±, y±
Fit (x±, y±) Dalitz plots:
Extract g:
BaBar: g = (92 ± 41 ± 11 ± 12)°
Belle: f3 = ( ± 3 ± 9)°
LHCb performance: 2g
BaBar: 232M BB
event yield
N(DK+)
N(DK-)
B±D0(K-p+)K±
B±D0CP+(K-K+)K±
B±D0CP+(p-p+)K±
B±D0CP-(K0Sp0)K±
B±D0CP-(K0Sf)K±
B±D0CP-(K0Sw)K±
649±29
26±9..
18±7..
39±9..
15±5..
25±7..
611±28
70±10
17±7..
42±9..
13±4..
14±6.. x y
PRD (R) (2006).
Sensitivity with 2 fb-1:
s(g) ~ 8°
current Dalitz uncertainty 11%
(to be improved)
Expected event yield / 2fb-1
B-(KSp+p-)DK- + c.c. 5k
0.2 < B/S < 1.0
(90% CL)
EPS 2007, Manchester,
Stephan Eisenhardt

11. Very rare B decays: BSm+m-
Very rare loop decay, sensitive to New Physics:
BR 3.4±0.410–9 in SM, can be strongly enhanced in SUSY
Current limit from CDF+D0 is:
1 fb–1: 7510–9 (90% CL )
CMSSM:
prediction of BR(BSm+m-)
wrt. gaugino mass m1/2
~ a few 10-9 – 10-7: much higher than SM
Main issue is background rejection
With limited MC statistics, indication that main background is bX, bX SM
(C)MSSM ?
~tan6b or ~tan4b
10-9
10-8
10-7
m1/2 [GeV]
BR(BSmm)
hint from
m: g-2
EPS 2007, Manchester,
Stephan Eisenhardt

12. BSm+m- sensitivity Limit at 90% C.L. 5 3 1 year of LHCb
0.05 fb–1  overtake CDF+D0
0.5 fb–1  exclude BR values down to SM
Limit at 90% C.L.
(only bkg is observed)
Integrated Luminosity (fb-1)
Uncertainty in
background prediction
Expected final CDF+D0 Limit
BR (x10–9)
SM prediction
LHCb Sensitivity
(signal+bkg is observed)
Integrated Luminosity (fb-1) 5 3
BR (x10–9)
SM prediction
2 fb–1  3 evidence of SM signal
10 fb–1  >5 observation of SM signal
1 year
of LHCb
EPS 2007, Manchester,
Stephan Eisenhardt

13. Rare B decays: B0K*0m+m-
Suppressed by loop decay: BR ~1.210–6
Forward-Backward Asymmetry AFB(s)
in the  rest-frame
is sensitive probe of New Physics
LHCb sensitivity:
7.7k signal events/2fb–1 (~1yr LHCb)
Bbb/S = 0.4 ± 0.1
S0= S(AFB(s)=0): s(S0) = ±0.52 GeV2
 determine ratio of Wilson coefficients C7eff/C9eff with 13% stat error (SM)
s = (m)2 [GeV2]
AFB(s), theory
position
of S0
integral + – K* B0 q
LHCb: 2 fb–1, fast MC
S0=4.0 GeV2
AFB(s)
s = (m)2 [GeV2]
EPS 2007, Manchester,
Stephan Eisenhardt

14. B0K*0m+m- transversity angles
Transversity amplitudes: LHCb study for 2 fb-1
Matias hep-ph/
Longitudinal polarisation FL
Asymmetry AT(2)
SUSY 1 SM
NLO
SUSY II
EPS 2007, Manchester,
Stephan Eisenhardt

15. LHCb Status LHCb Construction on Schedule Muon Calorimeters RICH2
Trackers
Magnet
RICH1
VELO
EPS 2007, Manchester,
Stephan Eisenhardt

16. Conclusions BSJ/Y(l+l-)f(K+K-):
sensitivity on fS with 2 fb-1: s(fS) = ±0.023 rad
significant coverage of phase space for NP with 0.2 fb-1
B±D0K± : clean channel, different methods explored
sensitivity on g with 2 fb-1: s(g) ~ 5°-15°
rare decays : big potential for search for NP
BSm+m- : with 2 fb-1  3 evidence of SM signal
B0K*0m+m- : with 2 fb-1  s(S0)= ±0.52 GeV2
LHCb waiting for physics data in 2008
many new and exciting physics results in flavour physics (and NP?)
stay tuned!
EPS 2007, Manchester,
Stephan Eisenhardt