1. Jacopo Nardulli NIKHEF (On behalf of the LHCb collaboration)
B(s) LHCb
Jacopo Nardulli NIKHEF (On behalf of the LHCb collaboration)
Outline:
B(s)h+h’- (h,h’ = π, K)
U-spin symmetry
Extraction of the CKM angle γ
Event Selection
Sensitivity on direct and mixing induced CP violation parameters

2. Why B(s) h+h’are interesting ?
Since CLEO measurement [BR(BdK+-)~4 BR(Bd+-)], penguin diagrams cannot be neglected in the two-body B-decay amplitude
Extraction of CKM phases gets more complicated
However unknown hadronic quantities can be eliminated relying on U-spin symmetry
The presence of penguins is an opportunity
New Physics might show up in loops of the penguin diagrams
CKM quantities from these modes can differ from the ones from tree-level modes, unaffected from NP

3. Trees, Penguins and γ
Sensitivity to  from the interference of T and P amplitudes
Where:
deiθ, d’eiθ’ : penguin-to-tree ratios
λ from CKM Matrix
C, C’ ~ CP-conserving factors
Two amplitudes can be related by U-spin symmetry: d=d’ and =’
Using method and parametrization from R. Fleischer, PLB 459 (1999) 306

4. U spin symmetry d  s exchange Bd+- BsK+K-
T+P+PCEW+PA+E T+P+PCEW+PA+E
Bd + Bs+K-
T+P+PCEW+PA+E T+P+PCEW
BsK+K Bd K+-
Where:
T : tree
P : penguin
PCEW: colour suppressed electroweak penguin
PA : penguin
annihilation
E: exchange
U-spin symmetry not exact for flavour specific decays: E and PA missing
E and PA contributions very small  can be seen in Bs+- and BdK+K- (BR ~ 10-8)

5. Extraction of γ
Where :
Measure the direct and mixing-induced CP-violating terms
 7 unknowns and 4 equations
The mixing phase d (s) can be measured from BdJ/KS (BsJ/)  5 unknowns
Finally, relying on U-spin symmetry it is possible to eliminate two further unknowns  3 unknowns, system over-constrained,  can be extracted unambiguously

6. B(s) h+h’- events at LHCb
Large b production at 14TeV p-p collisions. (All b mesons produced)
B hadrons are mostly produced in the
forward direction
 LHCb is forward spectrometer mrad
At nominal luminosity about 1012 bb in 107 s (L=2fb-1)
 Millions of B(s) h+h’- per year (BR ~10-5/10-6)
σbb ~ 500μb ; σinel ~ 80mb  σbb / σinel ~ 0.006
Many min-bias needed for background studies
 Main background comes from b events (min-bias cut at trigger level)
In this study 300k signal events and 27M inclusive b events have been used - b
Parton 2
Parton 1 p p b
Boost
(PYTHIA) - -
bb correlation - -

7. B(s) h+h’- selection cuts
, K
, K
IP1
IP2
IPB L
For each pair of charged
tracks we cut on
max (pT1, pT2)
min (pT1, pT2)
max (IP1/IP1, IP2/IP2)
min (IP1/IP1, IP2/IP2)
2 of common vertex
Then, the B candidate is
selected with cuts on pT
IPB/IP
L/L
Parameters used
for selection
h,h
Smallest pt
GeV/c
> 1
largest pt 3
smallest IP/IP 6
largest IP/IP 12
h, h
vertex fit 2
< 5 B pt
IP/IP
2.5
L/L 18

8. Particle identification through RICH system p/K/π separation
Invariant mass (no PID)
Kinematic separation weak
 Efficient hadron PID crucial for B(s)h+h’-
 PID discriminant built as difference between log likelihoods of particle hypotheses
K separation for Bh+h’- decays at LHCb
Every Channel is potentially background of the others
For true pions
For true kaons
K/π PID calibration will be done using decay chain: D*+ D0π+, D0K+π-Dedicated D* trigger (300Hz) for large “PID unbiased” sample

9. Mass resolution performance allows clean separation
PID performance
Mass resolution performance
B mass -
Separation between Bd K-π+/Bs  K-π + fully relies on the mass resolution
Bd K-π+ is 16 times more abundant  x 4 comes from the branching ratio  x 4 comes from hadronization fraction
ππ hypothesis -
B mass
Clean samples through expected PID performance of RICH system
Nominal mass
resolution of 16 MeV/c2
allows clean separation
between the two
signals
πK hypothesis

10. Proper time resolution
Excellent proper time resolution
allows to resolve fast Bs oscillations
t = ~40 fs
Proper time resolution (from full GEANT4 simulation)
=~40 fs
TOY MC
Decay rate for BsK+K- events tagged as B at LHCb (integrated luminosity L=2fb-1)
Calibration of proper time resolution by
disentangling prompt J/+ (affected
by intrinsic resolution) from non-prompt
component from B decays
“Lifetime unbiased” prompt J/ events
will be acquired with dedicated high-mass
di-muon trigger (600 Hz bandwidth)
Δms 20 ps-1 in this simulation, a bit larger than the truth…
Bkg

11. Selection summary - Yields are calculated for L= 2 fb-1
BR 10-6
Yield
B/S bb
B/S
spec
Channel
Eff. (%) -
Yields are calculated for L= 2 fb-1
Limited background-to-signal ratios  Both combinatorial and from the other Bh+h’- modes (wrong particle ID)
Hundreds of thousands of Bh+h’- decays triggered, reconstructed and selected per year with high purity
K spectrum selected from a sample of 27M bb MC events
Partially reco BK*+-
BdK+-

12. Flavour tagging Same side e-, m- Qvertex, QJet Opposite side
High pT leptons
K± from b → c → s
Vertex charge
B0opposite K- D PV
Bs0signal K-
Same side
K + K+
Same side
Fragmentation K± accompanying Bs
± from B** → B(*)±
Tagging power in %
Tag Bd
Muon
1.1
Electron
0.39
Kaon opp.side
2.1
Jet/ Vertex Charge
1.0
Same side π / K
0.73 (π)
Combined
5.1 Bs
D2=(1-2)2: tagging power
: tagging efficiency
: mistag probability
3.5 K
9.5
Work in progress

13. Background proper time Proper time acceptance
Fast MC Generation
Large Signal (S) and Background (B) samples through a TOY MC.
 To estimate sensitivity to CP Parameters
S generated simulating CP violation, proper time acceptance, proper time resolution and tagging
 For each event the toy MC generates mass, proper time, tagging and PID response from the full GEANT4 simulations
Background mass and proper time spectra generated from the full GEANT4 simulation
Background proper time
Proper time acceptance
B0  +-
B0  +-
will be extracted
from real data using
mass sidebands
will be calibrated on real data using event by event acceptance functions – studies going on in LHCb

14. Sensitivity on CP asymmetries (for L=2fb-1)
CP sensitivities are then estimated with an extended unbinned maximum likelihood fit to the toy MC sample
Likelihood fit simultaneously to all the Bhh channels (both tagged and untagged samples)
Channels and background separated with PID observables and invariant mass
C and S coefficients for Bd+- and BsK+K- events tagged as B (q=+1) or B (q=-1) are given by
LHCb can reach a sensitivity ~ 2
times better than the current
world average in 107 s of running
at nominal luminosity for the B0d
system and can provide measurements
in the B0s system with similar sensitivity
Fit results corresponding to L=2fb-1
Bd+-
BsK+K-
(C)
0.043 (0.07*)
0.042
(S)
0.037 (0.09*)
0.044
BdK+-
Bs+K-
(ACP)
0.003 (0.015*)
0.02
*From current world average

15. Sensitivity on γ (for L=2fb-1) (secondary fake solution appears)
Extraction of  performed using UTfit bayesian approach and software tools in 3 different scenarios (in this exercise =65o is assumed)
(1) Perfect U-spin symmetry
d=d’ -  = ’
(2) Weaker assumption: perfect U-
spin symmetry just for d, d’
d=d’ - no constraint on , ’
(3) Even weaker: given U-spin
breaking for d, d’
d’/d =[0.8, 1.2] no constraint on , ’
Perfect U-spin : Sensitivity ~ 4o
Scenario (2) & (3) : Sensitivity ~ 7°-10°
(secondary fake solution appears) 2 3
But sensitivity depends on the actual values of C and S…

16. An exercise: using current world averages of Bd+
and BdK+- (not using LHCb results)
Using BdK+- instead of BsK+K-
Neglecting PA and E it just differs for the spectator quark
Assuming U-spin symmetry the direct asymmetry of BsK+K- CKK = AK , the charge asymmetry of BdK+-
However SKK still missing  We can solve the system for 
Using Current world averages from HFAG
C = ± 0.07 (BaBar/Belle)
S = ± 0.09 (BaBar/Belle)
AK = ± (BaBar/Belle/CLEO/CDF)
p.d.f. for  obtained allowing for a U-spin
breaking:  = ’-  = ±20o
d’/d = [0.8, 1.2]
p.d.f. for 
 = (75±10)°
Unitarity Triangle
fits expectation

17. Conclusion LHCb will collect large samples of Bh+h’- decays
Its excellent vertexing and PID capabilities will allow to collect several hundreds of thousands of Bh+h’- events with very high purity
The CP sensitivity reachable (in 107 s at L = 2·1032 cm-2s-1 ) is about 2 times better than the current world averages from the b-factories and the Tevatron in the Bd sector, and will provide first measurements in the Bs sector with similar sensitivity
The Bh+h’- modes can be used to constrain the angle  with the U-spin flavour symmetry Useful information on γ can be extracted, even if the U-spin symmetry
will result to be broken to some extent Testing on the breaking of the U-spin symmetry will be possible
New Physics inside the Penguin loops can be revealed by the extraction of 
 obtained from these decay modes might thus be different from  from tree level modes, such as BDK, which can be assumed to be basically free of New Physics contributions

18. Backup

19. Some numbers Uncertainty phi_s 0.06 in 2 fb-1;
0.02 in phi_d 2fb-1 Taken from Reopt TDR
Taken from J. Piedra Talk FPCP 2006