1. B 0 , B 0  and the measurement of  at LHCb Patrick Robbe, LAL Orsay, 26 September 2006, for the LHCb Collaboration

2. 2 Introduction 1. How to measure  2.  Measurements in LHCb: 1. Performances and sensitivity with B 0   +  -  0 2. Performances and sensitivity with B 0   3. Combination and LHCb sensitivity to 

3. 3 The  angle of the Unitarity Triangle CKM Matrix B 0 decays to charmless CP final states are sensitive to  +  =  - , the relative weak phase between tree and penguin contributions.  V ub V ud * V tb V td * 

4. 4 Current status of  measurements Direct measurements at B factories: B   B   B   Combined (with  from B A B AR only): Indirect (without direct  measurements):         ) 5.176() 5.83( : ) 5.91(: 0.12 1.46 5.13 8.22 9.60 2.18    Belle B A B AR

5. 5  measurements in LHCb In LHCb,  measurement is performed with: Time dependant Dalitz analysis of B 0   +  -  0 SU(2) analysis of B 0   +  -, B 0   0  0 and B +   +  0. Typical event in LHCb: Challenge to reconstruct multi-track final states and final states with  .

6. 6 4 devices: Scintillator Pad Detector (SPD), Preshower (PRS), Electromagnetic Calorimeter (ECAL) and Hadronic Calorimeter (HCAL). Provides with acceptance 30 mrad to 300 (250) mrad: Level-0 trigger information (high transverse momentum hadrons, electrons, photons and  0, and multiplicity) Kinematic measurements for  and  0 with  E /E = Particle ID information for e, , and  0. LHCb Calorimeter EE  1% 10%

7. 7  0 reconstruction at LHCb Resolved  0 : reconstructed from 2 isolated photons  m = 10 MeV/c 2 Merged  0 : pair of photons from high energy pion which forms a single ECAL cluster, where the 2 showers are merged. The pair is reconstructed with a specific algorithm based on the expected shower shape.  m = 15 MeV/c 2 Reconstruction efficiency:   0 = 53 % for B 0  +  -  0 Resolved π 0 Merged π 0 π 0 mass (Mev/c²) Merged Resolved Transverse energy (GeV) 

8. 8  with B    (1) Assuming that the decay B 0  +  -  0 proceeds through the  resonance, 6 interfering decay modes contribute to the  +  -  0 Dalitz plot: B 0  +  -, B 0  -  +, and B 0  0  0 B 0  -  +, B 0  +  -, and B 0  0  0 Tree or Penguin transitions contribute to each decay mode. The time dependant analysis of the tagged Dalitz plot gives enough information to determine at the same time  and the relative amplitudes and strong phases between all processes. [Snyder, Quinn, 1993] t (ps) 0 2610 B0B0 B0B0 s+s+ s+s+ s+s+ s+s+ s+s+ s+s+ s-s- s-s- s-s- s-s- s-s- s-s- 0000 -+-+ +-+-

9. 9  with B    (2) Maximize a Likelihood with 9 parameters  ( + background fractions r ) Experimental acceptances Experimental resolutions Experimental (mis)tagging tag = +1/0/-1 Background contamination Experimental ingredients Theoretical ingredientsPhenomenological ingredients The ρ line-shape Event Yield  ),,(G r),t,s,(sM )t,s, ξ)r1( r, t ss N bkg k B,Bb 2 kkk 3 b tag bkkk 3 N k bkg evt               LL  = ( , T -+,  -+, T 00,  00, P -+,  -+, P +-,  +- )

10. 10 B    Selection Multivariate Selection based on: Particle Identification: Charged pion ID, neutral  0 clusters, … Kinematical criteria: transverse momenta, … Vertexing criteria: impact parameters, vertex isolation Combined PDF: Signal Inclusive bb X PDF signal inclusive bb Θ(PV-SV,P B ) Momenta sum vertices-B-momentum. alignment ΣP t (π ±o )/B (GeV) inclusive bb π + π - vertex isolation signal inclusive bb d min (mm) π±π± e,μ,K,p π ± identification ΔLL(π)

11. 11 B    Results and Backgrounds N 3π = 14x10 3 events / 2 fb -1 Eq. LHCb timeN sel B/S B0→ρ+ρ-B0→ρ+ρ- 4 days409% B0→K*γB0→K*γ1.3 days106% B 0 →Kππ 0 12 days905% Other B 0 → charmless1.5h529% B+→ρ+ρ0B+→ρ+ρ0 5 days163% Other B + → charmless1.5 h317% Assume B/S = 1 in the following Consistent with : B/S = 20% (B/S < 80% @ 90% CL) 33 millions of inclusive BB events ➛ 15 min of LHCb at 2.10 32 cm -2 s -1 3 signal events selected and passing the trigger 5 background events in side-bands (D (s) π,D (s)  ) and rejected by the trigger 1 million of fully simulated B  events ➛ 10 days of LHCb at 2.10 32 cm -2 s -1 ➛ 1300 events selected = B A B AR ρπ statistics up to 2004, efficiency of 7x10 -4 ➛ 50% with merged π 0 s Few millions of specific charmless B decays

12. 12 B    Fit: Signal acceptance Acceptance in Dalitz plane: selected produced Proper time acceptance: s+s+ s-s- s+s+ s-s- t (ps) ε (%) The lower corner of the Dalitz plot is highly depopulated due to the cut on the  0 energy. However, the upper region of the Dalitz figure contains enough information to allow the  extraction. Region of low lifetime depopulated due to the large impact parameters required in the selection  (%)

13. 13 B    Fit: Resolution and Tagging Flavour tagging: → Tagging efficiencyε = 40±2 % → Wrong tag fractionω = 31±2 % ε eff = ε (1-2ω)²= 6±2 % NB : the untagged sample also enters in the global fit. Expected resolutions: B mass (GeV/c²) Δt (ps) σ = 60 MeV/c² σ = 50 fs Resolutions are dominated by calorimeter energy resolution Performance estimated from full MC simulation: The tagging performance actually depends on the position in Dalitz plane. In the real experiment, the wrong tag fraction will be extracted from data (for example, using the self- tagged K + π - π 0 decay)

14. 14 LHCb Sensitivity on  with B    Method Simulate the experimental effects (resolution, acceptance, wrong tag,...) Maximize the likelihood with respect to:  fit and the background ratios r fit (12-D fit) Assume a set of theoretical parameters  gen Simulate a set of toy experiments accordingly Simulate backgrounds according to r gen ratios α T -+ Φ -+ T 00 Φ 00 P +- δ +- P -+ δ -+ 96.5° 0.470.000.140.00-0.2-0.50.152.0 Flat ++ ρ resonant B  (Kρ,K * π)  Kππ 50% 45% 5% Background structure poorly known. Assume B/S = 1 and use a mixture made of: Yield = 10 4 signal events = 2 fb -1 The same proper time distribution, resolutions and tagging dilution as signal are assumed. On real data, information on background will be extracted from the side-bands.

15. 15 LHCb Sensitivity on  with B    Results = 6.5 =2 Average 85% converge to the correct solution 15% converge to a pseudo-mirror solution. Fraction decreases with increasing luminosity (<1% @ 10 fb -1 ) α gen  gen  gen 70 toy experiments super-imposed ( L = 2 fb -1 ) Distribution of fit error 90% of experiments with σ  < 10° The correct solution generally corresponds to a deep (if not deepest) minimum.

16. 16 LHCb Sensitivity on  ρ η A typical LHCb toy experiment (2fb -1 ): Current B A B AR measurement (Stat + Syst):

17. 17  Measurement Systematics Estimates Extracting  via the 3π Dalitz analysis requires an accurate control of the inputs The final analysis will be much more difficult than this prospective study → Not likely to be a ‘first year’ analysis for LHCb but very promising results Non-uniform wrong-tag Δ  = 1° Proper time acceptance Δ  = 0° Dalitz acceptance Δ  = 5° ρ/ω mixing in signal Δ  = 0° ρ’ and ρ’’ contribution in signal Δ  = 7° Large ρ 3 contribution (weight 20%) in signal Δ  = 12° What is the impact of imperfect knowledge of quantities included in the likelihood:

18. 18  with B    Method: Recent measurements showed that the B 0  +  - decay is predominantly longitudinally polarized, and then a pure CP eigenstate. The time dependant asymmetry gives access to  eff =  + , shift due to penguin contributions: Constraints on  can be obtained measuring B +  +  0 and B 0  0  0 branching fractions. Analysis similar to B 0  +  - but with many advantages: B (B +  +  0 ) and B (B 0  +  - ) 5 times larger, B (B 0  0  0 ) is small: (1.2  0.4  0.3)x10 -6 Time dependant analysis of B 0  0  0 could also provide additional information. A oo Δα A +- /√2 A +o = A -o A +- /√2 A oo with

19. 19 LHCb performances for B 0      and B +     Expected annual yields (2 fb -1 ): Selection for B 0  ρ + ρ - and B +  ρ + ρ 0  Multivariate selection as for B  ρπ  2 and 1 neutral pion(s) in the final state, respectively  Overall efficiency : 0.01 % and 0.045 %  B mass resolution dominated by ECAL resolution : 80 MeV/c² and 52 MeV/c²  Proper time resolution : 85 fs and 47 fs  B   ρ  ρ 0 : 9000B/S ~ 1  B 0  ρ + ρ - : 2000B/S < 5 @ 90%CL One year of LHCb probably not competitive with current B factory performance. Will need several years to provide a sizeable contribution to C +-, S +- measurement. The main contribution of LHCb to the B  ρρ analysis could be the improvement of the measurement of the B 0  ρ 0 ρ 0 mode

20. 20 LHCb performances for B 0     Selection:  multivariate selection  overall efficiency : 0.16% Expected annual yield ( 2fb -1 /year): ICHEP06 : BR = (1.2  0.4  0.3)x10 -6 1000 Eq. LHCb timeN selected B bb inclusive15 min0< 4000 B 0 → π + π - π + π - (Non Res.)2.5 days7300 B 0 → K + π - π + π - (Non Res.)1 day0< 600 B mass σ(m B ) = 16 MeV/c² Proper time σ(t) = 32 fs Background contamination:

21. 21  with B  LHCb sensitivity  (1) Measuring B 00 B 00 = 1.2x10 -6 σ B 00 /B 00 = 20% + Measuring C 00 with time dependant analysis C 00 = 0.51 ; σ C 00 = 0.4 + Measuring S 00 S 00 = 0.30 ; σ S 00 = 0.4 2006 WA : With 2 fb -1 :

22. 22  with B  LHCb sensitivity  (2) e.g. large S 00 : S 00 = -0.61 ; σ S 00 = 0.4  resolution depends on the actual C 00 /S 00 central value The current indirect measurement is weakly constrained

23. 23  and  : 2 fb -1 at LHCb LHCb  measurement with  LHCb  0  0 (C 00 /S 00 ) + B factories  +  - and  0  + LHCb     (C +- /S +- ) + B factories  +  0 and  0  0 WA 2006 LHCb 2 fb -1

24. 24  The time-dependent B 0  (ρπ) 0 Dalitz plot analysis: No ambiguity on  in [0,π] but pseudo-mirror solutions. With 2 fb -1 LHCb may achieve σ stat < 10° on  Require an accurate control of the ρ-lineshapes and the experimental efficiencies. Ambitious but promising. Probably several years to setup the analysis. 8-fold ambiguity on  in [0,π]. Several years of LHCb needed to improve the current B 0  ρ + ρ - measurement. With 2 fb -1 the main LHCb contribution could be the improved measurement of B 0  ρ 0 ρ 0. Accessing the ρ 0 ρ 0 time-dependent asymmetry will reduce the degeneracy of mirror- solutions and improve the current  determination. Performance strongly depends of the actual values of C 00 and S 00.  During LHCb era the stat. error on  could reach the few degrees level SU(2) breaking effects, electroweak penguin contributions could be an issue Conclusions At LHCb, 2 complementary analyses developed to measure  :  The time-dependent B 0  +  - asymmetry and SU(2) analysis: