B 0 , B 0 and the measurement of at LHCb Patrick Robbe, LAL Orsay, 26 September 2006, for the LHCb Collaboration
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 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 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(: Belle B A B AR
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 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 EE 1% 10%
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 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) 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- 0000 -+-+ +-+-
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 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 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 < 90% CL) 33 millions of inclusive BB events ➛ 15 min of LHCb at 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 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 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 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 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 ° 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 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 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 LHCb Sensitivity on ρ η A typical LHCb toy experiment (2fb -1 ): Current B A B AR measurement (Stat + Syst):
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 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 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 % 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 < 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 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)x 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 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 = Measuring S 00 S 00 = 0.30 ; σ S 00 = WA : With 2 fb -1 :
22 with B LHCb sensitivity (2) e.g. large S 00 : S 00 = ; σ S 00 = 0.4 resolution depends on the actual C 00 /S 00 central value The current indirect measurement is weakly constrained
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 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: