γ determination from tree decays (B→DK) with LHCb Lake Louise Winter Institute 2007 Alberta, Canada (,) (0,0) (1,0) γ determination from tree decays (B→DK) with LHCb Jeroen van Tilburg (Universität Zürich) on behalf of the LHCb collaboration

Hunting for angle γ Current experimental status: From direct measurements with B→DK decays: γ=(82±20)° (BaBar and Belle) From the SM fit using only indirect measurements: γ=(64.2±4.3)° (UTFit) Diagrams with b→c and b→u transitions → sensitive to γ. Use only tree diagrams to allow clean extraction of γ. Bs→DsK Measures weak phase γ-2. Mixing phase: -2=-0.04 to be measured by LHCb using Bs→J/ψ φ channel (see tomorrow’s talk by Peter Vankov). Decay not yet been measured. B→D0K Measures weak phase γ directly. ADS+GLW method GGSZ (Dalitz) method

Bs→DsK decay Feynman tree diagrams Four time-dependent decay rates: Interference between direct decay and decay after oscillation → need flavour tagging to distinguish between initial and Four time-dependent decay rates: Sensitivity to γ

Experimental aspects: Bs→DsK Average Ds decay distance ~ 6 mm (Bs ~ 11 mm) Subsequent Ds decay: (BF=4.4%) Estimated branching fraction for full Bs decay: (1.0 ± 0.4) x 10-5 Bs decay time resolution: 39 fs Flavour tagging power (opposite and same side): Total trigger efficiency (L0 + HLT): 30% Ds mass resolution: 6 MeV Decay time error estimate

Specific background: Bs → Ds π Special background channel: Bs → Ds π 12 times larger BF than Bs → Ds K Use RICH detectors and mass resolution to distinguish both channels: Fraction of Bs→Dsπ in Bs→ DsK estimated to be B/S=0.15±0.05. Not only a background: Bs → Ds π is also a control channel: tagging dilution. Also, Bs → Ds π golden mode to measure Δms sensitivity with 2 fb-1 ~ 0.01 ps-1 PID likelihood from RICH detector Bs mass resolution 14 MeV Optimize significance

Signal yield and background Backgrounds considered: minimum bias, generic bb events, specific B events. Difficult to simulate enough background. Too few events are left after final selection. Only upper limit given for background estimate. Channel Events simulated min bias 48 M generic bb 27 M specific bkgr 2 M Bs → Ds K 5 M Bs → Ds π 4 M All cuts applied Expected event yields/2fb-1 B/S Bs → Ds π 140k <0.5 Bs → Ds K 6.2k <0.5 (2 fb-1 corresponds to nominal year in LHCb) Outlook: Bs→Ds*K also sensitive to γ-2. Challenge: reconstruct soft photon from decay Preliminary study: ~1.8k events per 2 fb-1.

Bs→DsK sensitivity on γ Sensitivity determination: Full realistic MC simulation. Determine performance numbers: Decay time resolution, trigger and reconstruction efficiency, tagging performance, mass resolution, … Fast MC study: only generate decay times, flavour tag, mass distribution. Simulate typically 100 LHCb experiments. Unbinned likelihood fit on decay time distributions of Bs→DsK and Bs→Dsπ. Observed decay times Bs→DsK Sensitivity with 2 fb-1 σ(γ) ~ 13° w/o tagging σ(γ) ~ 29°

B±→ D0K± with ADS rB=0.075±0.030 rD=0.060±0.003 Charged B decay Atwood, Dunietz and Soni, Phys. Rev. Lett. 78, 3257 (1997). Charged B decay rB=0.075±0.030 colour favoured colour suppressed Amplitude ratio D0 and D0 can both decay into K-π+ (or K+π- ) rD=0.060±0.003 doubly Cabibbo suppressed Cabibbo favoured Four decay rates: two favoured with small interference two suppressed with large interference Counting experiment: no flavour tagging, no measurement of decay time. Only sensitive to NP in D0 mixing 5 parameters (rB, rD, δB, δD, γ), but only 3 relative decay rates… (rD well-measured, but only a constraint expected on cosδD~20% from CLEO-c)

B→ D0K strategy: ADS+GLW Simultaneous fit for all B±→ D0K± decays: Add D0 decay mode: D0→Kπππ adds 3 observables and 1 unknown strong phase δK3π (rDK3π also well measured). Add CP eigenstate decays D0→KK/ππ (GLW method) Adds one observable, no additional unknowns. Combined fit: ADS+GLW LHCb performance: Charged B decays: Expected event yields/2fb-1 B/S Sensitivity with 2 fb-1 σ(γ) ~ 5°-15° (depends on strong phase δD) 112k 0.6 1.4k ~3 7.6k ~2 Neutral B decays: (same method can be applied) Expected event yields/2fb-1 B/S Sensitivity with 2 fb-1 σ(γ) ~ 7°-10° (depends on strong phase δD) 3.4k <0.3 0.5k <1.7 0.6k <1.4

current Dalitz uncertainty ~11° (to be improved) B±→ D0K± with GGSZ Giri, Grossman, Soffer, Zupan Phys. Rev. D68 054018 (2003). When D0 decays into a 3 (or 4) body CP eigenmode: → interference between D0 Dalitz plots. D0 decay considered: Dalitz analysis: Many resonances Expected event yields/2fb-1 0.2 < B/S < 1.0 (90% CL) Sensitivity with 2 fb-1 σ(γ) ~ 8° current Dalitz uncertainty ~11° (to be improved) 5k Similar method will be used for KsK+K-

Conclusions B→DK tree decays involve b→c and b→u transitions → allow a theoretically clean extraction of CKM angle γ. Direct measurements of γ needed to put severe constraints on the Unitarity Triangle. Bs mode: Bs → DsK Relies on good decay time resolution (~39 fs) and tagging power (~9%). Sensitivity determined from fast MC and likelihood fit ~13° with 2 fb-1. Charged and neutral B→D0K decays: Promising and clean channels. Different methods (ADS+GLW, GGSZ) explored. Combining all methods sensitivity on γ with 2 fb-1 estimated to be roughly 5°. Interesting comparison with indirect measurements and between the different methods.