1. 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

2. Hunting for angle γ • Current experimental status: • From direct measurements withB→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 phaseγ-2. • Mixing phase: -2=-0.04to 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 phaseγ directly. • ADS+GLW method • GGSZ (Dalitz) method

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

4. Experimental aspects: Bs→DsK • Average Ds decay distance ~ 6 mm (Bs ~ 11 mm) • Subsequent Ds decay: (BF=4.4%) • Estimated branching fraction for full Bsdecay: (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

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

6. 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. All cuts applied Expected event yields/2fb-1 B/S Bs→ Dsπ 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.

7. 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 ofBs→DsK andBs→Dsπ. Observed decay times Bs→DsK Sensitivity with 2 fb-1 σ(γ) ~ 13° w/o tagging σ(γ) ~ 29°

8. B±→ D0K± with ADS Atwood, Dunietz and Soni, Phys. Rev. Lett. 78, 3257 (1997). • Charged B decay rB=0.075±0.030 colour favoured colour suppressed Amplitude ratio • D0and D0 can both decay into K-π+ (or K+π- ) rD=0.060±0.003 Cabibbo favoured doubly Cabibbo suppressed • 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 D0mixing 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)

9. B→ D0K strategy: ADS+GLW • Simultaneous fit for allB±→ D0K±decays: • Add D0 decay mode:D0→Kπππ • adds 3 observables and 1 unknown strong phaseδK3π (rDK3πalso well measured). • AddCP 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

10. B±→ D0K± with GGSZ Giri, Grossman, Soffer, Zupan Phys. Rev. D68 054018 (2003). When D0decays 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-

11. 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.