1. γ determination from tree decays (B→DK) with LHCb
Lake Louise Winter Institute 2007
Alberta, Canada
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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 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

3. 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

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 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

5. 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

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.
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.

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 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°

8. 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)

9. 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

10. current Dalitz uncertainty ~11° (to be improved)
B±→ D0K± with GGSZ
Giri, Grossman, Soffer, Zupan Phys. Rev. D (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-

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.