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γ determination from tree decays (B→DK) with LHCb

Lake Louise Winter Institute 2007

Alberta, Canada

Jeroen van Tilburg (Universität Zürich)on behalf of the LHCb collaboration

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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)

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

Hunting for angle γ

• Diagrams with b→c and b→u transitions → sensitive to γ.• Use only tree diagrams to allow clean extraction of γ.

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Bs→DsK decay

tmtmGtt

Fe sfsfs

fs

ft

fBs sinImcos

2sinhRe

2cosh

Four time-dependent decay rates:

Sensitivity to γ

Feynman tree diagrams

sif eie2

sif e

KDs

KDs)(0 tBs

)(0 tBs

)0(0sB

s

su

cbs

0sB

KsD

s

sc

ubs

0sB K

sD

Interference between direct decay and decay after oscillation

→ need flavour tagging to distinguish between initial and 0sB0

sB

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• 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%

Experimental aspects: Bs→DsK

sD K K

%9)21( 2eff

Decay time error estimateDs mass resolution: 6 MeV

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• 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

Specific background: Bs → Ds π

PID likelihood from RICH detector Bs mass resolution 14 MeV Optimize significance

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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 simulatedmin bias 48 M

generic bb 27 Mspecific bkgr 2 MBs → Ds K 5 M

Bs → Ds π 4 M

Expected event yields/2fb-1 B/SBs → Ds π 140k <0.5Bs → Ds K 6.2k <0.5 (2 fb-1 corresponds to nominal year in LHCb)(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.

*s sD D

All cuts applied

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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.

Bs→DsK sensitivity on γ

Observed decay times Bs→DsK

Sensitivity with 2 fb-1

σ(γ) ~ 13°w/o tagging σ(γ) ~ 29°


σ(γ) ~ 13°w/o tagging σ(γ) ~ 29°

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B±→ D0K± with ADS

colour suppressedus

cub

u

B

0D

Ku

su

cbu

B

K

0Dcolour favoured

• Charged B decay

rB=0.075±0.030

Amplitude ratio

u

du

scu

0D K

Cabibbo favoureddoubly Cabibbo suppressedu

us

dcu

0D

K

rD=0.060±0.003

Atwood, Dunietz and Soni, Phys. Rev. Lett. 78, 3257 (1997).

• 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)

• D0 and D0 can both decay into K-π+ (or K+π- )

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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

c.c. ],[c.c. ]3,[c.c. ]3,[

0

0

0

KKKDBKKKDBKKKDB

CP 112k 0.6

1.4k ~37.6k ~2

Expected event yields/2fb-1 B/SSensitivity with 2 fb-1

σ(γ) ~ 5°-15°(depends on strong phase δD)







LHCb performance:

• Neutral B decays: (same method can be applied)

• Charged B decays:

0*00

0*00

0*00

],[][][

KKKDBKKDBKKDB

CP

3.4k <0.30.5k <1.70.6k <1.4

Expected event yields/2fb-1 B/S

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B±→ D0K± with GGSZ

When D0 decays into a 3 (or 4) body CP eigenmode:→ interference between D0 Dalitz plots.

Many resonances

Similar method will be used for KsK+K-

Dalitz analysis:

Giri, Grossman, Soffer, Zupan Phys. Rev. D68 054018 (2003).

amplitude Dalitz ),( 22 mmf

)( 0inv

SKmm

Expected event yields/2fb-1

0.2 < B/S < 1.0 (90% CL)c.c. )( KKB S 5k


σ(γ) ~ 8°current Dalitz uncertainty ~11°

(to be improved)


σ(γ) ~ 8°current Dalitz uncertainty ~11°

(to be improved)

0D

2m

2m

00SKDD0 decay considered:

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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.

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