Feasibility of sin(2β+γ) Measurement From Time Distribution of

B0 DKS Decay

Vivek SharmaUniversity of California

San Diego

2

sin(2β+γ) From TD analysis of B0/B0→ D(*)0K(*)0 Decays

• CPV due to Interference between decay and mixing as in B D(∗)π– Advantages:

• Expect large (40%) CPV since two processes of similar strength • Time-dependent measurement with K0 → KS• Probe rB in self-tagging final state B DK*0 with K∗0→K+π−

– Disadvantages:• Color suppressed decays, Br (B ->DKS) ≈λ2 Br(B ->ψKS)

– Smaller decay rates (x 100) than B D(∗)π• Possible competing effects from Doubly-Cabibbo-suppressed D0 decays

• “ Overall requires x3 less B sample to measure sin2(2β+γ) than B Dπ “ – Kayser & London, PRD 61, 116103, 2000

* i i iub cs BrV V e A e eδ γ δ−=*

cb usV V A=

( )( )

0 0 (*)0

0 0 (*)0

*

* ~ 0.4

→=

→

=

B

ub csB

cb us

A B D Kr

A B D K

V VrV V

Strong phasedifference

b c

d d

u

s

0(*)D

0(*)K

*cbV

usV0B

b

c

d

u

s

ubV

*csV0B

b

0B

d

d

0(*)K

0(*)D

3

B0/ B0→ D(*)0K(*)0

Decay Rate Measurements By Belle & BaBar (2004)

4

B0/B0→ D(∗)0KS Rates : What We Know Now (BaBar)

hep-ex/0408052

4.5 ±1.9 ±0.5B0 D∗0K0

6.2 ±1.2 ±0.4Β0 D0K0

BF (10-5)Mode

124 million BB

N=64 ± 11

N=11 ± 4

D Sidebands

Can measure sin(2β+γ) with some precisionwith D(*)0 Ks in 500 fb−1assuming r ~ 0.4 (?)

Cannot distinguishB0 from B0

Hidden strangenesswith KS in final state

Preliminary

5

B0/B0→ D(∗)0KS Rates : What We Know Now (Belle)

hep-ex/0408108 274 million BB

78±14

78±15

6

Isolating Vub and V cb Driven amplitudes in B D0K*0

• Vcb contribution: – B0 → D0bar K*0

D0bar → K+ π−,π−π0,3πK*0 → K+ π−

– Same sign kaons

• Vub contribution: – B0 → D0 K*0

D0 → K− π+,π+π0,3πK∗0 → K+ π−

– Kaons with opposite sign

• Determine rB by measuring the 2 branching fractions

• Different sources of background because of charge correlation– Treat them as 2 different decay modes

b

d

c

d

s

uB0

D0

K*0

Aλ2

λ

b

d

u

d

s

cB0

D0

K*0

Aλ3(ρ+iη)eiγ

7

What We don’t Know: Limit on rB from Self-Tagging B0→ D0K*0

< 4.1 @ 90% CLB0 D0K∗0

6.2 ±1.4 ±0.6B0 D0K∗0

BF (10-5)Mode

Need large Vub driven amplitude for measurement of γ !

0.8 @90% C.L. ; more sensitive analysis on way<Br

124 million BB

No Signal inVub mediatedDecay

N=45 ± 9

Charge correlation toseparate B0 decay from B0

Vcb transition

Vub driven

0 0 *0

0

*0

KK

B D KD X

K π+−

+−

→→

→

0 0 *0

0

*0 K

BXK

D KD

K π++

+−

→→

→

Preliminary

B0 D0 K*0 ; K*0 K+π-

8

What We don’t Know Now: Limit on rB from Self-Tagging B0→ D0K*0

Belle 274 million BB

=> rB < 0.39 @ 90% CL

Br < 1.9 x 10-5 90% CLBr < 0.5 x 10-5 @ 90% CL

9

Toy Study of B DKSSensitivity to sin(2β+γ)

(Shahram Rahatlou @ CKM Angles Workshop 2003)

10

Time-Dependent Decay Distributions

• Similar to B D*π time-distribution– But r expected to be much larger (x 10-20)

• Linear dependency on r: can it be measured in the fit (?)– Tag-side DCS effects are small compared to signal amplitude– But there are other potential complications due to DCS decays on reco side (20%)

( )

( )

( )

0

0

2

2 2

2

2 2

20

2 2

1 2( , ; ) 1 cos sin8 1 1

1 2( , ; ) 1 cos sin8 1

sin 21

1 2( , ; ) 1 cos sin8

sin

1

2

s1

in 2

t

t

t

e r rf tag X t m t m tr r

e r rf tag X t m t m tr r

e r rf tag X t m tr

B

K

K

KB

r

Bτ

β γ δ

β

δτ

γ

γ δτ

β

−Γ Δ+

−Γ Δ

−Γ+

−

−

Δ−

+ +

⎛ ⎞−Δ = + Δ Δ Δ Δ⎜ ⎟+ +⎝ ⎠

⎛ ⎞−Δ = −

−

Δ Δ Δ Δ⎜ ⎟+ +⎝ ⎠

−Δ = − Δ

+ −

+ −

+

++Δ

+

−

( )2

20

2

1 2( , ; ) 1 cos sin8 1

s1

in 2t

m t

e r rf tag X t m t m tr

Br

Kτ

β γ δ+−Γ Δ

−

⎛ ⎞Δ Δ⎜ ⎟

⎝ ⎠

⎛ ⎞−Δ = + Δ Δ + Δ Δ⎜ ⎟+ +⎝

+⎠

+

( ) ( )( )2 22 1sin 2 1 1 12

S SS Sβ γ + − −+⎡ ⎤+ = + ± − −⎢ ⎥⎣ ⎦

One solution: sin2(2β+γ)

The other one: cos2Δ

S+

S-

fit for rB and sin(2β+γ−δ) and sin(2β+γ+δ)

11

Assumptions Used In This Toy Study• Signal Yield: ≈ 0.3 events / fb-1 → 160 reconstructed events (B D0Ks only for now)

– Yields can be 50% higher (Br. Ratio knowledge, better event selection)– Additional modes can increase signal yield but wont be as clean

• No combinatorial or peaking background– Signal asymmetries expected to be weakly correlated with background parameters

β=23°±3°, γ=59°±19° → 2β+γ=105°±20° (1.83 rad)– Use 3 values in toys: 0.9, 1.88, and 2.8 rad

• No Knowledge of strong phase – Use different values δ = 0.0, 0.8, 2.4 rad

• Realistic BaBar Flavor Tagging circa ‘03– 105 tagged events in 500 fb-1

• Vertexing: realistic resolution function– 10% tail and 0.2% outliers with category dependent bias – Parameters fixed in the fit

0.0840.58219.4%Kaon 2

0.0580.36819.9%Other

0.0220.80117%Kaon 1

0.0280.93310.3%Lepton

Dilu. Diff.DilutionEfficiencyCategory

12

Summary of Signal efficiencies and yields circa 2003

• K∗0→Ksπ0:

– Expected events: N(K+π−) x 0.5 (BF) x 0.5 (π0 eff) x 0.75 (Ks eff) ~ 50 events– But more background from π0

• D0→Ksππ: done but not included for technical reason. Fewer events than D0→Kπ mode • D0→KK, ππ: Branching fraction ~ 10 smaller than BF(Kπ)

• B0→ D**0 K(∗)0: similar to B0→ D*0 K(∗)0 but reduced by intermediate branching fraction

74242525Reco0.040.020.08Efficiency

20936431124326ProducedD*0K*0(K+pi-)52161719Reco

0.050.030.12Efficiency1047322562163ProducedD*0Ks240798081Reco

0.080.040.15Efficiency338210401816527ProducedD0K*0(K+pi-)167515461Reco

0.100.060.23Efficiency1691520908263ProducedD0Ks

TotalK3piKpipi0Kpi

Yields for 500 fb-1

withBF = 4 x 10-5

Assuming D*0

reco. efficiencyof 50%

13

Fit Validation with 50 ab-1: rB

• Validate fit with 500 experiments of 50 ab-1

– rB(gen) = 0.4, 2β+γ = 1.88, δ=0.0

rB(fit) – rB(gen) rB(fit) uncertainty rB(fit) uncertainty vs. rB(fit)

No bias in the fitted values for any parameter

Slightly better errors for larger rB

Mean: 0.014RMS: 0.001

μ: -0.002±0.006σ: 0.013±0.006

σrB

14

First ToyFit Attempt for 500 fb-1 sample: fit 3 parameters rB, sin(2β+γ±δ)

• Problem with fit convergence

• Small values of rB are problematic– rB constrained to be positive in the fit

• ~10% of fits with rB close to the limit

3.4%2.2%2.6%2β+γ=1.88

3.6%2.4%3.0%2β+γ=0.90

3.0%2.4%3.8%2β+γ=2.80

δ=2.4δ=0.8δ=0.0Frac. Failed Fits

2β+γ=1.88δ=0.8

2β+γ=1.88δ=0.0

15

Plan B Sensitivity for sin(2β+γ±δ) with rB=0.4 (fixed)

• All fits successful!– Problems with MINOS errors in some fits

• Under investigation

0.600.690.642β+γ=1.88

0.650.700.632β+γ=0.90

0.560.630.652β+γ=2.80

δ=2.4δ=0.8δ=0.0Residue sin(2β+γ+δ) RMS

0.610.620.642β+γ=1.88

0.660.640.652β+γ=0.90

0.590.610.602β+γ=2.80

δ=2.4δ=0.8δ=0.0Residue sin(2β+γ−δ) RMS

Not perfect Gaussian shape

Bad errors mostlyfor the positive error

Probably hitting non-physicalregion in LL

16

Summary of Preliminary Toy Study

• Sensitivity with 0.5 ab-1?– Simultaneous determination of rB, and sin(2β+γ±δ) probably not be feasible

with current method with ≈ 500 fb-1 samples (too few data)– With 500 fb-1, expected uncertainty on sin(2β+γ±δ) ~ 0.6-0.7 provided rB

known from elsewhere.

• ignoring DCS effects which at ~22% is small compared to expected errors and where CLEO-c can help ?

• Sensitivity with 5 ab-1?– No problem measuring rB and sin(2β+γ±δ) – All simultaneous fits successful

• Uncertainty on rB: ~ 0.04-0.05• Uncertainty on sin(2β+γ): ~0.15-0.20• The errors now scale with luminosity

17

Getting to rB “By Hook or By Crook” ! : Exercise@CKM2005 by Viola Sordini etal

Learning Today From Data on B DK Family of Decays

18

Getting to rB “ By Hook or By Crook” ! : Exercise@CKM2005 by Viola Sordini

19

Viola Sordini et alsi

n(2β

+γ) R

elat

ive

Erro

r

20

Bottom Line: B DKS

• Like with most pursuits of γ, strength of the b u amplitude is key• So far no observation, only limits on rB from B0→D(*)0K*0 modes, rB <0.39 (Belle)• Playing with measured B -> DK rates and constraining various contributing amplitudes

suggests rB→DKs=0.26±0.16. Is this approach theoretically kosher?• ToyMC based time-dependent CPV studies indicate that with 500 fb-1 samples, mild

information only on sin(2β+γ) provided rB obtained from elsewhere• More B modes need to be added

– Self tagging decay B D**0 KS decays (poor Br. for self tagging modes)– B DKs, D Ks ππ mode not prolific (yield ~4x smaller than D Kπ mode)

• Precise measurements require > ab-1 data samples• Can LHCb do such modes (Large Ks decay lengths)• There are no shortcuts in clean measurements of γ !