Feasibility of sin Measurement From Time Distribution of

B0 DKS Decay

Vivek SharmaUniversity of California

San Diego

2

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

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

• Expect large (40%) CPV since two processes of similar strength • Time-dependent measurement with K KS

• Probe rB in self-tagging final state BDK*0 with KK

– Disadvantages:• Color suppressed decays, Br (B ->DKS)2 Br(B ->KS)

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

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

* i i iub cs BrV V e A e e *

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 Vr

V 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 DKS Rates : What We Know Now (BaBar)

hep-ex/0408052

Mode BF (10-5)

DK 6.2 ±1.2 ±0.4

B DK 4.5 ±1.9 ±0.5

124 million BB

N=64 ± 11

N=11 ± 4

D Sidebands

Can measure sin() with some precisionwith D(*)Ks in 500 fbassuming r ~ 0.4 (?)

Cannot distinguishB from B

Hidden strangenesswith KS in final state

Preliminary

5

B0/B0 DKS Rates : What We Know Now (Belle)

hep-ex/0408108 274 million BB

7814

7815

6

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

• Vcb contribution: – B0 D0bar K*0

D0bar K , K*0 K

– Same sign kaons

• Vub contribution: – B0 D0 K*0

D K , K K

– 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

ds

uB0

D0

K*0

A2

b

d

u

ds

cB0

D0

K*0

A3(+i)ei

7

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

Mode BF (10-5)

B DK 6.2 ±1.4 ±0.6

BDK < 4.1 @ 90% CL

Need large Vub driven amplitude for measurement of !

0.8 @90% C.L. ; more sensitive analysis on wayBr

124 million BB

No Signal inVub mediatedDecay

N=45 ± 9

Charge correlation toseparate B decay from B

Vcb transition

Vub driven

0 0 *0

0

*0

KK

B D KD X

K

0 0 *0

0

*0 K

BXK

D KD

K

Preliminary

B0 D0 K*0 ; K*0 K+-

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 DKS

Sensitivity to sin(2+)

(Shahram Rahatlou @ CKM Angles Workshop 2003)

10

Time-Dependent Decay Distributions

• Similar to BD* 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

B

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

K

2 22 1sin 2 1 1 12

S SS S

One solution: sin2()

The other one: cos

S+

S-

fit for rB and sin() and sin()

11

Assumptions Used In This Toy Study• Signal Yield: 0.3 events / fb-1 160 reconstructed events (BD0Ks 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 =23±3, =59±19 2=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 = 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

Category Efficiency Dilution Dilu. Diff.

Lepton 10.3% 0.933 0.028

Kaon 1 17% 0.801 0.022

Kaon 2 19.4% 0.582 0.084

Other 19.9% 0.368 0.058

12

Summary of Signal efficiencies and yields circa 2003

• KKs:

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

• DKs: done but not included for technical reason. Fewer events than D0K mode • DKK, : Branching fraction ~ 10 smaller than BF(K)

• BD**K: similar to BD*K but reduced by intermediate branching fraction

    Kpi Kpipi0 K3pi TotalD0Ks Produced 263 908 520 1691  Efficiency 0.23 0.06 0.10    Reco 61 54 51 167D0K*0(K+pi-) Produced 527 1816 1040 3382  Efficiency 0.15 0.04 0.08    Reco 81 80 79 240D*0Ks Produced 163 562 322 1047  Efficiency 0.12 0.03 0.05    Reco 19 17 16 52D*0K*0(K+pi-) Produced 326 1124 643 2093  Efficiency 0.08 0.02 0.04    Reco 25 25 24 74

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, 2 = 1.88, =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

: -0.002±0.006: 0.013±0.006

rB

14

First ToyFit Attempt for 500 fb-1 sample: fit 3 parameters rB, sin(±)

• 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

Frac. Failed Fits

3.0% 2.4% 3.6%

2.6% 2.2% 3.4%

3.8% 2.4% 3.0%

15

Plan B Sensitivity for sin(±) with rB=0.4 (fixed)

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

• Under investigation

Residue sin() RMS =0.0 =0.8 =2.4

=0.90 0.63 0.70 0.65

=1.88 0.64 0.69 0.60

=2.80 0.65 0.63 0.56

Residue sin() RMS =0.0 =0.8 =2.4

=0.90 0.65 0.64 0.66

=1.88 0.64 0.62 0.61

=2.80 0.60 0.61 0.59

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(±) probably not be feasible

with current method with 500 fb-1 samples (too few data)– With 500 fb-1, expected uncertainty on sin(±) ~ 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(±) – All simultaneous fits successful

• Uncertainty on rB: ~ 0.04-0.05• Uncertainty on sin(): ~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(2

+) R

elat

ive

Erro

r

20

Bottom Line: B DKS

• Like with most pursuits of , strength of the bu amplitude is key• So far no observation, only limits on rB from B0D(*)0K*0 modes, rB <0.39 (Belle)• Playing with measured B -> DK rates and constraining various contributing amplitudes

suggests rBDKs=0.260.16. Is this approach theoretically kosher?• ToyMC based time-dependent CPV studies indicate that with 500 fb-1 samples, mild

information only on sin() 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 mode not prolific (yield ~4x smaller than DK 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 !