Probing The B0 D0 K0 System:A Quick Update

Vivek SharmaUniversity of California

San Diego

2

Motivation: sin(2+) From B D(*)0K(*)0 Decays

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

• Expect large CP Violation since two processes of comparable strength (?) • Experimentally probe rB in self-tagging final state BDK*0 with KK

– Disadvantages:• CKM suppressed, Color suppressed decays, Br (B0 ->DK0) 2 Br(B0 ->D0 )

– Much smaller decay rates (x 102) than B D

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

cb usV V A

0 0 (*)0 *

*0 0 (*)0{ } ~ 0.4 ?

ub cs

Bcb us

A B D K V Vr Hadronic Stuff

V VA B D K

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

crucial parameter

3

Estimating B0 D (*) 0 K(*)0 Rates From Measured Rates

0 0 0 4B(B D ) 3 10 ;

Naively

0 0 0

2 0 0 0

5

Br(B D K )

Br(B D )

1.5 10

;

;

BaBar

4

Improved B0/ B0 D(*)0K(*)0 Rate Measurements

• Analysis described in BAD 484V8 improves over analysis described in past ICHEP04 conf paper BAD 884

• Current analysis Runs1-4, 205.5 fb-1 at (4S)

• Largely eliminate reliance on MC for unobserved modes which can contribute to “peaking” background in mES but don’t peak near E=0

• Analysis tuned towards measurement/constraint on rB

– 2-dimensional fit to mES and E distributions

• Signal and background model:

Five free parameters: Nsig ,argus ,slope pE ,Npeak ,Ncomb

5

B DK0 Yields and Rates: Combining 3 D0 Modes

BAD 484V8

Mode BF (10-5)

DK 5.3 ±0.7 ±0.3(syst)

B DK 3.6 ±1.2 ±0.3(syst)

205 million BBPreliminary

N104 ± 14 N17 ± 5D0 Sidebands

Com

b./0

.01

GeV

Com

b./0

.01

GeV

D0 Sidebands

E(GeV)E(GeV)

BaBar

Signal Yields are as expected * The E fits shown above are for illustration onlyActual fits are per D decay mode and in mes Vs E

*

6

B0/B0 DKS Yields & Rates From Belle

hep-ex/0408108 274 million BB Preliminary ICHEP04

196

Belle

7814

-0.2 E 0.2

7

Motivation for rB : Study of B DK Sensitivity to sin(2+)

• Study based on Toy MC reported by Shahram Rahatlou @ CKM Angles Workshop 2003, assumptions in the study still valid

– http://www.slac.stanford.edu/BFROOT/www/Organization/CollabMtgs/2003/workshops/ckm2003/Thur2/rahatlou.pdf

• Fit simulated proper time distribution of BD0 K0 events expected in 500 fb-1 to simultaneously extract amplitude ratio rB , sin(2+), phase diff

Too few data!fit converges

always when rB isinput/constrained from elsewhere

8

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

• Vcb only: – B0 D0bar K*0

D0bar K , K*0 K

– Same sign kaons

• Vub only: – B0 D0 K*0

D K , K K

– Kaons with opposite sign

b

d

c

d

s

uB0

D0

K*0

A2

b

d

u

d

s

cB0

D0

K*0

A3(+i)ei

*0

*0 0

DKB

DK DKB B

- Probe r by isolating and measuring these 2 modes

- Assume that r r

9

Probing rB From Self-Tagging B0 D0K*0 & B0 D0K*0

Mode B.F. (in 10-5)

B DK 4.0 ±0.7 ±0.3(syst)

B DK -0.50.50.3(syst)

<0.24 @ 90% CL

205 million BB Preliminary

Kaon Charge correlation to separate Vcb & Vub driven modes

N=77 ± 13

Vcb transition Vub transition

0 0 *0 0

*0;

B D K D X

KKK

0 0 *0 0

*0;

B D K D XK K

K

BAD 484V8

BaBar

Br 0.42@90%CL

E (GeV)E (GeV)

See SR’s talk at next Breco meeting

10

Belle Search For The Self-Tagging B0 D0K*0

Belle 274 million BB (Preliminary

Br<0.5x10-5@90%CL Br<1.9x10-5 @90%CL

Belle do not quote a rB limit in ICHEP04 conf paper: unlikely to be better than Babar’s

hep-ex/0408108

VcbVub

11

Related Documents not explored in this 10’ talk: • Study of Time-dependent CPV in BD0K0 http://www.slac.stanford.edu/BFROOT/www/Organization/CollabMtgs/2003/ workshops/ckm2003/Thur2/rahatlou.pdf

•Viola Sordini’s exercise at CKM2005 combining phenomenology and exptal results to obtain constraints on rB and projected sensitivity to Sin2+ from B D(*)0K0 decays : http://ckm2005.ucsd.edu/WG/WG5/thu2/Sordini-WG5-S3.pdf

Near Term Plans

• The main aim in the first analysis phase was to map out the decays rates and probe rB

– This is now done as well as one can with 200 fb-1 data, have comparable precision to Belle with smaller data sample

– need to finish the paperwork

• BAD484 V9, the final version of the analysis BAD expected out by 7th Oct, together with a PRD-RC draft

• Hope to send to journal well before Xmas holidays

0DKBr 0.26 0.16@68%CL

12

Bottom Line: B DKS

• Like with most pursuits of , knowing the bu amplitude is key• So far no observation, only limits on rB from B0D(*)0K*0 modes,

rB <0.42 (BaBar)• 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

• There are no shortcuts in clean measurements of !

Unused Slides

DPF2004, 30 Aug 2004

Shahram Rahatlou 14

rB from fits to 2D fit to mES and E

Ratio rB defined as

Signal yields measured with separate 2D fits to distributions of mES and E for Vub (B0D0K*0) and Vcb (B0D0K*0) modes Each D0 mode fitted seperately

Modify fit to determine directly rB

Fix yield and efficiency of Vcb mode Use uncertainties assigned as systematic error

Fit provides ‘raw’ likelihood versus rB2 for each D0 mode

Convolve with Gaussian to account for systematic errors

Total likelihood given by product of likelihoods from 3 D0 modes

Determine limit on rB2 by integrating the convolved likelihood

function

2 ub cb

ub cb

V VB

V V

Nr

N

2 cb

ub cb

ub

VV B V

V

N r N

DPF2004, 30 Aug 2004

Shahram Rahatlou 15

Upper Limit on rB2 with Bayesian Approach

Upper limit x at 90% confidence level computed as

Two different priors used to determine the limit

2 2 20

2 2 20

( ) ( )

0.90

( ) ( )

x

B B B

B B B

L r p r dr

L r p r dr

L(rB2): likelihood function

convoluted with systematic error

p0(rB2): prior with different

hypothesis

Flat in Rb2p0=1 if rB

2>0p0=0 if rB

2<0rB

2 < 0.248 rB < 0.50

Flat in rB

p0=1 if rB>0p0=0 if rB<0

rB2 < 0.176 rB < 0.42

DPF2004, 30 Aug 2004

Shahram Rahatlou 16

Likelihood functions including systematic error

K K

K All modes

Shahram’s TD Sensitivity Studies (Angles03 WS)

18

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 sin

8 1 1

1 2( , ; ) 1 cos sin

8 1sin 2

1

1 2( , ; ) 1 cos sin

8

sin

1

2

s1

in 2

t

t

t

e r rf tag X t m t m t

r r

e r rf tag X t m t m t

r r

e r rf tag X t m t

rB

K

K

KB

r

B

2

20

2

1 2( , ; ) 1 cos sin

8 1s

1in 2

t

m t

e r rf tag X t m t m t

rB

rK

2 22 1sin 2 1 1 1

2S SS S

One solution: sin2()

The other one: cos

S+

S-

fit for rB and sin() and sin()

19

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

20

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

    KpiKpipi0 K3pi Total

D0KsProduced 263 908 520 1691

 Efficiency

0.23 0.06 0.10  

  Reco 61 54 51 167

D0K*0(K+pi-)

Produced 527 1816 1040 3382

 Efficiency

0.15 0.04 0.08  

  Reco 81 80 79 240

D*0KsProduced 163 562 322 1047

 Efficiency

0.12 0.03 0.05  

  Reco 19 17 16 52

D*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%

21

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

22

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%

23

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

24

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

Estimating rB “by Hook or by Crook”

Viola Sordini

26

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

Learning Today From Data on B DK Family of Decays

27

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

28

Viola Sordini et alsi

n(2

+)

Rel

ativ

e E

rror