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Feasibility of sin (2b+g) Measurement From Time Distribution of B 0  DK S Decay

Feasibility of sin (2b+g) Measurement From Time Distribution of B 0  DK S Decay. Vivek Sharma University of California San Diego. sin(2 b + g ) From TD analysis of B 0 / B 0  D (*)0 K (*)0 Decays. CPV due to Interference between decay and mixing as in B  D (*) p Advantages:

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Feasibility of sin (2b+g) Measurement From Time Distribution of B 0  DK S Decay

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  1. Feasibility of sin(2b+g) Measurement From Time Distribution of B0 DKS Decay Vivek Sharma University of California San Diego

  2. sin(2b+g) From TD analysis of B0/B0 D(*)0K(*)0 Decays • CPV due to Interference between decay and mixing as in B D(*)p • 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+p- • Disadvantages: • Color suppressed decays, Br (B ->DKS)2 Br(B ->KS) • Smaller decay rates (x 100) than B  D(*)p • 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 Strong phase difference

  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 N=64 ± 11 Cannot distinguishB0 from B0 Hidden strangenesswith KS in final state D0 Sidebands 124 million BB N=11 ± 4 Preliminary Can measure sin(2b+g) with some precisionwith D(*)0Ks in 500 fb-1assuming r ~ 0.4 (?)

  5. B0/B0 D(*)0KS Rates : What We Know Now (Belle) hep-ex/0408108 274 million BB 7814 7815

  6. Al3(r+ih)eig Al2 u c b b D0 D0 c u B0 B0 l s s K*0 K*0 d d d d Isolating Vub and V cb Driven amplitudes in B D0K*0 • Vcb contribution: • B0 D0bar K*0 D0bar K+p-,p-p0,3p K*0K+p- • Same sign kaons • Vub contribution: • B0 D0 K*0 D0K-p+,p+p0,3p K*0K+p- • 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

  7. No Signal inVub mediatedDecay What We don’t Know: Limit on rB from Self-Tagging B0 D0K*0 Vcbtransition Charge correlation toseparate B0 decay from B0 124 million BB N=45 ± 9 Vub driven B0  D0 K*0 ; K*0 K+- Preliminary Need large Vub driven amplitude for measurement of g!

  8. What We don’t Know Now: Limit on rB from Self-Tagging B0 D0K*0 Belle 274 million BB Br < 0.5 x 10-5 @ 90% CL Br < 1.9 x 10-5 90% CL => rB < 0.39 @ 90% CL

  9. Toy Study of B DKSSensitivity to sin(2+)(Shahram Rahatlou @ CKM Angles Workshop 2003)

  10. Time-Dependent Decay Distributions S+ • Similar to BD*p 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%) S- One solution: sin2(2b+g) The other one: cos2D fit for rB and sin(2b+g-d) and sin(2b+g+d)

  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 • b=23±3, g=59±19 2b+g=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 d = 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

  12. Summary of Signal efficiencies and yields circa 2003 • K*0Ksp0: • Expected events: N(K+p-) x 0.5 (BF) x 0.5 (p0 eff) x 0.75 (Ks eff) ~ 50 events • But more background from p0 • D0Kspp: done but not included for technical reason. Fewer events than D0K mode • D0KK, pp: Branching fraction ~ 10 smaller than BF(Kp) • B0 D**0K(*)0: similar to B0 D*0K(*)0 but reduced by intermediate branching fraction Yields for 500 fb-1 withBF = 4 x 10-5 Assuming D*0reco. efficiencyof 50%

  13. Fit Validation with 50 ab-1: rB • Validate fit with 500 experiments of 50 ab-1 • rB(gen) = 0.4, 2b+g = 1.88, d=0.0 Slightly better errors for larger rB rB(fit) – rB(gen) rB(fit) uncertainty rB(fit) uncertainty vs. rB(fit) Mean: 0.014 RMS: 0.001 m: -0.002±0.006 s: 0.013±0.006 rB No bias in the fitted values for any parameter

  14. First ToyFit Attempt for 500 fb-1 sample: fit 3 parameters rB, sin(2b+g±d) • 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 2b+g=1.88d=0.8 2b+g=1.88d=0.0

  15. Plan B  Sensitivity for sin(2b+g±d) with rB=0.4 (fixed) • All fits successful! • Problems with MINOS errors in some fits • Under investigation Not perfect Gaussian shape Bad errors mostlyfor the positive errorProbably hitting non-physicalregion in LL

  16. Summary of Preliminary Toy Study • Sensitivity with 0.5 ab-1? • Simultaneous determination of rB, and sin(2b+g±d) probably not be feasible with current method with  500 fb-1 samples  (too few data) • With 500 fb-1, expected uncertainty on sin(2b+g±d) ~ 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(2b+g±d) • All simultaneous fits successful • Uncertainty on rB: ~ 0.04-0.05 • Uncertainty on sin(2b+g): ~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 al sin(2+) Relative Error

  20. Bottom Line: B  DKS • Like with most pursuits of , 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(2b+g) 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 DKp 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  !

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