1. Feasibility of sin  Measurement From Time Distribution of B 0  DK S Decay Vivek Sharma University of California San Diego

2. 2 sin(2  +  ) 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   –Advantages: Expect large (40%) CPV since two processes of similar strength Time-dependent measurement with K   K S Probe r B in self-tagging final state B  DK *0 with K   K    –Disadvantages: Color suppressed decays, Br (B ->DK S )  2 Br(B ->  K S ) –Smaller decay rates (x 100) than B  D   Possible competing effects from Doubly-Cabibbo-suppressed D 0 decays “ Overall requires x3 less B sample to measure sin 2 (2  +  ) than B  D  “ – Kayser & London, PRD 61, 116103, 2000 Strong phase difference

3. 3 B 0 / B 0  D (*)0 K (*)0 Decay Rate Measurements By Belle & BaBar (2004)

4. 4 B 0 / B 0  D  K S Rates : What We Know Now (BaBar) hep-ex/0408052 ModeBF (10 -5 ) DKDK 6.2 ±1.2 ±0.4 B   D  K  4.5 ±1.9 ±0.5 124 million BB N=64 ± 11 N=11 ± 4 D  Sidebands Can measure sin(  ) with some precision with D (*)   K s in 500 fb  assuming r ~ 0.4 (?) Cannot distinguish B  from B  Hidden strangeness with K S in final state Preliminary

5. 5 B 0 / B 0  D  K S Rates : What We Know Now (Belle) hep-ex/0408108 274 million BB 78  14 78  15

6. 6 Isolating V ub and V cb Driven amplitudes in B  D 0 K *0 V cb contribution: –B 0  D 0 bar K *0 D 0 bar  K   ,      K *0  K    –Same sign kaons V ub contribution: –B 0  D 0 K *0 D   K   ,      K   K    –Kaons with opposite sign Determine r B 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 u B0B0 D0D0 K *0 A 2 b d u d s c B0B0 D0D0 K *0 A 3 (  +i  )e i 

7. 7 What We don’t Know: Limit on r B from Self-Tagging B 0  D 0 K *0 ModeBF (10 -5 ) B   D  K  6.2 ±1.4 ±0.6 B   D  K  < 4.1 @ 90% CL Need large V ub driven amplitude for measurement of   ! 124 million BB No Signal in V ub mediated Decay N=45 ± 9 Charge correlation to separate B  decay from B  V cb transition V ub driven Preliminary B 0  D 0 K *0 ; K *0  K +  -

8. 8 What We don’t Know Now: Limit on r B from Self-Tagging B 0  D 0 K *0 Belle 274 million BB  r B < 0.39 @ 90% CL Br < 1.9 x 10 -5 90% CL Br < 0.5 x 10 -5 @ 90% CL

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

10. 10 Time-Dependent Decay Distributions Similar to B  D*  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%) One solution: sin 2 (  ) The other one: cos   S+S+ S-S- fit for r B and sin(  ) and sin(  )

11. 11 Assumptions Used In This Toy Study Signal Yield:  0.3 events / fb -1  160 reconstructed events (B  D 0 Ks 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 CategoryEfficiencyDilutionDilu. Diff. Lepton10.3%0.9330.028 Kaon 117%0.8010.022 Kaon 219.4%0.5820.084 Other19.9%0.3680.058

12. 12 Summary of Signal efficiencies and yields circa 2003 K   K s   : –Expected events: N(K +   ) x 0.5 (BF) x 0.5 (   eff) x 0.75 (Ks eff) ~ 50 events –But more background from   D   K s  : done but not included for technical reason. Fewer events than D 0  K  mode D   KK,  : Branching fraction ~ 10 smaller than BF(K  ) B   D**   K  : similar to B   D*   K  but reduced by intermediate branching fraction KpiKpipi0K3piTotal D0KsProduced2639085201691 Efficiency0.230.060.10 Reco615451167 D0K*0(K+pi-)Produced527181610403382 Efficiency0.150.040.08 Reco818079240 D*0KsProduced1635623221047 Efficiency0.120.030.05 Reco19171652 D*0K*0(K+pi-)Produced32611246432093 Efficiency0.080.020.04 Reco25 2474 Yields for 500 fb -1 with BF = 4 x 10 -5 Assuming D *0 reco. efficiency of 50%

13. 13 Fit Validation with 50 ab -1 : r B Validate fit with 500 experiments of 50 ab -1 –r B (gen) = 0.4, 2  = 1.88,  =0.0 r B (fit) – r B (gen)r B (fit) uncertaintyr B (fit) uncertainty vs. r B (fit) No bias in the fitted values for any parameter Slightly better errors for larger r B Mean: 0.014 RMS: 0.001  : -0.002±0.006  : 0.013±0.006  rB

14. 14 First ToyFit Attempt for 500 fb -1 sample: fit 3 parameters r B, sin(  ±  ) Problem with fit convergence Small values of r B are problematic –r B constrained to be positive in the fit ~10% of fits with r B 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. 15 Plan B  Sensitivity for sin(  ±  ) with r B =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 0.630.700.65  =1.88 0.640.690.60  =2.80 0.650.630.56 Residue sin(  ) RMS  =0.0  =0.8  =2.4  =0.90 0.650.640.66  =1.88 0.640.620.61  =2.80 0.600.610.59 Not perfect Gaussian shape Bad errors mostly for the positive error Probably hitting non-physical region in LL

16. 16 Summary of Preliminary Toy Study Sensitivity with 0.5 ab -1 ? –Simultaneous determination of r B, 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 r B 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 r B and sin(  ±  ) –All simultaneous fits successful Uncertainty on r B : ~ 0.04-0.05 Uncertainty on sin(  ): ~0.15-0.20 The errors now scale with luminosity

17. 17 Getting to r B “By Hook or By Crook” ! : Exercise@CKM2005 by Viola Sordini etal Learning Today From Data on B  DK Family of Decays

18. 18 Getting to r B “ By Hook or By Crook” ! : Exercise@CKM2005 by Viola Sordini

19. 19 Viola Sordini et al sin(2  +  ) Relative Error

20. 20 Bottom Line: B  DK S Like with most pursuits of , strength of the b  u amplitude is key So far no observation, only limits on r B from B 0  D (*)0 K *0 modes, r B <0.39 (Belle) Playing with measured B -> DK rates and constraining various contributing amplitudes suggests r B  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(  ) provided r B obtained from elsewhere More B modes need to be added –Self tagging decay B  D**0 K S decays (poor Br. for self tagging modes) –B  DKs, D  Ks  mode not prolific (yield ~4x smaller than D  K  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  !