Probing The B 0  D 0 K 0 System: A Quick Update Vivek Sharma University of California San Diego

2 Motivation: sin(2  +  ) From B  D (*)0 K (*)0 Decays CPV due to Interference between decay and mixing as in B  D   system –Advantages: Expect large CP Violation since two processes of comparable strength (?) Experimentally probe r B in self-tagging final state B  DK *0 with K   K    –Disadvantages: CKM suppressed, Color suppressed decays, Br (B 0 ->DK 0 )  2 Br(B 0 ->D  0 ) –Much smaller decay rates (  x  10 2 ) than B  D   Strong phase difference crucial parameter

3 Estimating B 0  D (*) 0 K (*)0 Rates From Measured Rates Naively BaBar

4 Improved B 0 / B 0  D (*)0 K (*)0 Rate Measurements Analysis described in BAD 484V8 improves over analysis described in past ICHEP04 conf paper BAD 884 Current analysis  Runs1-4, fb -1 at  (4S) Largely eliminate reliance on MC for unobserved modes which can contribute to “peaking” background in m ES but don’t peak near  E=0 Analysis tuned towards measurement/constraint on r B –2-dimensional fit to m ES and  E distributions Signal and background model: Five free parameters: N sig,  argus,slope p  E,N peak,N comb

5 B  D  K 0 Yields and Rates: Combining 3 D 0 Modes BAD 484 V8 ModeBF (10 -5 ) DKDK 5.3 ±0.7 ±0.3(syst) B   D  K  3.6 ±1.2 ±0.3(syst) 205 million BB Preliminary N  104 ± 14 N  17 ± 5 D 0 Sidebands Comb./0.01 GeV D 0 Sidebands  E(GeV) BaBar Signal Yields are as expected * The  E fits shown above are for illustration only Actual fits are per D decay mode and in mes Vs  E *

6 B 0 / B 0  D  K S Yields & Rates From Belle hep-ex/ million BB Preliminary ICHEP04 19  6 Belle 78   E 0.2

7 Motivation for r B : Study of B  DK Sensitivity to sin(2  +  ) Study based on Toy MC reported by Shahram CKM Angles Workshop 2003, assumptions in the study still valid – www/Organization/CollabMtgs/2003/workshops/ckm2003/Thur2/rahatlou.pdf Fit simulated proper time distribution of B  D 0 K 0 events expected in 500 fb -1 to simultaneously extract amplitude ratio r B, sin(2  +  ), phase diff  Too few data! fit converges always when r B is input/constrained from elsewhere

8 Isolating V ub and V cb Driven Amplitudes in B  D 0 K *0 V cb only: –B 0  D 0 bar K *0 D 0 bar  K   ,      K *0  K    –Same sign kaons V ub only: –B 0  D 0 K *0 D   K   ,      K   K    –Kaons with opposite sign 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 

9 Probing r B From Self-Tagging B 0  D 0 K *0 & B 0  D 0 K *0 ModeB.F. (in ) B   D  K  4.0 ±0.7 ±0.3(syst) B   D  K  -0.5  0.5  0.3(syst) 90% CL 205 million BB Preliminary  Kaon Charge correlation to separate V cb & V ub driven modes N=77 ± 13 V cb transition V ub transition BAD 484V8 BaBar  E (GeV) See SR’s talk at next Breco meeting

10 Belle Search For The Self-Tagging B 0  D 0 K *0 Belle 274 million BB ( Preliminary Br<0.5x10 Br<1.9x10 Belle do not quote a r B limit in ICHEP04 conf paper: unlikely to be better than Babar’s hep-ex/ V cb V ub

11 Related Documents not explored in this 10’ talk: Study of Time-dependent CPV in B  D0K0 workshops/ckm2003/Thur2/rahatlou.pdf Viola Sordini’s exercise at CKM2005 combining phenomenology and exptal results to obtain constraints on r B and projected sensitivity to Sin2  +  from B  D (*)0 K 0 decays : Near Term Plans The main aim in the first analysis phase was to map out the decays rates and probe r B –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 7 th Oct, together with a PRD-RC draft Hope to send to journal well before Xmas holidays

12 Bottom Line: B  DK S Like with most pursuits of , knowing 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 <0.42 (BaBar) Playing with measured B -> DK rates and constraining various contributing amplitudes suggests r B  DKs =0.26  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 There are no shortcuts in clean measurements of  !

Unused Slides

DPF2004, 30 Aug 2004Shahram Rahatlou14 r B from fits to 2D fit to m ES and  E Ratio r B defined as Signal yields measured with separate 2D fits to distributions of m ES and  E for Vub (B 0  D 0 K *0 ) and Vcb (B 0  D 0 K *0 ) modes Each D0 mode fitted seperately Modify fit to determine directly r B Fix yield and efficiency of V cb mode Use uncertainties assigned as systematic error Fit provides ‘raw’ likelihood versus r B 2 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 r B 2 by integrating the convolved likelihood function

DPF2004, 30 Aug 2004Shahram Rahatlou15 Upper Limit on r B 2 with Bayesian Approach Upper limit x at 90% confidence level computed as Two different priors used to determine the limit L(r B 2 ): likelihood function convoluted with systematic error p 0 (r B 2 ): prior with different hypothesis Flat in Rb 2 p0=1 if r B 2 >0 p0=0 if r B 2 <0 r B 2 < 0.248r B < 0.50 Flat in r B p0=1 if r B >0 p0=0 if r B <0 r B 2 < 0.176r B < 0.42

DPF2004, 30 Aug 2004Shahram Rahatlou16 Likelihood functions including systematic error KK K   K  All modes

Shahram’s TD Sensitivity Studies (Angles03 WS)

18 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(  )

19 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% Kaon 117% Kaon 219.4% Other19.9%

20 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 Kpi Kpip i0K3piTotal D0KsProduced Efficien cy Reco D0K*0(K+pi -)Produced Efficien cy Reco D*0KsProduced Efficien cy Reco D*0K*0(K+p i-)Produced Efficien cy Reco Yields for 500 fb -1 with BF = 4 x Assuming D *0 reco. efficiency of 50%

21 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: RMS:  : ±0.006  : 0.013±0.006  rB

22 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%    

23 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  =  =  = Residue sin(  ) RMS  =0. 0  =0. 8  =2. 4  =  =  = Not perfect Gaussian shape Bad errors mostly for the positive error Probably hitting non-physical region in LL

24 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(  ±  ) ~ 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 : ~ Uncertainty on sin(  ): ~ The errors now scale with luminosity

Estimating r B “by Hook or by Crook” Viola Sordini

26 Getting to r B “By Hook or By Crook” ! : by Viola Sordini et al Learning Today From Data on B  DK Family of Decays

27 Getting to r B “ By Hook or By Crook” ! : by Viola Sordini

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