1. Measurements of sin2  1 in processes at Belle CKM workshop at Nagoya 2006/12/13 Yu Nakahama (University of Tokyo) for the Belle Collaboration Analysis procedures Results in 2006 Sensitivity of sin2  1 at Belle Summary Outline

2. 2 Principle of Measurement Reconstruct B  f CP(b  ccs) decays Measure  t and Determine flavor of B tag Evaluate CP asymmetry from the  t and flavor information e-e- e+e+ e - :8.0 GeV e + :3.5 GeV B CP zz B tag  (4S)  ~ 0.425 f CP(b  ccs)  z  c  t B ~ 200   m Flavor tag 

3. 3 B CP  J/  K 0 Reconstruction in 535M BB B 0  J/  K S B 0  J/  K L 00 Beam energy substituted B mass (GeV/c 2 ) B momentum in the cms (GeV/c) Events / 50 MeV/c Events / 1 MeV/c 2 + data MC: J  K L X  MC: signal MC: J/  X MC: comb. N sig = 6512 Purity 59 % CP even N sig = 7482 Purity 97% CP odd  S  →      only) p KL information is poor.  lower purity

4. 4 –IP (interaction point) tube constraint fit IP profile –Size:  x ~100  m,  y ~5  m. –Smearing due to B flight is taken into account by 21  m in the x-y plane. No constraint in the beam direction (z-axis). Measured track IP profile IP tube  t measurement -Vertex fit CP side (J/ψ)Tag side 2-trk1-trkFailedn-trk 1-trkFailed Fraction (%)93.70.95.482.510.37.2 Resolution  m) 52.5 ±0.2 108.9 ±3.2 107.5 ±1.0 256.4 ±4.3 z-axis B decays vertices are reconstructed using the tracks coming from their decay particles using kinematical vertex fit.

5. 5 Flavor Tagging For the B CP -B tag coherency originated from Y(4S) decay, B tag flavor determines B CP flavor (B 0 or B 0 ) at B tag decay time. Flavor information is determined from B tag decay products. 0+10+1 B tag =B 0 B0B0 B0B0 B0B0 qr Flavor information is parametrized using qr: q: MC determined discrete flavor (1 or -1) r: MC determined flavor ambiguity (0~1) Event fraction

6. 6 Evaluation of CP asymmetries B tag = B 0 Smeared by Detector resolution Wrong flavor tag effect (Bkg. contribution) Signal Background Maximum Likelihood Fit Wrong flavor tag effect Detector resolution  t (ps) Measured  tTrue  t

7. 7 R CP R Tag We understand the following resolution components: –Detector resolution: –Effect of non-primary particles: –Kinematic approximation of B 0 flight: We determine the models and their parameters using control samples: B 0 →D (*)- l +  D (*)-    D*    B + →D 0  +, J/ψK + Overview of Resolution function: R(  t) R(  t) = R CP R Tag R NP R K R NP RKRK B B zz B D l Non-primary particles B rec Ks l l J/ψ Residuals =Z rec ― Z gen B gen [NIM A533: 370,2004]

8. 8 Resolution function Using event-by-event vertex quality:  z and , (  Vertex fit  2 along the z direction only) Detector resolution is modeled using MC as: - Event-by-event Double Gaussian - Sigma of Gaussian ~ Error  z - Scaled up according to  Entries  t (ps) Neutral B Lifetime fit (  B0 = 1.530 +/- 0.009ps [PDG2006]) All resolution parameters are determined from fits to data/MC samples. We verify the fitted lifetime using this model is self-consistent to the one we used in the sin2  1,A fit. J/ψK 0  Data  B0 = 1.544 +/- 0.016(stat) ps

9. 9 Wrong flavor tag effect Wrong tag effect for each r bin is estimated from time-dependent B 0 -B 0 mixing fit using self-tagged control samples: B 0  D (*)- l +  D (*)-    D*    Events are classified into 6 categories according to the r. |  t| (ps) Measured time-dependent flavor asymmetry Dilution due to mis-flavor tagging Wrong flavor tag effect Time-dependent flavor asymmetry: Measured asymmetry:

10. 10 KEKB Integrated luminosity as a function of time B 0  J/  K S 0 B 0  J/  K L 0 History of the measurements of sin2  1 at Belle Results based on 535MBB will be described. and the expected sensitivity in the future

11. 11 2006 results with 535MBB Δt (ps)  CP = -1  CP = +1 Raw Asymmetry (= －  CP  sin2  1 sin  m  t) Entries / 0.5ps Raw Asymmetry sole (total) Entries / 0.5ps

12. 12 Combined results with 535MBB (stat.) Combined The other ccs processes are not included. (syst.) Entries / 0.5ps Raw Asymmetry -  CP Δt (ps) hep-ex/0608039, to appear in PRL

13. 13 Prospect of sin2  1 uncertainty TotalStatisticalSystematic 0.492/ab0.0350.0310.017 5/ab0.0170.0100.014 50/ab0.0140.0030.013 L /ab Assumption: Use the same analysis methods as of now. Use B  J/ψK 0 only. 5/ab 50/ab 535MBB ↑0.492/ab ー Total error ー Statistical error ー Systematic error In L ~>2/ab region, the systematic error will be larger than the statistical one.

14. 14 Systematic error of sin2  1 Categories  sin2  1 ) with 535MBB 1.Vertexing0.012 2.Possible fit bias 0.007  t Resolution function 0.006 4. BG fractions (J/  K L ) 0.005 5.Wrong tag probability0.004 6.BG fractions (J/  K S ) 0.003 7.Fixed Physics parameters:  m d,  B0 0.001 8. BG  t 0.001 9.Tag-Side interference0.001 Total0.017  sin2  1 ) with 5/ab 0.012 0.002 0.006 0.002 0.001 >0.000 0.001 ±0.013±0.003 Independent of the luminosity increase. large small 0.014

15. 15 Breakdown of the systematic error from Vertexing  sin2  1 ) with 535MBB 1.IP tube constraint vertex fit 0.0072 2.Poor-quality vertex rejection0.0064 3.Imperfect SVD alignment0.0056  z bias 0.0050 5.Track error estimation0.0033 6.Track rejection in B tag decay vertexing 0.0026  t fit range 0.0002 Total±0.012 Dominant Irreducible even with more data 1. IP tube constraint fit –Select only the events with the 2 tracks in CP side 2. Poor-quality vertex cut –Tighten a criteria for the vertex selection. Limiting factor is imperfect SVD alignment. Possible improvement idea As we have more data, we can reject the events with poorer quality to reduce the systematic error.

16. 16 With the current data set (492/fb), Dominating source of the systematic error is vertexing, especially imperfect SVD alignment. In L ~>2/ab region, the systematic error will be larger than the statistical one. With 5/ab data, 50/ab data, Summary As we have more data, we can reject the events with poorer quality The systematic error could be reduced. ±0.010±0.014 ±0.003±0.013 (stat.) (syst.) (stat.) (syst.) Sensitivity of sin2  1 using B  J/ψK 0 at Belle

17. 17 Supporting Results sin2   fit on non-CP eigenstate – consistent to zero Lifetime fits – consistent to input lifetime for S, A fits [t B0 = 1.530ps,  m d = 0.507/ps]

18. 18 Systematic errors of B 0  J/  K 0 Sin2  1 A 1.Vertexing0.0120.009 2.Wrong tag probability0.0040.003  t Resolution function 0.0060.001 4.Fixed Physics parameters0.001 5.Possible fit bias0.0070.004 6.BG fractions (J/  K S ) 0.0030.001 BG fractions (J/  K L ) 0.0050.002 7. BG  t 0.001 8.Tag-Side interference0.0010.009 total0.0170.014

19. 19 More on Vertex errors Error of Imperfect SVD alignment Misalign DSSDs in MC to reproduce IP resolution (15  m shift and 0.15mrad rotation.) Generate signal MC with and w/o misalignment Obtain sin2  1 for two cases and take the difference. Effect of Vertex section (cut poor quality vertices: (default :  >250)) Obtain sin2  1 with  and  and take the larger variation. Error of IP tube constraint fit is obtained by changing the smearing effect due to B flight (default: 21  m) Obtain sin2  1 with IP tube smearing by 11  m and 41  m and take the larger variation.

20. 20 Flavor tagging q: discrete flavor Effective tagging efficiency: 29.2+-1.4[%] [NIM A 533, 516 (2004)]

21. 21 Tag Side Interference Interference between CKM-favored and CKM- suppressed B  D transitions in tag side. Estimated by pseudo-experiments whose parameters are obtained from B 0  D*l samples No interference for semi-leptonic decay in tag side (It was included till last year)

22. 22 Prospects for less systematic errors IP tube constraint fit –Select only the events with the 2 tracks in CP side –Easy and little gain Poor-quality vertex cut –Select only the events with good vertex qualities. –Easy and effective but need data Imperfect SVD misalignment: –Difficult to improve and almost hopeless. –If better methods are found, need reprocess all data. Vertexing  t Resolution function –Select only the events with good qualities –We could model simply using less parameters. –Potentially promising, but not so easy

23. 23 Effect of non-primary particles Most of tag-side B has a secondary vertex coming from D decays. The effects of these non-primary tracks cannot be 100% eliminated in our vertexing algorythm. Modeled by –Gauss’s  function : the effects of the tracks from the primary vertex. –Exponential function :the effects of Lifetime components of D decaying into non-primary particles. A tagging lepton is expected to be from a primary vertex. –We determine the parameters of Gauss’s  func. for the events w/ tagging lepton w/o tagging lepton, separately.. B D l Non-primary particles Tagging lepton Entries (Log)