1. Paolo Massarotti Kaon meeting 2007 9 March 2007  ±  X    X  Time measurement use neutral vertex only in order to obtain a completely independent measurement

2. Paolo Massarotti Kaon meeting 2007 9 March 2007 Summary:  Sample selection  Efficiency evaluation  Resolution functions   ± preliminary measurement  Conclusions

3. Paolo Massarotti Kaon meeting 2007 9 March 2007 00 E ,t ,x  ±± E ,x ,t  K  tag tt pKpK pKpK t0t0 lKlK xKxK E ,t ,x  Signal selection Self triggering muon tag Signal given only by kaon decays with a    X    X  we look for the neutral vertex asking  clusters on time: (t - r/c)  = (t – r/c)     invariant mass  agreement between kaon flight time and clusters time

4. Paolo Massarotti Kaon meeting 2007 9 March 2007 Time measurement: proper time distribution The background due to K ± →  ±  and K ± →  ±     is smaller than 0.3% The number of the events with a neutral vertex reconstructed using a cluster from a charged particle (  e), is of the order of 1%. It can give a distortion smaller than 10 ps -

5. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation The efficiency is defined as the ratio of the events in which both the charged and the neutral vertices are reconstructed over the events in which the charged vertex is reconstructed it has to be compared with the efficiency of reconstructing a neutral vertex on MonteCarlo true. It is defined as the ratio of the events in which the neutral vertices is reconstructed over all the generated events:

6. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: MC kine vs MC datalike N vc = # charged vertex MC kine MC datalike After normalization between 0 and 70 ns

7. Paolo Massarotti Kaon meeting 2007 9 March 2007 N vc = # charged vertex Efficiency evaluation: MC kine vs MC datalike MC kine MC datalike After normalization between 10 and 45 ns

8. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: ratio (slope) The ratio of the MC true efficiency and of the MC reco efficiency is constant Without any normalization

9. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: ratio (slope) Slope (-.3±9.1)*10 -6  2 /ndf = 55/34  nv true /  nv reco T * (ns) P1 fit Perfect agreement in the region beetwen 10 to 45 ns (…about 3 lifetimes…)  corr / corr  10 -5

10. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: the normalization question N vc  0 = # charged vertex with a  0 MC kine MC datalike In order to check the rightness of the procedure we have normalized MC true and MC datalike efficiencies to the number of events with a  0 in the final state N  0 = # generated events with a  0

11. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: the normalization question MC kine MC datalike N vc  0 = # charged vertex with a  0 In order to check the rightness of the procedure we have normalized MC true and MC datalike efficiencies to the number of events with a  0 in the final state N  0 = # generated events with a  0

12. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: normalization Excellent normalization: A0 = 1.005±0.003

13. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: Data vs MC datalike Very good agreement between MC datalike and Data Data MC datalike

14. Paolo Massarotti Kaon meeting 2007 9 March 2007 Data MC datalike Very good agreement between MC datalike and Data Efficiency evaluation: Data vs MC datalike

15. Paolo Massarotti Kaon meeting 2007 9 March 2007 Resolution effects: distribution core We have to evaluate on MonteCarlo the resolution functions, defined as the difference between the reconstructed proper time and the kine proper time. The functions are proper time dependent. In order to smear the resolution functions, we had also evaluate, both on MonteCarlo datalike and on Data, the difference between the proper time given by any single cluster.

16. Paolo Massarotti Kaon meeting 2007 9 March 2007 MC datalike Data Resolution effects: T 0  effects We smear only the gaussian associated to a wrong bunch cross using the difference between the proper time given by the time technique and the proper time given by the length technique, calculated on MonteCarlo datalike and on data.

17. Paolo Massarotti Kaon meeting 2007 9 March 2007 Fit procedure We make the fit in the region between 12 and 42 ns. To fit the proper time distribution we construct an histogram, expected histo, between 10 and 45 ns, in a region larger than the actual fit region to take into account border effects. The number of entries in each bin is given by the integral of the exponential decay function (depending only on one parameter, the lifetime), convoluted with the efficiency curve. A smearing matrix accounts for the effects of the resolution. We take also into account the tiny correction to be applied to the efficiency given by the ratio of the MonteCarlo data-like and MonteCarlo kine efficiencies. N exp j =  C smear ij ×  i ×  i corr × N i theo i = 1 nbins

18. Paolo Massarotti Kaon meeting 2007 9 March 2007 MC   measurement: largest fit window  + MC = (12.41 ± 0.06) ns  2 /ndf = 46/27 P  2 =1.4% Best value between 13 and 41 ns (more than 2 lifetimes…) Fit ° MC datalike T * (ns)  MC true = 12.36 ns

19. Paolo Massarotti Kaon meeting 2007 9 March 2007 MC   measurement  + MC = (12. 41± 0.06) ns Fit region between 13 and 41 ns The fit reproduces the dist. very well also outside the fit region ! T * (ns) Fit ° MC datalike

20. Paolo Massarotti Kaon meeting 2007 9 March 2007 MC   measurement: largest fit window  - MC = (12.32 ± 0.06) ns  2 /ndf = 26/25 P  2 =40% Best value between 14 and 40 ns (more than 2 lifetimes…) T * (ns)  MC true = 12.36 ns Fit ° MC datalike

21. Paolo Massarotti Kaon meeting 2007 9 March 2007 MC   measurement  - MC = (12. 32± 0.06) ns Fit region between 14 and 40 ns The fit reproduces the dist. very well also outside the fit region ! T * (ns) Fit ° MC datalike

22. Paolo Massarotti Kaon meeting 2007 9 March 2007  + Data = (12.370 ± 0.056) ns  2 /ndf = 39/27 P  2 = 6% Data   measurement: largest fit window Fit between 13 and ns 41 (more than 2 lifetimes…) ° Data Fit

23. Paolo Massarotti Kaon meeting 2007 9 March 2007 Data   measurement ° Data Fit Fit between 13 and ns 41 (more than 2 lifetime…)  + Data = (12.370 ± 0.056) ns  2 /ndf = 39/27 P  2 = 6%

24. Paolo Massarotti Kaon meeting 2007 9 March 2007 Data   residual evaluation p 0 = 135.7±116.8 p 1 = -4.8±3.6  2 /ndf = 38/ 26 T * (ns)

25. Paolo Massarotti Kaon meeting 2007 9 March 2007 Data   normalized residual evaluation p 0 =.9±.7 p 1 = -.037±.025  2 /ndf = 38/ 25 T * (ns)

26. Paolo Massarotti Kaon meeting 2007 9 March 2007  - Data = (12.414 ± 0.059) ns  2 /ndf = 46/27 P  2 = 1.3% Data   measurement: largest fit window Fit between 14 and ns 42 (more than 2 lifetimes…) ° Data Fit T * (ns)

27. Paolo Massarotti Kaon meeting 2007 9 March 2007 Data   measurement ° Data Fit Fit between 14 and ns 42 (more than 2 lifetime…)  - Data = (12.414 ± 0.059) ns  2 /ndf = 46/27 P  2 = 1.3% T * (ns)

28. Paolo Massarotti Kaon meeting 2007 9 March 2007 Data   residual evaluation p 0 = -28±112 p 1 =.6±3.3  2 /ndf = 47/ 26 T * (ns)

29. Paolo Massarotti Kaon meeting 2007 9 March 2007 Data   normalized residual evaluation p 0 =.33±.71 p 1 = -.014±.025  2 /ndf = 45/ 25 T * (ns)

30. Paolo Massarotti Kaon meeting 2007 9 March 2007 Preliminary systematics check  Fit stability as a function of the range used - done  Fit stability as a function of the bin size - done  Fit stability with or without the efficiency correction - done  Correction due to a not correct evaluation of the Beam Pipe and Drift Chamber walls thickness - done  Correction due to a not correct evaluation of the decay time - done  Correction due to a not correct evaluation of the resolution smearing - done  Systematic on efficiency - missing

31. Paolo Massarotti Kaon meeting 2007 9 March 2007 Preliminary systematics checks Systematic uncertaintiesps Range stability± 35 Bin stability± 20 Efficiency correction± 10 Beam Pipe wall± 10 Drift Chamber wall± 15 Systematic uncertainties of the order of 45 ps Using the K ±  ±  0 tag we have checked that the systematic error given by a wrong  decay time is negligible. The systematic error given by a wrong smearing of the resolution funcions is negligible too.

32. Paolo Massarotti Kaon meeting 2007 9 March 2007 To Do Finish systematic checks Tuning of the virtual vertex procedure in order to enlarge the statistics We have to evaluate the length measurement using the K ± →  ±   tag and then we can evaluate the weight mean between the two technique

33. Paolo Massarotti Kaon meeting 2007 9 March 2007 Conclusions We had obtained, for the Length measurement  K± = (12.367±0.044 stat ± 0.070 sys ) ns in agreement with PDG 2006 fit. We have obtained, for the Time measurement  K± = (12.391±0.040 stat ± 0.045 sys ) ns in agreement with PDG 2006 fit.

34. Paolo Massarotti Kaon meeting 2007 9 March 2007  L = (12.367±0.044 stat ±0.070 sys ) ns Time and length results weighted mean between    and   KLOE time KLOE length 0.024  T = (12.391±0.041 stat ±0.045 sys ) ns

35. Paolo Massarotti Kaon meeting 2007 9 March 2007 Spare slides

36. Paolo Massarotti Kaon meeting 2007 9 March 2007 Using the time technique, taking into account the different reconstruction efficiency, we have half of the statistic given by the length technique Time measurement: proper time distribution WE HAVE TO ENLARGE STATISTIC

37. Paolo Massarotti Kaon meeting 2007 9 March 2007 It’s possible to reconstruct kaon neutral vertices before DC inner wall in the same way in which the neutral vertex can be reconstructed in the drift chamber: we look for neutral clusters in the calorimeter then, taking into account the energy loss in the material, using tag information we reconstruct the kaon helix in the region before DC inner wall and we look for a neutral vertex. Time measurement: add kaon decays before DC inner wall E ,t ,x  00 K  tag tt pKpK pKpK t0t0 xKxK

38. Paolo Massarotti Kaon meeting 2007 9 March 2007 Time measurement: proper time distribution The region in red is given by kaon decays before the DC inner wall

39. Paolo Massarotti Kaon meeting 2007 9 March 2007 Before DC inner wall Inside DC Time measurement: resolution

40. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation Our goal is the evaluation of the neutral vertex reconstruction efficiency before the DC inner wall. In the DC the efficiency is defined as the ratio of the events in which both the charged and the neutral vertices are reconstructed over the events in which the charged vertex is reconstructed In the region before the DC inner wall we can construct a virtual charged vertex given by the secondary track and the kaon helix

41. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation  meson Kaon helix secondary track Virtual charged vertex In the the region before the DC inner wall the efficiency to reconstruct a neutral vertex is defined as the ratio of the events in which both the virtual charged and the neutral vertices are reconstructed and the events in which the virtual charged vertex is reconstructed

42. Paolo Massarotti Kaon meeting 2007 9 March 2007 Virtual vertex technique: two cuts applied After two cuts applied, one on the secondary P* in kaon mass hypotesis (100 MeV) and one on the number of hits associated to the secondary track (25), we obtain very good time of flight resolutions which are comparable with the resolution given by the usual vertex technique

43. Paolo Massarotti Kaon meeting 2007 9 March 2007 Virtual vertex tecnique: two cuts Virtual vertex tecnique Virtual and normal vertex tecnique After two cuts applied, one on the secondary P* in kaon mass hypotesis (100 MeV) and one on the number of hits associated to the secondary track (25), we obtain very good time of flight resolutions which are comparable with the resolution given by the usual vertex technique

44. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: MC true and MC reco comparison N vc = usual charged vertex or virtual charged vertex

45. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: the normalization question N vc  0 = usual charged vertex or virtual charged vertex both with a  0

46. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: ratio (slope) Slope (7.7±1.4)*10 -4  2 /ndf = 43/44 P1 fit N vc  0 = usual charged vertex or virtual charged vertex both with a  0

47. Paolo Massarotti Kaon meeting 2007 9 March 2007 Efficiency evaluation: ratio (const) Con (99.85±.12)*10 -2  2 /ndf= 72/45 P0 fit Con (99.81±.12)*10 -2  2 /ndf = 46/30 N vc  0 = usual charged vertex or virtual charged vertex both with a  0

48. Paolo Massarotti Kaon meeting 2007 9 March 2007 Virtual vertex tecnique validation Not good time of flight resolution: we have to evaluate and cut background

49. Paolo Massarotti Kaon meeting 2007 9 March 2007 Virtual vertex tecnique: background evaluation Looking at the trk type of the daughter track on Montecarlo we estimate that we about 13% of kaon track… that we have to reject We reconstruct a virtual vertex using the kaon virtual helix and the kaon track

50. Paolo Massarotti Kaon meeting 2007 9 March 2007 Virtual vertex tecnique: backgroung rejection To reject the virtual verteces obtained using a kaon track we study the time of flight resolution as a function of the number of hits of the daughter track To be carefull we have to applay a cut on 50 hits but we loose many statistics

51. Paolo Massarotti Kaon meeting 2007 9 March 2007 Virtual vertex tecnique: backgroung rejection To reject the virtual verteces obtained using a kaon track we study the time oh flight resolution as a function of daughter momentum in the kaon rest frame in kaon mass hypotesis We can applay the usual cut at 100 Mev

52. Paolo Massarotti Kaon meeting 2007 9 March 2007 Virtual vertex tecnique: first cut After the cut in daughter P * we don’t reject all the kaon track and the time of flight resolution is not good…

53. Paolo Massarotti Kaon meeting 2007 9 March 2007 Virtual vertex tecnique: first cut Looking at time of flight resolution as a function the number of hits of the daughter track, after the cut in daughter P *, we applay a cut at 25 hits…

54. Paolo Massarotti Kaon meeting 2007 9 March 2007 Virtual vertex tecnique: first cut Looking at time of flight resolution as a function the number of hits of the daughter track, after the cut in daughter P *, we applay a cut at 25hits

55. Paolo Massarotti Kaon meeting 2007 9 March 2007  0 bias E ,t ,x  00 K  tag tt pKpK pKpK t0t0 xKxK Short T * Bad reconstruction No tag E ,t ,x  00 K  tag tt pKpK t0t0 xKxK Long T * Tag