1. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) 1 Final Results Γ(Ke3)/ Γ(pipi0) Anne Dabrowski Northwestern University NA48/2 Collaboration Meeting 08 June 2005

2. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Outline ● Data & MC samples ● DATA / MC of final selection ● Particle ID efficiency ● Background ● Trigger Efficiency ● Correction to acceptance for ke3 γ events outside dalitz plot in data ● Γ(Ke3)/ Γ(pipi0) result – K+ / K- ● Error analysis – Statistical contributions – Systematic Errors, stability under variation of selection cuts, and form factor (λ + ) ● Final result – Consistent with ICHEP – but reduced systematic error ● Conclusion

3. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Data: ● Compact 7.2 & Database (database-2005-02-11) pass 5 Min bias 2003 (runs 15745,15746 and 15747) – Bad burst ● Check: DCH,MBX,HODC,LKR,MUV,PMB and MNP33Current ne 0) ● Reject 31 bursts for which momentum = 10.0 GeV ● Total number of bursts after bad burst rejection: 2244 – Alphas and betas – Projectivity and Blue Field (Alan algorithm to remove phi dependence) ● Note: Result from August 2004 (ICHEP), used Compact 7.1 (no baseline energy correction) MC Sample: – Ginsberg correction – Constants from PDG 2004 ( λ + = 0.02780) – Pi0 decays according to its branching ratio – CMC005 corrections including corrections of May 9th 2005 – Result based on sample size of 10 M pipi0 and 8 M ke3 – Pipi0 mc has 0.438% pipi0g (IB) included in it at generation level ● Note Result from August 2004 (ICHEP) used cmc003 (improved DCH resolution in cmc005 among other changes) based on 2 M pipi0 and 2 M ke3. Dalitz and non dalitz decays were generated separately, pipi0 and pipi0g generated separately and ( PDG 2002 λ + = 0.02760) was used as input to MC Data and MC samples

4. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Common Selection for Ke3 and pipi0 ● Track Section (no extra tracks allowed): – 1 track after excluding Ghost-tracks – Hodoscope time window (-17. 20. ns) – Track quality > 0.8 CDA < 2.5, Beta, alpha corrections from database – x,y vertex (-1.8,1.8) cm, z charge vertex (-500,8000) cm – Blue Field correction applied ● Pi0 Selection (extra gammas allowed for both) – Energy of gamma (3, 65) GeV – Separation between gammas > 10 cm – Time difference between gammas (-5., 5.) ns – Energy scale – Projectivity correction – Calculate neutral vertex for each pair of gammas, and choose gammas based on best difference between charge and neutral vertex ● Use this neutral vertex in the blue field routine to correct the slopes of the track (reason: phi dependence studies of Alan) ● August 2004 (ICHEP) result used the “charge” vertex reconstruction, and cut on pi0 mass as function of energy

5. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Ke3pipi0 Difference between Ke3 and pipi0 Selections Kaon Mass 0.5102 (3 sigma from the mean) Momentum (5, 35) GeV PT track (0.01, 0.2) GeV Nu mass (-0.012, 0.012) GeV 2 Dist between track & gammas > 10 cm COM Track < 0.22 GeV COM pi0 < 0.27 GeV Mass (eπ0 ) < 0.425 GeV Particle ID for electrons: Particle ID for electrons: EOP > 0.95 EOP > 0.95 Kaon Mass (0.4772,0.5102) GeV Momentum (10, 50) GeV PT track < 0.215 GeV Nu mass (-0.0025, 0.001) GeV 2 Distance between track & gammas > 35 cm PT pi0 < 0.220 GeV E/P < 0.95

6. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Pipi0 E/P < 0.95   Allow muons Ke3 E/P > 0.95   Reject muons Summary of particle ID used:

7. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Ke3 Data / MC Momentum track Once the momentum dependent E/P particle ID efficiency is taken into account  distribution OK

8. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Ke3 Data / MC Energy Pi0  Good energy calibration LKr

9. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Ke3 Data / MC PT of pi0 sensitive to backgrounds and neutral reconstruction  seems OK

10. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Ke3 Data / MC PT of track sensitive to backgrounds  seems OK

11. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Ke3 Data/MC COM energy pi0 sensitive to backgrounds  seems OK

12. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Ke3 Data/MC COM energy track  sensitive to radiative corrections, Ginsberg implementation of radiative corrections OK!

13. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Electron ID and Pion ID Selected electrons from tight ke3 selection and pions from tight pipi0 selection Used same data sample, and timing and fiducial cuts as in analysis E/P > 0.95 for electrons Global efficiency (97.37 ± 0.09) % E/P < 0.95 for pions Global efficiency (99.522 ± 0.001) %

14. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Background contributions ChannelBackground contributions Pipi0 (E/P<0.95) Kmu3 (0.280±0.0058) % ▪ Ke3 (0.0100±0.0015) % Ke3 (E/P>0.95) Reject muons Pipi0 (0.0043 ± 0.0002) % Pipi0pi0 (0.0070 ±0.0003) % Recall:electrons rejected by E/P in pipi0 pions rejected by E/P in Ke3 muons rejected in Ke3 only Muons allowed Kmu3 background can be made negligable if we want to reject muons … see kmu3 talk.

15. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Summary of acceptance and background Kmu3 background can be made negligable if we want to reject muons … see kmu3 talk. Raw # Events Data Raw Acc MC Acc* Particle ID (E/P > 0.95 or E/P < 0.95) Backgrounds (Accbk*Br_bk)/ (AccS*BR_signal)% Ke3 K+ 57,9050.0751 ± 0.00010.0731 ± 0.0002 Pipi0 (when pion doesn’t decay) (0.0076 ± 0.0003) Pipi0pi0 (when pion doesn’t decay) (0.0089 ± 0.0004) ke3 K- 31,8600.0747 ± 0.00010.0728 ± 0.0001 Pipi0 (when pion doesn’t decay) (0.0079 ± 0.0004 ) Pipi0pi0 (when pion doesn’t decay) (0.0095 ± 0.0005 ) Pipi0 K+ 473,6160.1470 ± 0.0001 0.1463 ± 0.0001 Kmu3 (0.2803 ± 0.0058 ) Ke3 (0.0097 ± 0.0038) Pipi0 K- 262,7520.1467 ± 0.00010.1460 ± 0.0001 Kmu3 (0.2800 ± 0.0058) Ke3 (0.0089 ± 0.0023)

16. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Sources of background to ke3 K+/K- Source of Background Particle ID used RAW MC acceptance no particle ID (%) Acceptance* particle ID(%) Background (Accbk*Br_bk)/ (AccS*BR_signal) (%) Pipi0+ (note when pion doesn’t decay) E/P > 0.95 Muon veto 0.026810 ± 0.000518 0.000129 ± 0.000005 0.0076 ± 0.0003 Pipi0- (note when pion doesn’t decay) E/P > 0.95 Muon veto 0.025640 ± 0.000506 0.000132 ± 0.000007 0.0079 ± 0.0004 Pipi0pi0+ (note when pion doesn’t decay) E/P > 0.95 Muon veto 0.3845 ± 0.00250.0018 ± 0.00010.0089 ± 0.0004 Pipi0pi0- (note when pion doesn’t decay) E/P > 0.95 Muon veto 0.3844 ± 0.00270.0019 ± 0.00010.0095 ± 0.0005

17. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Sources of background pipi0 K+/K- Source of Background Particle ID used Raw Acceptance (%) Acc*Particle ID (%) Background (Accbk*Br_bk)/ (AccS*BR_signal) (%) Kmu3+ E/P < 0.95 0.2650 ± 0.0018 0.2803 ± 0.0058 kmu3- E/P < 0.95 0.2641 ± 0.0018 0.2800 ± 0.0058 Ke3+ E/P < 0.95 0.1947 ± 0.00160.0061 ± 0.00240.0097 ± 0.0038 Ke3- E/P < 0.95 0.1898 ± 0.00150.0056 ± 0.00140.0089 ± 0.0023

18. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Calculating Γ(Ke3)/ Γ(pipi0) We have all the ingredients for calculating the ratio … Other corrections needed: 1.Trigger Efficiency 2.Correction to radiative decays  Pipi0 γ mixed with pipi0 at generation level i.e. no further correction needed, correctly described by acceptance  Ke3 γ Ginsberg correction, events only generated inside dalitz plane. Need to correct acceptance for Ke3 γ events in data lie outside dalitz plane

19. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Main Trigger Q1/4 Min bias trigger for trigger efficiency calculation Trackloose/100 channelK+K- pipi0 0.9987 ± 0.00020.9990 ± 0.0002 Ke3 0.9987 ± 0.00050.9983 ± 0.0008 kmu30.9986 ± 0.00060.9988 ± 0.0007 Trigger Efficiency K+/K-

20. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Events are only generated (and corrected for radiative events) inside the dalitz plane in ke3 MC. Hence we need to correct for the acceptance of ke3(γ) for events in the data which lie outside of the dalitz plane. Look at data  events in v.s. out of dalitz plot K+ – events selected out:152 – Events selected in: 57550 – Correction to Ke3+ acceptance: 1.0026±0.0002 K- – Events selected out: 63 – Events selected in: 31683 – Correction to Ke3- acceptance: 1.0020±0.0004 Assume that in the data, all events outside of the dalitz plot are ke3(γ) candidates, have not corrected this ratio yet for possible sources of background – but this is assumed small K e3γ events outside dalitz plane Correction Ke3g K+/K- K e3(γ) events inside dalitz plane

21. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Ratio resultMain Error contributions SignalNormalization Systematics (MC,particle ID, background subtraction, ke3g correction and trigger) K+ Γ(Ke3)/Γ(pipi0) 0.24462 ± 0.00119 0.001020.00036 0.00049 Recall (~0.0011 in August 2004) K- Γ(Ke3)/Γ(pipi0) 0.24354 ± 0.00155 0.001360.000480.00057 The error in the Br includes: – Statistical (signal and normalization) – Systematic Trigger efficiency MC statistics (10 M pipi0 and 8 M ke3 of each charge) Errors in particle ID efficiency (particle ID error bin by bin and propagated) Errors due to background subtraction (including particle ID) YET No additional systematic errors due to kinematic cuts or form factor changes have been included YET in this table Result Γ(Ke3)/ Γ(pipi0) K+/K- Recall PDG 2004: Br(Ke3) = 0.0487± 0.0006 Br(pipi0) = 0.2113 ± 0.0014 Fit Ratio(ke3/pipi0) = 0.230±0.004

22. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Details of error contributions to Γ(Ke3)/ Γ(pipi0) K+/K- Ratio of Γ(Ke3)/ Γ(pipi0) K+K- 0.24462 ± 0.00118 0.24354 ± 0.00155 Statistics from signal (number of Ke3 events data) 0.00102 0.00136 Statistics from normalization (number of pipi0 events data) 0.00036 0.00048 Background subtraction 0.000017 0.000015 Trigger efficiency in pipi0 events 0.00005 Trigger efficiency in ke3 events 0.00012 0.00020 Acceptance * Particle ID ke3 0.00042 0.00048 Acceptance * Particle ID pipi0 0.00020 0.00021 Error due to Ke3g correction for acceptance outside dalitz plot 0.00005 0.00010 Number of ke3 events data 57,905 31,860 Number of pipi0 events data473,616262,752

23. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Summary of results: Ratio resultMain Error contributions SignalNorm Systematics (MC,particle ID, background subtraction, ke3g correction and trigger) Ke3/pipi0 K+ 0.24462 ± 0.00119 0.001020.000360.00049 Ke3/pipi0 K- 0.24354 ± 0.00155 0.001360.000480.00057 (combined result)0.24422 ± 0.00087 (stat) ± 0.00038 (sys)

24. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Do we have any addition effects?

25. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Χ 2 /ndf 12.25 / 11 Check Ratio of Ke3/ pipi0 as a function of momentum K+ K- Χ 2 /ndf 9.155 / 11  The ratio is stable as a function of momentum (plotted in momentum region where ke3 and pipi0 events overlap)

26. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Ke3 Data / MC Vertex  problem at high vertex, seems to be feature for K+ and K- What is the source? Does it affect our result? …

27. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Beam Tuning  DATA/MC for vertex in August was fine at high vertex (cmc003, and my beam tuning for special run)  Now use default cmc005, and beam tuning only done for assymetry runs (hypercompact)…  High vertex problem is an effect of insufficient beam tuning for our run.  But Does it affect our result? NO Recall August 2004

28. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Effects due to choice of vertex cut? Analysis fuducial volume (-500, 8000) cm K+ K- Check I (-1000, 7000) cm Result of fit doesn’t depend on fiducial region  result insensitive to vertex

29. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Effects due to choice of vertex cut? Analysis fuducial volume (-500, 8000) cm K+ K- Check II (0, 8000) cm Result of fit doesn’t depend on fiducial region  result insensitive to vertex

30. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Effects due to choice of vertex cut? Result of fit doesn’t depend on fiducial region  result insensitive to vertex Cut varied Ratio result Statistical Error Systemati c Error Difference ratio ± correlated error K+ Nominal (-500, 8000 cm) 0.244620.001080.00049 K- Nominal (-500, 8000 cm) 0.243540.001440.00057 ( 0, 8000 cm) K+0.244380.001080.00049-0.00024 ± 0.00017 ( 0, 8000 cm) K-0.243550.001460.00076+0.00002 ± 0.00023 (-1000,8000 cm) K+0.244660.001080.00048+0.00003 ± 0.00015 (-1000,8000 cm) K-0.243660.001430.00057+0.00012 ± 0.00020 (-500,7000 cm) K+0.245260.001120.00050+0.00064 ± 0.00033 (-500,7000 cm) K-0.243500.001500.00058-0.00004 ± 0.00044 Error Assigned No effect  no error

31. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Cut variedRatio Statistical Error Systematic Error (MC,particle ID, background subtraction, ke3g correction and trigger) Difference ratio ± correlated error Default K+ (min g 3 Gev) 0.244620.001080.00049 ( min g 5 GeV)0.245020.001180.00051+0.00040 ± 0.00056 Error Assigned K+ No effect  no error assigned Default K- (min g 3 GeV) 0.243540.001440.00057 ( min g 5 GeV)0.242770.001580.00059-0.00077 ± 0.00076 Error Assigned K- No effect  no error assigned Energy γ 2 Energy γ 1 Low neutral energy scale Recall, in August checks  shift in ratio 0.00095 due to final calibration missing in compact 7.1

32. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Varying the form factor λ + K+/K- Form factor model Ratio result (K+) ± 0.00108(stat) for all K+ numbers Difference Ratio result (K-) ± 0.00144 (stat) for all K- numbers Difference 0.0278 K + (PDG 2004: 0.0278±0.0070) 0.24462 ± 0.00049 (sys from MC) 0.24354 ± 0.00057 (sys from MC) 0.0271 K+ (PDG 2004 –1 σ) 0.24590 ± 0.00058 (sys from MC) +0.00127 0.24351 ± 0.00065 (sys from MC) -0.00002 0.0285 K+ (PDG 2004 +1 σ) 0.24511 ± 0.00058 (sys from MC) +0.00049 0.24318 ± 0.00065 (sys from MC) -0.00036 Systematic to be added ± 0.00062 This procedure was done with uncorrelated montecarlo. Based on the statistics, one cannot draw a conclusion. Error assigned the error due to the average MC statistics ± 0.00062 re-weighting In future, I will redo by using the default MC, and re-weighting each events based on the ratio of the form factors. ± 0.00062 should be a conservative estimate for now, until I re-do

33. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Momentum No systematic effect seen Vertex CutNo systematic effect seen Min Energy CutNo systematic effect seen Parameterization of form factor ± 0.00062 Additional Systematic Error ± 0.00062 Total Error systematic error K+ ± 0.00072 Total Error systematic error K- ± 0.00079 Summary Systematic checks

34. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Details of error contributions Γ(Ke3) / Γ(pipi0) Ratio of Γ(Ke3) / Γ(pipi0) K+K- 0.24462 ± 0.00134 0.24354 ±0.00164 Statistics from signal (number of Ke3 events data) 0.00102 0.00136 Statistics from normalization (number of pipi0 events data) 0.00036 0.00048 Total Statistical Error0.001180.00144 Background subtraction 0.000017 0.000015 Trigger efficiency in pipi0 events 0.00005 Trigger efficiency in ke3 events 0.00012 0.00020 Acceptance * Particle ID ke3 0.00042 0.00048 Acceptance * Particle ID pipi0 0.00020 0.00021 Error due to Ke3g correction for acceptance outside dalitz plot 0.00005 0.00010 Total systematic error (excluding Lambda)0.000490.00057 Error due to Lambda 0.00062

35. A. Dabrowski, June 08 2005 Ratio(ke3/pipi0) Summary of results K+ Γ(Ke3)/ Γ(pipi0) = 0.2446 ± 0.0010 (signal) ± 0.0004 (norm) ± 0.0005 (sys) ± 0.0006 (form factor) K- Γ(ke3)/ Γ(pipi0) = 0.2435 ± 0.0014 (signal) ± 0.0005 (norm) ± 0.0006 (sys) ± 0.0006 (form factor) K ± Γ(ke3)/ Γ(pipi0) = 0.2442 ± 0.0009 (stat) ± 0.0004 (sys) ± 0.0006 (form factor)  Result dominated by statistics not systematics! Recall ICHEP: Γ(ke3)/ Γ(pipi0) = 0.2433 +- 0.0009 (stat) +-0.0028 (sys) We are completely consistent!