1. Optimization of  exclusion cut for the  + and  (1520) analysis Takashi Nakano Based on Draft version of Technical Note 42

2. What are the optimization criteria? Large signal acceptance Good S/N ratio No bias, no kinematical reflection

3. Photon energy in rest frame of the struck nucleon,

4. M KK (GeV) a)b) c) E  (GeV) M KK (GeV) E  (GeV) KK invariant mass distribution vs. photon energy: a) for a proton target, b) for a deuteron target in respect to the lab photon energy, and c) for a proton target in respect to the reconstructed photon energy in the nucleon rest frame.

5. M KK (GeV) M NK (GeV) a) ｂ)ｂ) ｃ)ｃ) M KK vs. MNK for non-resonant events (MC) at = 2 GeV (a), 2.2 GeV (b), and 2.4 GeV (c).  exclusion cut point must be as close to the  peak as possible in the low energy region.

6. E  (GeV) a)b) E  (GeV) M nK+ (GeV) Rejection of  exclusion cut can be refined by using E  in the nucleon frame.  exclusion can be tight in the high energy region E  in “n”rest frame E  in lab frame

7. Optimization procedure Step 1 Change the  exclusion cut parameters while keeping the acceptance the same. Step 2 Select the best set of the parameters by analyzing  (1520) events. Step 3 Apply the cut with the best set to the  analysis and also check the cut dependence. consistency check in the wide parameter region is very important

8. E  (GeV) M KK (GeV) Mibe’s  exclusion cut Cut was designed to keep N(  )/N(  ) constant (energy independent). Signal acceptance nor the S/N ratio was not optimized. The cut line is almost linear in the energy region above 2.2 GeV. The acceptance for 2-track KK events was about 14 %.

9. Definition of cut parameters slope offset M KK > slope(E g -2.0) + offset offset slope The slope parameter was changed from 0 to 0.15. The acceptance was kept at 15% for 2-track KK events. Other conditions with Acc=13% and 17% were also tested. Cuts with two lines were also tested. ACC = 15 %

10. N S Peak fitting Spectrum is fitted with a gaussian + linear background. Significance is calculated from the peak height (S) divided by its error. Signal to noise ratio (S/N) is defined at the peak position. Background level (N or BG) is defined at the peak position.

11. Fitting result:  (1520) in this 2x2 presentation, a fitted line is not correctly drawn. PAW’s bug? But the quality of the actual fit was fine!

12. Significance and S/N:  (1520) Both significance and S/N are the highest at slope=0.09

13. Fitting result:  

14. Significance and S/N:  + Both significance and S/N are the highest at slope=0.09

15. The best cut E   GeV) M KK  GeV) significance: 6.83 S/N: 1.38

16. Peak height and BG level

17. Check by LH2 data analysis narrower peak less background less affected by change of BG level and shape.

18. Yield and BG ratios Both peak height and BG level ratios are stable against change of the cut parameters. The yield ratio of  + to  (1520) is 0.5 x 0.5 x (11/16) = 0.17 yield ratio background ratio

19. Changing the slope The best fitting result was obtained with slope=0.09 and offset=1.02. Now, anchor the offset at 1.02 and change the slope parameter from 0 to 0.15. Signal acceptance is bigger for smaller slope. Background level (mainly due to  ) is bigger for smaller slope.

20. Fitting result:  (1520)

21. Fitting result:  

22. Peak heights of  (1520) and  +   BG Peak heights become lower with a smaller value of the slope parameter. Note: acceptance should not decrease

23. Check by LH2 data analysis LH2 LD2 slope=0.02  (1520) yield does not drop at small slope for LH2.

24. Effect of  background AB CD A slope=0.09 B slope=0.02-0.09 (  MC) C slope=0.02 D A+B Sharp rise of the  BG around 1.55 GeV dilutes the signal peak structure.

25.  BG subtraction at slope=0.04 Peak structure with a correct magnitude was reproduced by subtracting  contributions.

26.  BG subtraction at slope=0.02

27. Changing the low energy limit The low energy limit was varied from 2.0 to 1.9 GeV. The f exclusion cut parameters were kept at slope=0.09 and offset=1.02. Signal acceptance is bigger for a smaller energy limit. Background level (mainly due to  ) is bigger for a smaller energy limit.

28. Fitting results:  +

29. P min Cut dependence for E limit =1.9 and 2.0 GeV E limit =1.9 GeV E limit =2.0 GeV ■ Total # of events (normalized)  + yield saturates in the large P min region for E limit =2.0 GeV, but it gradually increases for E limit =1.9 GeV, which is almost proportional to the total number of the events.

30. Comparison of Fermi motion corrected and uncorrected spectra at E limit =2.0 GeV Difference is about 20 counts at the center of the peak, 2/3 of the peak height. - consistent with MC study

31. Comparison of Fermi motion corrected and uncorrected spectra at E limit =1.9 GeV real data MC(  )

32. Difference between Fermi motion corrected and uncorrected spectra Real data MC (  (not normalized) About 1/3 of the excess can be due to  BG. Need refined MC study to improve the accuracy.

33.  BG subtraction at E limit =1.9 and 2.0 GeV The peak height dropped from 46 to 31 for E limit =1.9. The peak height is stable (29 to 28) for E limt = 2.0. To get the cross-section below 2.0 Gev, we need a refined MC study.

34. Comparison of peak heights E limit dependence

35. 3 track events 3-track (a proton track in addition to a kaon pair) is a clear indication that the struck nucleon is a proton. no ntrk cutntrk=2variation  (1520) LH2 47.043.3-8%  (1520) LD2 54.649.9-9%  29.329.7+1% BG  (1520) 30.829.0-6% BG  + 22.721.5-5%

36. Summary The  exclusion cut was optimized by keeping the cut acceptance constant and maximizing the  significance and S/N ratio. The both significance and S/N ratio for the  + peak was turned out be maximum with the same cut. The heights and BG levels depend on the cut parameters very similarly for  (1520) and  +. The yield ratio is about 0.17. The effects of  contamination was studied: The background dilutes the signal peaks in the high energy region and causes a possible kinematical reflection in the low energy region. The effects can be simulated, but need more refined study to make it quantitative.  + events seems to come from a neutron.