MC Check of Analysis Framework and Decay Asymmetry of 

1. MC Check of Analysis Frameworkand Decay Asymmetry of  W.C. Chang 11/12/2005 LEPS Collaboration Meeting in Taiwan

2. Photo-Production of  Mesonsat Forward Region (small |t|) • Pomeron: • Positive power-law scaling of s. • Dominating at large energy. • Natural parity (=+1). • Exchange particles unknown; likely to be glueball : P1(J=2+), P2 (J=0+, negative power-law scaling of s, Ref: T. Nakano and H.Toki, 1998) • Pseudo-scalar particle: • Negative power-law scaling of s. • Showing up at small energy. • Un-natural parity (= –1). • Exchange particles like ,. • OZI suppressed.

3. What causes this structure? • Could be due to: • Pseudo-scalar exchange? • 0+ glueball trajectory? • Utilize the extra scrutiny power of polarization observables. World data near threshold Solid curve : A model with Pomeron + Pseudo scalar exchange (A. Titov et. al, PRC 67 (2003), 065205) A local maximum seen in ds/dt (t=tmin) near Eg=2 GeV. Smaller t slope near threshold. A simple extrapolation from high Eg by Regge modelgives b ～5 GeV2

4. Peak and Off Peak Peak Off Peak

5. Decay angular distributions Forward angles; -0.2 < t+|t|min <0. GeV2 Curves: fit to the data. Peak 11-1=0.197 ±0.030 Off Peak 11-1=0.189 ±0.024 • W ∝ sin2qhelicity-conserving processesare dominating. • Positive 11-1natural parity exchangesare dominating. • Energy independence 11-1 N/UN ~const.

6. Consistent with the scenario: • not due to unnatural-parity processes ONLY. • possible presence of additional natural parity exchange • signature of 0+ glueball trajectory?? Peak and Off Peak

7. Coherent  Photoproduction from Deuteron • Large radius of deuteron leads to fast deceasing form factor. A steeper exponential slope in t distribution. • In scattering amplitude, the unnatural-parity iso-vector  exchange is completely eliminated due to Tn= Tp. Decay asymmetry  gets closer to +1. • The -meson exchange is about one order smaller than that of -exchange in pp. Positive-parity components are expected to dominate in a significant way. Decay asymmetry  gets very close to +1. • Energy dependence of cross section. Deviation from that of Pomeron exchange will signal the other component(s) with positive-parity exchange. Titov et al., PRC 66, 022202 (2002)

8. Isospin Effect in Decay Asymmetry of Quasi-free  Photoproduction from Nucleons Due to isospin factor 3: • gpp and gpp are of the same sign: constructive interference between -exchange and -exchange. • gnn (= gpp )and gnn (=gpp ) are of opposite sign: destructive interference between -exchange and -exchange. • Value of decay symmetry gets closer to +1 in nn, compared with pp. Titov et al., PRC 59, R2993 (1999)

10. One-dimensional Angular Distribution = /2, in Horie-san’s convention

11. Decay Asymmetry and Asymmetry of natural-parity and unnatural-parity exchange Decay Asymmetry Parity Asymmetry

12. Method • Cross Section • Standard technique as SLH2. Acceptance function is evaluated by MC events. • The separation of coherent and incoherent components is done by the fit of MMd distribution. • Decay Asymmetry • 1d fit: standard technique as SLH2. Acceptance function is evaluated by MC events. • Maximum likelihood fit: 9 ijk’s can be determined simultaneously. • Contributions from coherent and incoherent components are disentangled by the measurements with different MMd cuts, i.e. different relative percentage of mixture of these two components in the event samples under the assumption of linear contribution.

13. MMd(,KK) of LH2

14. MMd(,KK) of LD2

15. Coherent vs IncoherentProton vs Neutron • Determine of relative ratios of coherent component to incoherent one by fitting MMd spectra with MC simulation. • In LD2 data, disentangle decay asymmetry of coherent interaction and incoherent one as functions of Egamma and t. • By the decay asymmetry results from LH2 and coherent part of LD2, disentangle decay asymmetry of interactions with protons and neutrons.

16. MC LD2 event sample • Coherent events: • Exponential t-slope: 15 • All rho’s=0 except rho(1,1-1)=0.5, Im rho(2,1-1)=-0.5. • Incoherent events: • Exponential t-slope: 3 • All rho’s=0 except rho(1,1-1)=0.2, Im rho(2,1-1)=-0.2.

17. MC: Coherent in LD2 (OFFSHELL=ON, t bin=20 MeV, (E)=10 MeV)

18. MC: Incoherent in LD2

19. MC: 1-d angular distribution

20. MC: Asymmetry from 1d distribution

21. [Coherent/Total] versus MMd Cut

22. MC: 3 w/o and with different MMd cuts; 3 of coherent and incoherent components

23. MC: 3 w/o and with different MMd cuts; 3 of coherent and incoherent components

24. Maximum Likelihood Fit

26. MC:  from ML Fit

27. MC: 3 w/o and with different MMd cuts

28. MC: 3 of coherent and incoherent components

29. Coherent Components in LD2 (OFFSHELL=ON, t bin=20 MeV, (E)=10 MeV)

30. Incoherent Components in LD2

31. LH2

32. Energy dependence of t-slope :LD2 coherent :LD2 incoherent :LH2

33. Energy dependence of normalized intercept :LD2 coherent :LD2 incoherent :LH2

34. 1-d angular distribution

35. LD2: Asymmetry from 1d distribution

36. LH2: Asymmetry from 1d distribution

37. Asymmetry from 1d distribution:LD2 vs LH2

38. LD2 Data: 3 w/o and with different MMd cuts; 3 of coherent and incoherent components

39. LD2 Data:3 w/o and with different MMd cuts; 3 of coherent and incoherent components

40. LD2:  from ML Fit

41. LH2:  from ML Fit

42. from ML Fit : LD2 vs LH2

43. LD2: 3 w/o and with different MMd cuts

44. LD2: 3 of coherent and incoherent components

45. Consistency of Analysis Results Black: Horie Red: Chang, 1d Blue: Chang, ML

46. Estimate of Systematic Errors from MC trails

47. Estimate of Systematic Errors from MC trails

48. Summary • Large exponential slope about 15 and strong energy dependence of intercept at t=tmin are observed for the coherent  production off LD2. The energy dependence of intercept for coherent LD2 events is distinctively different from those of LH2 and LD2 incoherent events. • Large decay asymmetry around the value of +1 is disentangled for coherent LD2 interaction. Consistent with theoretical prediction based on the absence of unnatural-parity -exchange and small contribution of η-exchange.. • Estimation of systematic errors by MC trials will be done.