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

Photo-Production of  Mesons at 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.

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

Peak and Off Peak PeakOff Peak

Decay angular distributions Curves: fit to the data. W ∝ sin 2   helicity-conserving processes are dominating. Positive   natural parity exchanges are dominating. Energy independence   N/UN ~const. Forward angles; -0.2 < t+|t| min <0. GeV 2  =0.197 ±0.030  =0.189 ±0.024 Peak Off Peak

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

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 T n  =  T p . 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, (2002)

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)

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

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

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  i jk ’ 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.

MM d ( ,KK) of LH2

MM d ( ,KK) of LD2

Coherent vs Incoherent Proton 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.

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)= Incoherent events: –Exponential t-slope: 3 –All rho ’ s=0 except rho(1,1-1)=0.2, Im rho(2,1-1)=- 0.2.

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

MC: Incoherent in LD2

MC: 1-d angular distribution

MC: Asymmetry from 1d distribution

[Coherent/Total] versus MMd Cut

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

Maximum Likelihood Fit

MC:  from ML Fit

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

MC:  3 of coherent and incoherent components

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

Incoherent Components in LD2

LH2

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

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

1-d angular distribution

LD2: Asymmetry from 1d distribution

LH2: Asymmetry from 1d distribution

Asymmetry from 1d distribution: LD2 vs LH2

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

LD2:  from ML Fit

LH2:  from ML Fit

 from ML Fit : LD2 vs LH2

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

LD2:  3 of coherent and incoherent components

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

Estimate of Systematic Errors from MC trails

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.