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MC Check of Analysis Framework and Decay Asymmetry of
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Transcript of MC Check of Analysis Framework and Decay Asymmetry of
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MC Check of Analysis Frameworkand Decay Asymmetry of
W.C. Chang11/12/2005
LEPS Collaboration Meeting in Taiwan
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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; like
ly 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.
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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 model gives b ~5 GeV2
min||exp|| min
ttbttdt
ddtd
What causes this structure?Could be due to:
•Pseudo-scalar exchange?•0+ glueball trajectory?
Utilize the extra scrutiny power of polarization observables.
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Peak and Off Peak
Peak Off Peak
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Decay angular distributionsCurves: fit to the data.
•W sin∝ 2 helicity-conserving processes are dominating.•Positive 11-1natural parity exchanges are dominating.•Energy independence 11-1 N/UN ~const.
Forward angles; -0.2 < t+|t|min <0. GeV2
11-1=0.197 ±0.030
11-1=0.189 ±0.024
Peak
Off Peak
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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??
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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. Dec
ay asymmetry gets closer to +1.• The -meson exchange is about one o
rder smaller than that of -exchange in pp. 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)
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Isospin Effect in Decay Asymmetry of Quasi-free Photoproduction from NucleonsDue to isospin factor 3:• gpp and gpp are of the same
sign: constructive interference between -exchange and -exchange.
• gnn (= gpp )and gnn (=gpp ) are of opposite sign: destructive interference between -exchange and -exchange.
• Value of decay symmetry gets closer to +1 in nn, compared with pp.
Titov et al., PRC 59, R2993 (1999)
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One-dimensional Angular Distribution
= /2, in Horie-san’s convention
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Decay Asymmetry and Asymmetry of natural-parity and unnatural-parity exchange
Decay Asymmetry
Parity Asymmetry
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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 disentangle
d 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.
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MMd(,KK) of LH2
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MMd(,KK) of LD2
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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.
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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.
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MC: Coherent in LD2 (OFFSHELL=ON, t bin=20 MeV, (E)=10 MeV)
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MC: Incoherent in LD2
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MC: 1-d angular distribution
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MC: Asymmetry from 1d distribution
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[Coherent/Total] versus MMd Cut
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MC: 3 w/o and with different MMd cuts; 3 of coherent and incoherent components
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MC: 3 w/o and with different MMd cuts; 3 of coherent and incoherent components
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Maximum Likelihood Fit
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MC: from ML Fit
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MC: 3 w/o and with different MMd cuts
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MC: 3 of coherent and incoherent components
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Coherent Components in LD2 (OFFSHELL=ON, t bin=20 MeV, (E)=10 MeV)
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Incoherent Components in LD2
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LH2
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Energy dependence of t-slope
:LD2 coherent:LD2 incoherent:LH2
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Energy dependence of normalized intercept
:LD2 coherent:LD2 incoherent:LH2
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1-d angular distribution
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LD2: Asymmetry from 1d distribution
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LH2: Asymmetry from 1d distribution
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Asymmetry from 1d distribution:LD2 vs LH2
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LD2 Data: 3 w/o and with different MMd cuts; 3 of coherent and incoherent components
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LD2 Data: 3 w/o and with different MMd cuts; 3 of coherent and incoherent components
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LD2: from ML Fit
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LH2: from ML Fit
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from ML Fit : LD2 vs LH2
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LD2: 3 w/o and with different MMd cuts
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LD2: 3 of coherent and incoherent components
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Consistency of Analysis Results
Black: HorieRed: Chang, 1dBlue: Chang, ML
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Estimate of Systematic Errors from MC trails
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Estimate of Systematic Errors from MC trails
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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.