Dynamical coupled-channel analysis of p N ? p p N reaction

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Dynamical coupled-channel analysis ofp N ? p p N
reaction

• Hiroyuki Kamano
• Excited Baryon Analysis Center (EBAC), Jefferson
  Lab
• In collaboration with
• B. Julia-Diaz, T.-S.H. Lee, A. Matsuyama, T. Sato

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Outline of the talk

• Brief introduction of activities in EBAC _at_ JLab
• Motivation for the analysis of p N ? p p N
  reaction
• Dynamical coupled-channel model
• Results (very preliminary!)
• Summary

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Introduction activities in EBAC (1)
Excited Baryon Analysis Center (EBAC) _at_ Jefferson
Lab
http//ebac-theory.jlab.org/
Explore nature of nucleon resonances from
analyzing world data of meson production
reactions on the nucleon pN, ?N, ? N ?
pN, ppN, ?N, ?N, fN, KY,

• Transition form factors of Nstates
• Pole position of N states on the complex
  energy plane
• Search for new N states

Related to the quark-gluon substructure of N
states
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Introduction activities in EBAC (2)
Meson production data
(quark-gluon) structure of N
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Introduction activities in EBAC (3)
First stage of model construction has been
completed.
Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201
(2007)
Fix all parameters by fitting to the empirical pN
partial wave amp. from SAID analysis
Describe well up to W 2 GeV!
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Motivation why pi pi N reaction?
Above W 1.5 GeV, cross sections of p N elastic
and p p N reactions can be comparable with each
other
c.f.) p p total elastic cross sections

• Expect that
• large coupled-channel effect can occur
• between the p N and p p N channels.
• additional constraints (which may be
• even severe) on N parameters could
• be obtained.

Inelastic (p p N dominated)
s mb
Elastic
W GeV
Particularly for
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Predicted p N? p p N total cross sections
Need to refit the model parameters
s mb
W GeV
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Dynamical coupled-channel model for meson
production reactions (1)
Matsuyama, Sato, Lee Phys. Rep. 439 (2007) 193
M
M
M
M

B
B
B
B
Non-resonant amp.
Rsonant amp.
MB ? MB non-resonant amplitude
Dressed N-MB vertex
Bare propagator
Meson cloud
Bare vertex
Self energy
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Dynamical coupled-channel model for meson
production reactions (2)
(Half off-shell) two-body amplitude (nonres.
res. amp.)
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Dynamical coupled-channel model for meson
production reactions (3)

2 ? 3 effective potential (V23)




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Treatment of resonance states
All 4-star and most 3-star resonances below 2
GeV are included assuming them as CDD poles
(genuine 3-quark states).
of Resonances
CDD poles listed in PDG S31 1 D(1620) P31 1
D(1910) P33 2 D(1232) D(1600) D33 1
D(1700) D35 0 F35 1 D(1905) F37 1
D(1950)
of Resonances
CDD poles listed in PDG S11
2 N(1535) N(1650) P11 2 N(1440)
N(1710) P13 1 N(1720) D13 1 N(1520) D15 1 N(1675)
F15 1 N(1680) F17 0
( N, D -resonance , N, D -resonance
)
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Procedure

• Simultaneous fit of
• the p N elastic, p N ? p p N, p N total
  cross sections.
• Varying only parameters of the bare vertex
  functions
• associated with
  decays

Bare vertex for N ? MB with orbital angular
momentum L and total spin S
Coupling constant
Cutoff
parameters
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Result 1 (preliminary)
s mb
Allow 20-50 variation of the parameters
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Result 2 (preliminary)
-1.9 ? 9.5
s mb
solid original dashed changed
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Result 3 (preliminary)
s mb
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Summary

• Have performed simultaneous fit of the model
• to the p N and p p N channels.
• Allowing 20-50 variation of parameters just
  results in
• a little improvement of p N ? p p N total
  cross sections.
• Inclusion of p p N channel to fitting could
  cause
• significant rearrangements of the N
  parameters
• Simultaneous consideration of p N and p p N
  channel
• seems inevitable to construct any reliable
  hadron
• reaction model below 2 GeV
• Include g N ? p p N reactions in the fitting.

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Back up
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of parameters
? 6 x 2 x 2 24
2 1 2 1 1 2 1 1 1 0 1 0 1 1
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Off-shell behavior of the amplitude in the MSL
model
e.g. ) s-channel p N Born term
Unitary transformation method
Usual Feynman graph calculation
For off-shell, the two methods give different
result