Dynamical coupled-channels analysis of meson production reactions at EBAC@JLab

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Dynamical coupled-channels analysis ofmeson
production reactions at EBAC_at_JLab

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

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PDG s and Ns origin

• Most of their properties were extracted from
• Are they all genuine quark/gluon excitations
  (with meson cloud) ?
• Is their origin dynamical ?
• ? some could be understood as arising from
  meson-baryon dynamics

Need consistent analysis of pN and ppN channels
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Data change N structure study
Recent high precision data of meson photo- and
electro-production reactions open a great
opportunity of making quantitative study of the
N structure.
JLab, Bonn, GRAAL, Mainz, SPring-8,
e.g.) single pion electroproduction reactions
g
N
N
Corresponds to beam resolution
N
N-N e.m. transition form factors
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Excited Baryon Analysis Center _at_ Jefferson Lab
http//ebac-theory.jlab.org/
Founded in January 2006
Reaction Data

• Objectives and goals
• Through the comprehensive analysis
• of world data of pN, gN, N(e,e) reactions,
• Determine N spectrum
• (masses, widths)
• Extract N form factors, in particular
• the N-N electromagnetic transition
• form factors
• Develop a method to connect with
• hadron structure calculations and
• deduce the structure of N states

Dynamical Coupled-Channels Analysis _at_ EBAC
N parameters
Lattice QCD
Hadron Models
Explained in detail by Nobuhiko Suzuki
QCD
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Dynamical coupled-channels model _at_ EBAC
Meson production data
N spectrum, structure,
Reaction mechanism
Dynamical coupled-channels model of meson
production reactions
A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439
(2007) 193
Maintain coupled-channels unitarity of

• a
• a

Singular!
Can treat 3-body unitary cut
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Dynamical coupled-channels model _at_ EBAC
For details see Matsuyama, Sato, Lee, Phys. Rep.
439,193 (2007)

• Partial wave (LSJ) amplitude of a ? b reaction
• Reaction channels
• Potential

coupled-channels effect
Impose minimal number of bare N state at
present 16 of 18 ( of 3 and 4 Ns below 2
GeV)
meson exchange
bare N state
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Strategy for N study _at_ EBAC
Feedback
Application
Develop a method to connect our f.f.s with hadron
structure calculations
Feedback
Refit electro-magnetic part of parameters
Fit electro-magnetic part of parameters
Application
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Current status of the EBAC-DCC analysis
Hadronic part

• p N ? p N fitted to the SAID PWA up to W 2
  GeV.
• Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201
  (2007)
• p N ? p p N cross sections calculated with
  the pN model fit is ongoing.
• Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79
  025206 (2009)
• p N ? h N fitted to the data up to W 2 GeV
• Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78
  025204 (2008)
• g() N ? p N fitted to the data up to W
  1.6 GeV (and up to Q2 1.5 GeV2)
• (photoproduction) Julia-Diaz, Lee,
  Matsuyama, Sato, Smith, PRC77 045205 (2008)
• (electroproduction) Julia-Diaz, Kamano,
  Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)
• g N ? p p N cross sections calculated
  with the gN pN model fit is ongoing.
• Kamano, Julia-Diaz, Lee, Matsuyama, Sato,
  arXiv0909.1129 nucl-th
• g() N ? h N in progress
• g N ? K L in progress

Electromagnetic part

• Complete Experiment is planned by CLAS.
• Collaborated project on gp ? KL with
• A. Sandorfi (CLAS) and S. Hoblit (BNL)
• is in progress.

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Pion-induced hadronic reactions

1. scattering
2. reaction
3. reaction

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1. Pion-nucleon elastic scattering
Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201
(2007)

• coupled-channels is
  considered.
• Fitted to the SAID pN partial wave amplitudes
  up to 2 GeV.
• MINUIT library is employed for the numerical
  minimization.

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1. Pion-nucleon elastic scattering
Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201
(2007)
Angular distribution
Target polarization
EBAC
SAID06
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2. pi N ? pi pi N reaction
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79
025206 (2009)
Parameters used in the calculation are from pN ?
pN analysis.
Full result
C.C. effect off
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2. pi N ? pi pi N reaction
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79
025206 (2009)
Invariant mass distributions

• ( of pN ? ppN data) / ( of pN ? pN data)
  1200 / 24000
• Above W 1.5 GeV,
• All available data were measured more than 30
  years ago.
• No differential cross section data are
  available for
• quantitative fit (only the data without
  error bar exist).

Full result Phase space
Data handled with the help of R. Arndt
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3. pi N ? eta N reaction
Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78
025204 (2008)
N ? hN varied
Model constructed from pN ? pN analysis only
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Photon- and electron-induced reactions

1. reaction
2. reaction
3. reaction

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1. Single pion photoproduction (Q2 0)
Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77
045205 (2008)

• Fitted up to W 1.6 GeV.
• Only is varied.

• Comparison to data
• Total cross section
• Differential cross section
• Photon asymmetry

s (?b)
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2. Single pion electroproduction (Q2 gt 0)
Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki,
PRC80 025207 (2009)
Fit to the structure function data from CLAS
p (e,e p0) p
W lt 1.6 GeV Q2 lt 1.5 (GeV/c)2 is
determined at each Q2.
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3. Double pion photoproduction
Kamano, Julia-Diaz, Lee, Matsuyama, Sato,
arXiv0909.1129 nucl-th
Total cross sections at low energies W lt 1.4 GeV
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3. Double pion photoproduction
Kamano, Julia-Diaz, Lee, Matsuyama, Sato,
arXiv0909.1129 nucl-th
Full results gpND varied /- 20
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Summary and future plans
Summary

• The EBAC-DCC analysis has successfully
  constructed
• a reaction model describing pN ? pN, hN up
  to W 2 GeV and
• g()N ? pN up to W 1.6 GeV and Q2 1.5
  (GeV/c)2.
• The model has been applied to pN ? ppN and gN
  ? ppN.
• Refining model parameters by simultaneous,
• combined analysis of pN, gN ? pN, ppN, hN.
• Search for new N states via the analysis of
  pN, gN ? KY, wN.

Future plans for EBAC-DCC analysis
Problem Lack of hadronic data in ppN, KY, wN,
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back up
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Phase shift and inelasticity
W (MeV)
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Single pion photoproduction (Q2 0)
Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77
045205 (2008)
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2. Single pion electroproduction (Q2 gt 0)
Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki,
PRC80 025207 (2009)
Five-fold differential cross sections at Q2 0.4
(GeV/c)2
p (e,e p0) p
p (e,e p) n
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3. Double pion photoproduction
Kamano, Julia-Diaz, Lee, Matsuyama, Sato,
arXiv0909.1129 nucl-th
Invariant mass distributions
Full result (magnitude is normalized to the
data) Phase space
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Dynamical coupled-channels model for double pion
production reactions
All ingredients already prepared in 2-body
calculation !!
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Dynamical coupled-channels model for double pion
production reactions

2 ? 3 effective potential




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Approximate treatment of direct term


part of V23
part of
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Dynamical coupled-channels modelfor double pion
production reactions
To obtain g N ? p p N amplitude, just make
replacement below
where