Coupled-channels analysis of hadronic and Coupled-channels analysis of hadronic and electromagneticelectromagnetic

, , , two-, two- production reactions production reactions

Hiroyuki KamanoHiroyuki KamanoExcited Baryon Analysis Center, Jefferson LabExcited Baryon Analysis Center, Jefferson Lab

in collaboration within collaboration withB. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. SatoB. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato

DNP08 Oct. 23-26

Approaches to determining N-N* form factors

ElectromagneticN-N* form factors

QQCCDD

Lattice QCDHadron Models

Dynamical Coupled-Channels Analysis @ EBAC

Reaction Data

Partial wave (LSJ) amplitude of a b reaction:

Reaction channels:

Potential:

coupled-channels effect

Coupled-channels model @ EBAC

meson exchange bare N* state

For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)

Corresponds to the e.m. N-N* transition form factor!

Through the dynamical reaction processes, * N N* bare vertex functions get dressed:

+=

bare mesoncloud

1. Fixing hadronic parameters

2. Good model to describe N reactions at Q2 = 0.

What is needed for extracting electromagnetic N-N* form factors?

Pure hadronic process; Determined fromN N, N, N

Before analyzing eN e’ N, e’ N, … , we need

Determined fromN N, N, N

Critical for the model construction Starting point to explore Q2 > 0 region

Current status of the analysis @ EBAC

N N : fitted to the SAID PWA up to 2 GeV.Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)

N N : cross sections calculated; not fitted yet.Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC

N N : fitted to the data up to 2 GeV ( varied only bare N* N )Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)

N N : fitted to the data up to 1.6 GeV ( varied only )Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008)

N N : in progress

N N : in progress

Hadronic part

Electromagnetic part

pi N pi N & eta NJulia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)

Five coupled-channels:

Fitted up to 2 GeV

Differential cross sections and polarizations are also well reproduced !

gamma N pi Nσ T

OT (

b)

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

Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) Fitted up to 1.6 GeV.

Only is varied.

pi N pi pi NKamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC

Parameters used in the calculation are from N N analysis.

Need combined analysis of N and N !

N-D13(1520) electromagnetic transition amplitude

meson cloudbare

total ( preliminary ) ( preliminary )

Need *N N analysis to determine Q2 dependence of the bare amplitude !

Q2 dependence comes from NN, , etc. ( well determined )

Outlook

Retune parameters using the data of all three reactions. Extends energy region of N N : 1.6 2 GeV

Combined analysis of N N, N and N N

*N N (Julia-Diaz, Kamano, Lee, Matsuyama, Sato)

(*)N N (Julia-Diaz, Kamano, Lee, Matsuyama, Sato)

N N (Durand, Julia-Diaz, Lee, Saghai, Sato)

Improved parameters are applied to (& further retuned by)

Extract N-N* electromagnetic transition form factors beyond !!

(Julia-Diaz, Kamano, Lee, Matsuyama, Sato)

Back up

Pion-nucleon elastic scattering

N

Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)

Polarization1340 MeV1440 MeV1540 MeV1680 MeV1760 MeV1860 MeV

pi N eta NDurand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)

full result

phase space

Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC

pi N pi pi N reaction

invariant mass distributions

Data handled with the help of D. Arndt

Key to improving parameters: distributions at low W of

0 90 180 0 90 180

0 90 180 0 90 180

-1

1

0

-1

1

0

0

1154 MeV1232 MeV1285 MeV1417 MeV1513 MeV

Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008)

Single pion photoproduction reaction

pi N pi pi N reaction

full result

c.c. effect off

Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC

Parameters used in the calculation are from N N analysis.

W = 1420 MeV W = 1780 MeV

Shape is reasonable. Magnitude overestimates the data.

In most energy,

gamma N pi pi N reaction

invariant mass distributions(very preliminary)

Dynamical coupled-channels model for double pion production reactions

Attach appropriate Attach appropriate Green functionsGreen functions ( ) and ( ) and vertex functionsvertex functions ( ) ( )to to NN (on-shell) (on-shell) → → MBMB (off-shell) amplitude (off-shell) amplitude ( )( )

All ingredients already prepared in 2-body calculation !!

Dynamical coupled-channels model for double pion production reactions

+

2 2 → → 3 effective potential3 effective potential

= + …+

Not included inNot included inNo new parameter introducedNo new parameter introduced

Approximate treatment of direct term

part of V23 part of

+=

Dynamical coupled-channels modelfor double pion production reactions

To obtain N → N amplitude, just make replacement below:

where

Results

full

c.c. effect off

res. only

nonres. only

Results

W = 1790 MeVW = 1790 MeVfull

res. only

nonres. only

Results

W = 1440 MeVW = 1440 MeVfull

res. only

nonres. only