Current Status of EBAC ProjectCurrent Status of EBAC Project

Hiroyuki KamanoHiroyuki Kamano

Excited Baryon Analysis Center, Jefferson LabExcited Baryon Analysis Center, Jefferson Lab

in collaboration within collaboration with

B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama,

T. Sato, K. TsushimaT. Sato, K. Tsushima

Approaches to determining N-N* form factors

N-N* form factor

QQCCDD

Lattice QCDHadron Models

Dynamical Coupled-Channels Analysis @ EBACDynamical Coupled-Channels Analysis @ EBAC

Reaction Data

Partial wave (LSJ) amplitude of a b reaction:

Reaction channels:

Potential:

c.c. effect

Coupled-channels model @ EBAC

meson exchangemeson exchange bare N* statebare N* state

Impose minimal number of bare N* state: at present15 of 23 (3* and 4* from PDG)

Impose minimal number of bare N* state: at present15 of 23 (3* and 4* from PDG)

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

Corresponds to theN-N* transition form factor!Corresponds to theN-N* transition form factor!

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

+=

Strategy for analysis @ EBAC

ApplicationApplication

Fit hadronic part of parameters

Fit electro-magneticpart of parameters

FeedbackFeedback

ApplicationApplication

FeedbackFeedback

Pass hadronic parameters

Refit hadronic part of parameters

Refit electro-magneticpart of parameters

Pass hadronic parameters

Application Extract N* N, KY, N

Application

Extract N* N, KY, N

N NJulia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)

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

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

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

N, N NParis, submitted to PRC

Achievements at EBAC

Pion-nucleon elastic scatteringJulia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)

Five coupled-channels are considered:

Fitted to the SAID N partial wave amplitudes up to 2GeV.

Pion-nucleon elastic scattering

N

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

Polarization1340 MeV1340 MeV1440 MeV1440 MeV1540 MeV1540 MeV1680 MeV1680 MeV1760 MeV1760 MeV1860 MeV1860 MeV

Single pion photoproduction reaction

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

Fitted to the data up to 1.65 GeV.

Only N* N bare helicity amps. are varied for the fitting.

Includes 1st and 2nd resonance regionIncludes 1st and 2nd resonance region

0 90 180 0 90 180

0 90 180 0 90 180

-1

1

0

-1

1

0

0

1154 MeV1154 MeV1232 MeV1232 MeV1285 MeV1285 MeV1417 MeV1417 MeV1513 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.

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

Outlook

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

~ end of 2008

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

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

~ end of 2009

Improved parameters are applied for (& further retuned by)

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

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

Back upBack up

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(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 !!

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 MeV

full

res. only

nonres. only

Results

W = 1440 MeVW = 1440 MeV

full

res. only

nonres. only

EBAC @ JLab

Excited Baryon Analysis Center (EBAC) at Jefferson LabExcited Baryon Analysis Center (EBAC) at Jefferson Labhtthttpp://ebac-theor://ebac-theoryy..jjlab.orlab.orgg//

Explore nature of the nucleon resonancesExplore nature of the nucleon resonances from analyzing world data from analyzing world dataof meson production reactions on the nucleon target: of meson production reactions on the nucleon target:

N, γN, γN, γN, γ** N N → → πN, ππN, ηN, ωN, φN, KY, …πN, ππN, ηN, ωN, φN, KY, …

Pole position of N* states on the complex energy plane

Transition form factors of N* states

Search for new N* states

… Closely related to the quark-gluon substructure of N* statesClosely related to the quark-gluon substructure of N* states

Contribution of V23

PRC result

PRC result + V23

0 90 180 0 90 180

0 90 180 0 90 180

-1

1

0

-1

1

0

0

1154 MeV1154 MeV1232 MeV1232 MeV1285 MeV1285 MeV1417 MeV1417 MeV1513 MeV1513 MeV1603 MeV1603 MeV

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

Single pion photoproduction reaction