Current Status of EBAC Project

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



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

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1

0

-1

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0

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



Current Status of EBAC Project

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