1. Current Status of EBAC Project
Hiroyuki Kamano
Excited Baryon Analysis Center, Jefferson Lab
in collaboration with
B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama,
T. Sato, K. Tsushima

2. Approaches to determining N-N* form factors
Reaction Data
Dynamical Coupled-Channels EBAC
N-N* form factor
Hadron Models
Lattice QCD
QCD

3. Coupled-channels model @ EBAC
For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
Partial wave (LSJ) amplitude of a  b reaction:
Reaction channels:
Potential:
Corresponds to the
N-N* transition form factor!
Through the dynamical reaction processes,
N*  a bare vertex functions get dressed: + =
c.c. effect
Impose minimal number of
bare N* state: at present
15 of 23 (3* and 4* from PDG)
meson exchange
bare N* state

4. Strategy for analysis @ EBAC
Application
Extract N*  hN, KY, wN
p N  p N
Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)
g N  p N
Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC (2008)
p N  p p N
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC
p N  h N
Durand, Julia-Diaz, Lee, Saghai, Sato, PRC (2008)
p N, g N  w N
Paris, submitted to PRC
Achievements at EBAC
Fit hadronic part
of parameters
Refit hadronic part
of parameters
Feedback
Application
Pass hadronic parameters
Pass hadronic parameters
Feedback
Fit electro-magnetic
part of parameters
Refit electro-magnetic
part of parameters
Application
Application
Extract N*  hN, KY, wN

5. Pion-nucleon elastic scattering
Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)
Five coupled-channels are considered:
Fitted to the SAID pN partial wave amplitudes up to 2GeV.

6. Pion-nucleon elastic scattering
Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)
1680 MeV
1860 MeV
1760 MeV
1540 MeV
1340 MeV
1440 MeV
Polarization N

7. Single pion photoproduction reaction
Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC (2008)
Includes 1st and 2nd resonance region
Fitted to the data up to 1.65 GeV.
Only N* g N bare helicity amps. are varied for the fitting. 

8. Single pion photoproduction reaction
Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC (2008)
1417 MeV
1285 MeV
1232 MeV
1513 MeV
1154 MeV 1 1 -1 -1

9. 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 pN  pN analysis.
full result
c.c. effect off

10. pi N  pi pi N reaction invariant mass distributions
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC
invariant mass
distributions
full result
phase space
Key to improving parameters:
pp distributions at low W of
Data handled with the help of D. Arndt

11. Outlook Combined analysis of p N  p N, p p N and g N  p N
~ end of 2008
Combined analysis of p N  p N, p p N and g N  p N
(Julia-Diaz, Kamano, Lee, Matsuyama, Sato)
Retune parameters using the data of all three reactions.
Extends energy region of g N  p N up to 2 GeV
*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 D !!

12. Back up

13. gamma N  pi pi N reaction
W = 1420 MeV
W = 1780 MeV
invariant mass
distributions
(preliminary)
In most energy,
Shape is reasonable.
Magnitude
overestimates the data.

14. Dynamical coupled-channels model for double pion production reactions
All ingredients already prepared in 2-body calculation !!
Attach appropriate Green functions ( ) and vertex functions ( )
to p N (on-shell) → MB (off-shell) amplitude ( )

15. Dynamical coupled-channels model for double pion production reactions+
Not included in
No new parameter introduced
2 → 3 effective potential … + + =

16. Approximate treatment of direct term= +
part of V23
part of

17. Dynamical coupled-channels model for double pion production reactions
To obtain g N → p p N amplitude, just make replacement below:
where

19. Results
full
c.c. effect off
res. only
nonres. only

20. Results
full
res. only
nonres. only
W = 1790 MeV

21. Results
full
res. only
nonres. only
W = 1440 MeV

22. EBAC @ JLab … Pole position of N* states on the complex energy plane
Excited Baryon Analysis Center (EBAC) at Jefferson Lab
Explore nature of the nucleon resonances from analyzing world data
of meson production reactions on the nucleon target:
πN, γN, γ* N → 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* states

23. Pion-nucleon elastic scattering
Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)
Five coupled-channels are considered:
Fitted to the SAID pN partial wave amplitudes up to 2GeV.
Unitarity (optical theorem) is checked numerically!

24. Single pion photoproduction reaction
Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC (2008)
1513 MeV
1232 MeV
1603 MeV
1154 MeV
1417 MeV
1285 MeV 1 1 -1 -1