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

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

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

Strategy for analysis @ EBAC Application Extract N*  hN, KY, wN p N  p N Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) g N  p N Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (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, PRC78 025204 (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

Pion-nucleon elastic scattering Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Five coupled-channels are considered: Fitted to the SAID pN partial wave amplitudes up to 2GeV.

Pion-nucleon elastic scattering Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) 1680 MeV 1860 MeV 1760 MeV 1540 MeV 1340 MeV 1440 MeV Polarization N

Single pion photoproduction reaction Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (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. 

Single pion photoproduction reaction Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) 1417 MeV 1285 MeV 1232 MeV 1513 MeV 1154 MeV 0 90 180 0 90 180 1 1 -1 -1 0 90 180 0 90 180

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

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

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 !!

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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.

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 ( )

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

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

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

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

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

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

EBAC @ JLab … Pole position of N* states on the complex energy plane Excited Baryon Analysis Center (EBAC) at Jefferson Lab http://ebac-theory.jlab.org/ 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

Pion-nucleon elastic scattering Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Five coupled-channels are considered: Fitted to the SAID pN partial wave amplitudes up to 2GeV. Unitarity (optical theorem) is checked numerically!

Single pion photoproduction reaction Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) 1513 MeV 1232 MeV 1603 MeV 1154 MeV 1417 MeV 1285 MeV 0 90 180 0 90 180 1 1 -1 -1 0 90 180 0 90 180