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Current Status of EBAC Project

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. Dynamical Coupled-Channels Analysis @ EBAC. Approaches to determining N-N* form factors. Reaction Data.

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Current Status of EBAC Project

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

  3. Through the dynamical reaction processes, N*  a bare vertex functions get dressed: = + Corresponds to the N-N* transition form factor! 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: 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. Extract N*  hN, KY, wN Application Achievements at EBAC Fit hadronic part of parameters Refit hadronic part of parameters • p N  pN Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) • g N  p N Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) • p N  pp 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 Application Extract N*  hN, KY, wN Strategy for analysis @ EBAC Feedback Application Pass hadronic parameters Pass hadronic parameters Feedback Refit electro-magnetic part of parameters Fit electro-magnetic part of parameters Application

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

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

  7. 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. 

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

  9. Parameters used in the calculation are from pN  pN analysis. pi N  pi pi N reaction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC full result c.c. effect off

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

  11. ~ end of 2009 Improved parameters are applied for (& further retuned by) *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) Extract N-N* electromagnetic transition form factors beyond D !! Outlook ~ end of 2008 Combined analysis of p N  p N, pp 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

  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. 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 All ingredientsalready prepared in 2-body calculation !!

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

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

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

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

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

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

  21. EBAC @ JLab 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

  22. Contribution of V23 PRC result PRC result + V23

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

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