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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
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Approaches to determining N-N* form factors
Reaction Data Dynamical Coupled-Channels EBAC N-N* form factor Hadron Models Lattice QCD QCD
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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
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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
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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.
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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
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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.
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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
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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
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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
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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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Back up
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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.
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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 ( )
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Dynamical coupled-channels model for double pion production reactions
+ Not included in No new parameter introduced 2 → 3 effective potential … + + =
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Approximate treatment of direct term
= + part of V23 part of
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Dynamical coupled-channels model for double pion production reactions
To obtain g N → p p N amplitude, just make replacement below: where
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Results full c.c. effect off res. only nonres. only
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Results full res. only nonres. only W = 1790 MeV
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Results full res. only nonres. only W = 1440 MeV
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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
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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!
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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
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