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Coupled-channels analysis of hadronic and electromagnetic p , h , two- p production reactions. Hiroyuki Kamano Excited Baryon Analysis Center, Jefferson Lab in collaboration with B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato. DNP08 Oct. 23-26.
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Coupled-channels analysis of hadronic and electromagneticp, h, two-p production reactions Hiroyuki Kamano Excited Baryon Analysis Center, Jefferson Lab in collaboration with B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato DNP08 Oct. 23-26
Dynamical Coupled-Channels Analysis @ EBAC Approaches to determining N-N* form factors Reaction Data Electromagnetic N-N* form factors Hadron Models Lattice QCD QCD
Through the dynamical reaction processes, g(*) N N* bare vertex functions get dressed: = + meson cloud bare Corresponds to the e.m.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: coupled-channels effect meson exchange bare N* state
What is needed for extracting electromagnetic N-N* form factors? Before analyzing eN e’ pN, e’ ppN, … , we need 1. Fixing hadronic parameters 2. Good model to describe gN reactions at Q2 = 0. Pure hadronic process; Determined from pN pN, ppN, hN • Critical for the model construction • Starting point to explore Q2 > 0 region Determined from gN pN, ppN, hN
Current status of the analysis @ EBAC Hadronic part • p N pN : fitted to the SAID PWA up to 2 GeV. Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) • p N pp N : cross sections calculated; notfitted yet. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC • p N h N : fitted to the data up to 2 GeV ( varied only bare N* hN ) Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008) • g N p N : fitted to the data up to 1.6 GeV ( varied only) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) • g N pp N : in progress • g N h N : in progress Electromagnetic part
pi N pi N & eta N Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008) • Five coupled-channels: • Fitted up to 2 GeV Differential cross sections and polarizations are also well reproduced !
gamma N pi N Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) • Fitted up to 1.6 GeV. • Only is varied. • Comparison to data • Total cross section • Differential cross section • Photon asymmetry σTOT (b)
Parameters used in the calculation are from pN pN analysis. pi N pi pi N Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC Need combined analysis of p N and pp N !
N-D13(1520) electromagnetic transition amplitude Q2 dependence comes from gNN, gpp, etc. ( well determined ) ( preliminary ) ( preliminary ) total meson cloud bare Need g*N pN analysis to determine Q2 dependence ofthe bare amplitude !
Improved parameters are applied to(& further retuned by) *N N (Julia-Diaz, Kamano, Lee, Matsuyama, Sato) (*)N N (Julia-Diaz, Kamano, Lee, Matsuyama, Sato) N N (Durand, Julia-Diaz, Lee, Saghai, Sato) Extract N-N* electromagnetic transition form factors beyond D !! Outlook 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 : 1.6 2 GeV
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
pi N eta N Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)
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
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
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
gamma N pi pi N reaction W = 1420 MeV W = 1780 MeV invariant mass distributions (very preliminary) In most energy, • Shape is reasonable. • Magnitude overestimates the data.
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 !!
Not included in No new parameter introduced Dynamical coupled-channels model for double pion production reactions + 2 → 3 effective potential … + + =
Approximate treatment of direct term = + part of V23 part of
Dynamical coupled-channels modelfor 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