Dynamical coupled-channels analysis of meson production reactions at Hiroyuki Kamano (Excited Baryon Analysis Center, Jefferson Lab) in collaboration with B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, S. Nakamura, T. Sato, N. Suzuki

Need consistent analysis of  N and  N channels Need consistent analysis of  N and  N channels PDG *s and N*’s origin Most of their properties were extracted from Are they all genuine quark/gluon excitations (with meson cloud) ? Is their origin dynamical ?  some could be understood as arising from meson-baryon dynamics core meson cloud mesonbaryon ? ? ? ? ? Arndt, Briscoe, Strakovsky, Workman PRC (2006)

** N N* Recent high precision data of meson photo- and electro-production reactions open a great opportunity of making quantitative study of the N* structure. JLab, Bonn, GRAAL, Mainz, SPring-8, … Data change N* structure study Corresponds to beam resolution N-N* e.m. transition form factors N e.g.) single pion electroproduction reactions

Excited Baryon Analysis Jefferson Lab N* parameters QCDQCDQCDQCD Lattice QCDHadron Models Dynamical Coupled-Channels EBAC Reaction Data Founded in January 2006 Objectives and goals: Through the comprehensive analysis of world data of  N,  N, N(e,e’) reactions, Determine N* spectrum (masses, widths) Extract N* form factors, in particular the N-N* electromagnetic transition form factors Develop a method to connect with hadron structure calculations and deduce the structure of N* states Explained in detail by Nobuhiko Suzuki

A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439 (2007) 193 Dynamical coupled-channels model of meson production reactions Singular! a Dynamical coupled-channels EBAC Meson production data N* spectrum, structure, … Reaction mechanism Maintain coupled-channels unitarity of Can treat 3-body unitary cut

Partial wave (LSJ) amplitude of a  b reaction: Reaction channels: Potential: coupled-channels effect Dynamical coupled-channels EBAC meson exchange bare N* state Impose minimal number of bare N* state: at present 16 of 18 (= # of 3* and 4* N*s below 2 GeV) Impose minimal number of bare N* state: at present 16 of 18 (= # of 3* and 4* N*s below 2 GeV) For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)

Application Feedback Pass hadronic parameters Application Extract N*   N, KY,  N Application Extract N*   N, KY,  N Application Feedback Extraction of N-N* ele.-mag. transition form factors Extraction of N* poles and N*  MB decay vertices Strategy for N* EBAC Fit hadronic part of parameters Fit electro-magnetic part of parameters Refit hadronic part of parameters Refit electro-magnetic part of parameters Develop a method to connect our f.f.s with hadron structure calculations

Current status of the EBAC-DCC analysis  N   N : fitted to the SAID PWA up to W = 2 GeV. Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)  N    N : cross sections calculated with the  N model; fit is ongoing. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009)  N   N : fitted to the data up to W = 2 GeV Durand, Julia-Diaz, Lee, Saghai, Sato, PRC (2008)   N   N : fitted to the data up to W = 1.6 GeV (and up to Q 2 = 1.5 GeV 2 ) (photoproduction) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC (2008) (electroproduction)Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009)  N    N : cross sections calculated with the  N &  N model; fit is ongoing. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, arXiv: [nucl-th]   N   N : in progress  N  K  : in progress Hadronic part Electromagnetic part “Complete Experiment” is planned by CLAS.  Collaborated project on  p  K +  with A. Sandorfi (CLAS) and S. Hoblit (BNL) is in progress. “Complete Experiment” is planned by CLAS.  Collaborated project on  p  K +  with A. Sandorfi (CLAS) and S. Hoblit (BNL) is in progress.

1. scattering 2. reaction 3. reaction Pion-induced hadronic reactions

1. Pion-nucleon elastic scattering Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007) coupled-channels is considered. Fitted to the SAID  N partial wave amplitudes up to 2 GeV. MINUIT library is employed for the numerical minimization. Re(T) with I = 1/2

1. Pion-nucleon elastic scattering EBAC SAID06 Angular distribution Target polarization Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)

2. pi N  pi pi N reaction Parameters used in the calculation are from  N   N analysis. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009) Full result C.C. effect off

Full result Phase space Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009) Invariant mass distributions Data handled with the help of R. Arndt 2. pi N  pi pi N reaction (# of  N   N data) / (# of  N   N data) ~ 1200 / Above W = 1.5 GeV, All available data were measured more than 30 years ago. No differential cross section data are available for quantitative fit (only the data without error bar exist). (# of  N   N data) / (# of  N   N data) ~ 1200 / Above W = 1.5 GeV, All available data were measured more than 30 years ago. No differential cross section data are available for quantitative fit (only the data without error bar exist).

3. pi N  eta N reaction Durand, Julia-Diaz, Lee, Saghai, Sato, PRC (2008) N*   N varied Model constructed from  N   N analysis only

Photon- and electron-induced reactions 1. reaction 2. reaction 3. reaction

1. Single pion photoproduction (Q 2 = 0)  (  b)  Comparison to data –Total cross section –Differential cross section –Photon asymmetry Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC (2008) Fitted up to W = 1.6 GeV. Only is varied.

2. Single pion electroproduction (Q 2 > 0) Fit to the structure function data from CLAS Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009) p (e,e’  0 ) p W < 1.6 GeV Q 2 < 1.5 (GeV/c) 2 is determined at each Q 2.

3. Double pion photoproduction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, arXiv: [nucl-th] Parameters used in the calculation are from  N   N &  N   N analyses. Total cross sections at low energies W < 1.4 GeV

3. Double pion photoproduction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, arXiv: [nucl-th] Full results g  N  varied +/- 20%

Summary and future plans The EBAC-DCC analysis has successfully constructed a reaction model describing  N   N,  N up to W = 2 GeV and  ( * ) N   N up to W = 1.6 GeV and Q 2 = 1.5 (GeV/c) 2. The model has been applied to  N   N and  N   N. Refining model parameters by simultaneous, combined analysis of  N,  N   N,  N,  N. Search for new N* states via the analysis of  N,  N  KY,  N. Problem: Lack of hadronic data in  N, KY,  N,… Problem: Lack of hadronic data in  N, KY,  N,… Summary Future plans for EBAC-DCC analysis

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Phase shift and inelasticity W (MeV)

Single pion photoproduction (Q 2 = 0) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC (2008)

2. Single pion electroproduction (Q 2 > 0) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009) p (e,e’  0 ) p p (e,e’  + ) n Five-fold differential cross sections at Q 2 = 0.4 (GeV/c) 2

3. Double pion photoproduction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, arXiv: [nucl-th] Full result (magnitude is normalized to the data) Phase space Invariant mass distributions

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

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

Approximate treatment of direct term part of V 23 part of + =

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