Study of Excited Nucleon States at EBAC: Status and Plans Hiroyuki Kamano (Excited Baryon Analysis Center, Jefferson Lab) in collaboration with B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki NSTAR 2009, April 19-22, 2009

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 are 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. ELSA, JLab, MAMI, … Data will change N* structure study Corresponds to beam resolution N-N* e.m. transition form factors N e.g.) single pion electroproduction

Approaches to extracting N* properties N* properties QCDQCDQCDQCD Lattice QCDHadron Models Reaction Data Dynamical Coupled-Channels EBAC

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 form factors 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  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 not finished. 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, arXiv:   N    N : in progress   N   N : in progress  N  K  : in progress Hadronic part Electromagnetic part Explained in detail by Bruno Julia-Diaz (PS7, Apr :15-11:40) Explained in detail by Bruno Julia-Diaz (PS7, Apr :15-11:40)

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 2GeV. MINUIT library is employed for the numerical minimization. Unitarity is satisfied in ~ 1 % !! Re(T) with I = 1/2

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

pi N  pi pi N reaction Parameters used in the calculation are from  N   N analysis. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009) Need combined analysis of  N and   N !

Full result Phase space Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009) Invariant mass distributions Data handled with the help of R. Arndt pi N  pi pi N reaction

How can we extract N* information? PROPER definition of N* mass and width  Pole position of the amplitudes N*  MB,  N decay vertices  Residue at the pole N* pole position ( Im(E 0 ) < 0 ) N* pole position ( Im(E 0 ) < 0 ) N*  b decay vertex N*  b decay vertex Need analytic continuation of the amplitudes !! Explained in detail by Toru Sato (Apr :00-14:30) Explained in detail by Toru Sato (Apr :00-14:30)

All extracted N*s originate from bare N* states. (At present it is found no pole associated with meson exchanges.) Comparison with PDG values Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, in preparationPRELIMINARY PDG values are close to ours! 1540 –191i 1642 –41i

Future works Extracting N*  MB,  N decay form factors from the EBAC model Searching for new N* states via the analysis of  N  K Y,  N Developing a method linking our form factors to Hadron models and Lattice QCD calculations Refinement of the model parameters with the combined analysis of  N,   N   N,  N Full treatment of the direct  N 3-body unitarity cut. Model Upgrade N* Study

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All extracted N*s originate from bare N* states. (At present it is found no pole associated with meson exchanges.) Comparison with PDG values Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, in preparationPRELIMINARY PDG values are close to ours! 1540 –191i 1642 –41i

Meson-baryon potentials (Driving terms of LS eq.) All potentials are described in Matsuyama, Sato, Lee, Phys. Rep (2007)

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

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

Contribution of V23 PRC result PRC result + V23