Dynamical coupled-channels approach to meson production reactions in the N* region and its application to neutrino-nucleon/nucleus reactions Hiroyuki Kamano (RCNP, Osaka Univ.) Seminar at J-PARC, March 19, 2012

Since the late 90s, huge amount of high precision data of meson photo-production reactions on the nucleon target has been reported from electron/photon beam facilities. JLab, MAMI, ELSA, GRAAL, LEPS/SPring-8, … Experimental developments E. Pasyuk’s talk at Hall-B/EBAC meeting Opens a great opportunity to make quantitative study of the N* states !!

Objectives and goals: Through the comprehensive analysis of world data of  N,  N, N(e,e’) reactions, Determine N* spectrum (pole masses) Extract N* form factors (e.g., N-N* e.m. transition form factors) Provide reaction mechanism information necessary for interpreting N* spectrum, structures and dynamical origins Dynamical coupled-channels analysis of meson production reactions Spectrum, structure,… of N* states QCDQCDQCDQCD Lattice QCDHadron Models Analysis Based on Reaction Theory Reaction Data H. Kamano (RCNP), T.-S. H. Lee (ANL), S. Nakamura (JLab), T. Sato (Osaka U./KEK) B. Julia-Diaz (Barcelona U.), A. Matsuyama (Shizuoka U.), N. Suzuki (Osaka U.)

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 model for meson production reactions Meson production data N* spectrum, structure, … Reaction dynamics

Hadronic amplitudes in the DCC model + Non-resonant amp. Rsonant amp. M B B’ M’ B B’ MM’ Amplitudes of two-body meson-baryon reactions For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) Reaction channels:

Hadronic amplitudes in the DCC model For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) + Non-resonant amp. Rsonant amp. M B B’ M’ B B’ MM’ = = + … M’’ B’’  N N,  s-channel u-channel t-channelcontact   N    N   Exchange potentials “Z-diagrams” ~ 150 Feynman diagrams Meson-Baryon Green functions Stable channels N       N N Quasi 2-body channels   Produce 2-body and 3-body  N cuts required by the unitarity !! 

Hadronic amplitudes in the DCC model For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) + Non-resonant amp. Rsonant amp. M B B’ M’ B B’ MM’ = = + … M’’ B’’

Hadronic amplitudes in the DCC model For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) + Non-resonant amp. Rsonant amp. M B B’ M’ B B’ MM’ + = Dressed N*-MB vertex Meson cloud Bare vertex Bare propagator (Bare mass) Bare propagator (Bare mass) Self energy = + Dressed N* propagator Non-resonant amp. Effects of rescattering processes (reaction dynamics) are included consistently with the unitarity of S-matrix.

Electromagnetic amplitudes in the DCC model + Non-resonant amp. Rsonant amp.  B B’ M’ B B’ M’ E.M. current interactions are treated perturbatively. For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)  + = + = Dressed  N  N* vertex Bare vertex Rescattering effect

DCC analysis of meson production reactions (current status)  p   N  p   N  -p   n  p   p  p  K , K   p  K ,  K  2006 ~ channels (  N,  N, ,  N,  N) < 2 GeV < 1.6 GeV < 2 GeV ― 2010 ~ channels (  N,  N, ,  N,  N,K ,K  ) < 2.1 GeV < 2 GeV < 2.2 GeV # of coupled channels Fully combined analysis of  N,  N   N,  N, K , K  reactions !! Kamano, Nakamura, Lee, Sato (2012)

Analysis Database Pion-induced reactions (purely strong reactions) Pion-induced reactions (purely strong reactions) Photo- production reactions Photo- production reactions ~ 28,000 data points to fit

Partial wave amplitudes of pi N scattering Kamano, Nakamura, Lee, Sato 2012 Previous model (fitted to  N   N data only) [PRC (2007)] Real partImaginary part

Pion-nucleon elastic scattering Target polarization 1234 MeV 1449 MeV 1678 MeV 1900 MeV Kamano, Nakamura, Lee, Sato, 2012

pi N  MB reactions Kamano, Nakamura, Lee, Sato, MeV 1845 MeV 1985 MeV 2031 MeV 1757 MeV 1879 MeV 1966 MeV 2059 MeV 1792 MeV 1879 MeV 1966 MeV 2059 MeV

Data handled with the help of R. Arndt 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 Phase spaceFull result W (GeV)  (mb) C. C. effect off

Single pion photoproduction Kamano, Nakamura, Lee, Sato, 2012 up to 1.6 GeV Previous model (fitted to  N   N data up to 1.6 GeV ) [PRC (2008)] Angular distribution Photon asymmetry 1137 MeV1232 MeV1334 MeV 1462 MeV1527 MeV1617 MeV 1729 MeV1834 MeV1958 MeV Kamano, Nakamura, Lee, Sato, MeV1232 MeV1334 MeV 1462 MeV1527 MeV1617 MeV 1729 MeV1834 MeV1958 MeV

Kamano, Nakamura, Lee, Sato 2012

Kamano, Nakamura, Lee, Sato 2012

Kamano, Nakamura, Lee, Sato 2012

Kamano, Nakamura, Lee, Sato 2012

Kamano, Nakamura, Lee, Sato 2012

Kamano, Nakamura, Lee, Sato 2012

Double pion photoproduction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009) Parameters used in the calculation are from  N   N &  N   N analyses. Good description near threshold Reasonable shape of invariant mass distributions Above 1.5 GeV, the total cross sections of p  0  0 and p  +  - overestimate the data.

Single pion electroproduction (Q 2 > 0) Fit to the structure function data (~ 20000) 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. N*N  (q 2 = -Q 2 ) q N-N* e.m. transition form factor

N, N* Meson cloud effect in gamma N  N* form factors G M (Q 2 ) for  N   (1232) transition Note: Most of the available static hadron models give G M (Q 2 ) close to “Bare” form factor. Full Bare

How to extend the DCC model to neutrino reactions + Non-resonant amp. Rsonant amp.  B B’ M’ B B’ M’ Just replace E.M. current by vector and axial currents.  + = + = Dressed  N  N* vertex Bare vertex Rescattering effect V, A Dressed VN or AN  N* vertex V, A

How to extend the DCC model to neutrino reactions V, A Vector partAxial part What we need to do: Ready for neutrino reaction (We can get all isospin components simply by isospin rotation.) Evaluation of  neutron  N* vertices for I = ½ N* states For N*s except  (1232), as a first step, we evaluate A N  N* vertices from  NN* couplings by making use of PCAC. Construct AN  MB potential for MB = ,  N,  N, K , K  (We already have the potential for MB =  N case.)