Electroweak Meson Production Reaction in the Nucleon resonance Region T. Sato Osaka U Collaborators : H. Kamano(RCNP),S.Nakamura(Osaka), T. Murata(Osaka), T. –S. H. Lee(ANL), Jiajun Wu(ANL) Contents Coupled channel approach of weak meson production reactions in resonance region Pion production reaction on deuteron in the Delta resonance region Aug. 2014 CETUP* Coupled channel approach of weak meson production reactions in resonance region QE DIS Resonance region W < 2GeV RES DIS Atmospheric W > 2GeV Q^2 > 1 GeV^2 T2K Collaboration at J-PARC Branch of KEK theory center Y. Hayato(ICRR, U. of Tokyo), M. Hirai(Tokyo Science U.),H. Kamano(RCNP,Osaka U.),S. Kumano(KEK),S. Nakamura(YITP,Kyoto U.),T. Murata(Osaka U.),K. Saito(Tokyo Science U.),T. Sato(Osaka U.),M. Sakuda(Okayama U.) πN X, πN Δ (1232) Delta(1232) resonance stands as clear peak N*: 1440, 1520, 1535, 1650, 1675, 1680, ... πN X, πN Δ : 1600, 1620, 1700, 1750, 1900, … Delta(1232) resonance stands as clear peak 1.4 < W < 2GeV ~20 resonances N*: 1440, 1520, 1535, 1650, 1675, 1680, ... πN X, πN Δ : 1600, 1620, 1700, 1750, 1900, … Feature of N*,Δ resonances • excite states of nucleons are unstable particles and appear as resonances • strong coupling of excited states with meson-baryon continuum large width (~> 100MeV) and overlapping resonances • resonance informations are extracted from the partial wave analysis of the meson production reaction amplitudes amplitudes of MB channels are related through unitarity Need for the coupled channel analysis of various Meson-Baryon channel to disentangle nucleon resonances Reaction Data past two decades, high precision data from Jlab,Mainz, Bonn, GRALL, Spring8 • Combined analysis of available single pion,eta, kaon production incorporating two pion finat state with Coupled-Channels approach • Extraction of resonance parameters(Mass, transition form factor) from the partial wave amplitudes Mass, Width, Electromagnetic N-N* form factors Hadron Models Lattice QCD QCD Dynamical Coupled channel approach: ANL-Osaka, Julich model of meson production reaction in resonance region D. Rein, L.M. Sehgal, Ann. Phys. 133, 79(1981) O. Lalakulich, E. A. Paschos, G. Piranishvik,PRD74, 014009(2006) T. Leitnerm, O. Buss,L. Alvarez-Ruso, U. Mosel, PRC79, 034601(2009) dynamical coupled-channels (DCC) model Building block of our model s-channel u-channel t-channel contact p, r, s, w,.. N N, D Effective interaction generated by eliminating 1,3 particles channel Bare N* N*bare Z-diagrams Self energy in piD green function each potential affects many partial waves partial waves, W-region, MB channels are related simultaneous analysis MB channels restricts model, but time consuming to fit data Scattering amplitude of pion and photon induced meson production amplitudes are obtained by solving two body, coupled channel integral equation (3-dim reduction) in momentum space (partial waves [I,J,P] ) Scattering amplitude can be rewritten as Dynamical Coupled-Channels analysis (JLMS) (SL) 1996-2001 pp pN W<1.3 • 2006-2009 2010-2013 (gN,pN,hN,pD,rN,sN) (gN,pN,hN,pD,rN,sN,KL,KS) W < 2 GeV < 2.3 GeV < 1.6 GeV < 2 .1GeV p-p hn < 2 GeV < 2.1 GeV gp hp ― < 2.1 GeV pp KL, KS ― < 2.1 GeV gp KL, KS ― < 2.1 GeV gp pN • • (ANL-Osaka) < 1.3 Extended to include KY production reaction, higher W Fully combined analysis of gN , pN pN , hN , KL, KS reactions SU(3) Meson (P,V octet), Baryon(octet,decuplet) omega N, pipi N are not included in fit SL PRC 54, 2660(96), PRC63, 055201(01) JLMS PRC76, 065201(07) ANL-Osaka PRC88, 035209(13) • • Extensive data of differential cross section can be fitted very well for W<1.9GeV. Not able to account forward peak W>1.933GeV pi N pi pi N reaction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) Parameters used in the calculation are from pN pN analysis. Full result Full result C.C. effect off Phase space Data handled with the help of R. Arndt resonance poles and residues of scattering amplitudes Spectrum of N* and Delta (ANL-Osaka) Half width Some freedom exists on the definition of partial width from the residue of the amplitude. The numbers should be taken as a one estimation of the MB-res coupling strength . weak meson production reaction DCC model for neutrino interaction n Vector current Q2=0 gp MB gn pN Q2≠0 isospin separation necessary (electromagnetic form factors for VNN* couplings) from (e,e’ p), (e,e’ X) data analysis We’ve done first analysis of all these reactions VNN*(Q2) fixed neutrino reactions Axial current S N* i Q2=0 non-resonant mechanisms i + + + ... A N* PCAC p N* resonant mechanisms Interference among resonances and background can be made under control within DCC model Caveat for this presentation : phenomenological axial currents are added to maintain PCAC relation ds / dW (g n p-p) for W=1.1 – 2.0 GeV Q2=0 Analysis of electron-proton scattering data Purpose : Determine Q2 –dependence of vector coupling of p-N* : VpN*(Q2) Data : * 1p electroproduction * Empirical inclusive inelastic structure functions sT , sL Christy et al, PRC 81 (2010) Database • p(e,e’p0)p • p(e,e’p+)n • both region where inclusive sT & sL are fitted N(e,e’pi)N cross section Inclusive structure function Result on single pion electroproduction sT + e sL for W=1.1 – 1.68 GeV p(e,e’p0)p Q2=0.40 (GeV/c)2 p(e,e’p+)n sT & sL (inclusive inelastic) DCC sT sL Christy et al PRC 81 region where inclusive sT & sL are fitted Q2=0.40 (GeV/c)2 Mechanisms for nm N m p N D dominates for nm p m- p+ p (I=3/2) for En ~ 2 GeV Non-resonant mechanisms contribute significantly Higher N*s becomes important En ~2 GeV for nm n m- p N Cross section for nm N m- X pN & ppN are main channels in few-GeV region hN, KY cross sections are 10-1 – 10-2 smaller single and two pion production cross section Development of DCC model for nN interaction in resonance region Start with DCC model for gN, pN pN, ppN, hN, KL, KS extension of vector current to Q2≠0 region, isospin separation through analysis of e—- p & e—-’n’ data for W ≤ 2 GeV , Q2≤ 3 (GeV/c)2 Development of axial current for nN interaction; more study needed Summary pN & ppN are main channels in few-GeV region DCC model prediction is consistent with ANL data D, N*s, non-resonant are all important in few-GeV region (for nm n m- X ) essential to understand interference pattern among them DCC model can do this; consistency between p interaction and axial current Pion production reaction on deuteron in the Delta(1232) Region Pion production reaction on deuteron in the Delta(1232) Region J. Wu, T. –S. H. Lee, T. Sato Data of neutrino induced pion production on nucleus nu-d data ANL(PRD19,2521, PRD26,1161), BNL(PRD34,2554,PRD42, 1331) Fermi-motion L. Alvarez-Ruso et al. PRD59,3386 How large nuclear effects? Final State Interaction (nucleon-nucleon, pion-nucleon rescattering) Deuteron reaction: microscopic theoretical estimation of FSI is possible model can be tested by comparing data of pion photoproduction predict nuclear effects on neutrino reaction Impulse amplitude Fermi motion is included Final state interaction(one-loop) ~ DWIA Nucleon-nucleon scattering Pion-N rescattering FSI in pion photoproduction J.M. Laget Phys.Rep 69,1(1981),M.Schwamb Phys.Rep. 485,109(2010) M.I.Levchuk et al., PRC74,014004(2006) Model of pi-N, electroweak pion production T-matrix for the delta(1232) resonance region (W<1.3GeV, SL model) Start from Lagrangian based on chiral symmetry and electroweak Standard Model Sato,Uno,Lee PRC67(2003) Matsui,Sato,Lee PRC72(2005) CC NC, PV(e,e’) Effective Hamiltonian resonance Vector Axial vector Non-resonant int. g N D(1232) form factors compared with Lattice QCD data (2006) DCC 3/2+ 1/ 2 + Kitagaki et al. (90) BNL Barish et al.(79) ANL FSI : pion production reaction on deuteron Pion photoproduction (Differential cross section) With FSI, both pi- and pi0 production angular distribution is well reproduced. Pion photoproduction(Total cross section) and role of FSI Impulse Impulse + NN Impulse+NN+piN Large FSI(NN) for pi0 production Impulse Impulse + NN Impulse+NN+piN ~ Delta-QF kinematics Summary Rescattering effects are examined for electroweak deuteron reactions Using, pion production model of SL and Bonn-Pot, pion(pi^-,pi^0) photoproduction on deuteron are reasonably well described. Neutrino induced pion production reaction(CC): Within the kinematical region we have examined: Large effects of nucleon rescattering even Delta-QE peak especially FSI in 3S1 >1S0 Effects of piN rescattering were small