S. X. Nakamura

Nucleon resonances within a dynamical coupled-channels model of

The nucleon resonances are investigated within a dynamical coupled-channels model of pi N and gamma N reactions up to the invariant mass W = 2 GeV. The meson-baryon (MB) channels included in the calculations are MB = pi N, eta N, K Lambda, K Sigma, and pi pi N that has pi Delta, rho N, and sigma N resonant components. The meson-baryon amplitudes T_{MB,MB}(W) are calculated from solving a set of coupled-channels integral equations defined by an interaction Hamiltonian consisting of (a) meson-exchange interactions v_{MB,MB} derived from phenomenological Lagrangian, and (b) vertex interactions N* --> MB for describing the transition of a bare excited nucleon state N* to a channel MB. The parameters of v_{MB,MB} are mainly constrained by the fit to the data of pi N --> pi N in the low energy region up to W =1.4 GeV. The bare masses of N* and the N* --> MB parameters are then determined in simultaneous fits to the data of pi N --> pi N up to W =2.3 GeV and those of pi N --> eta N, K Lambda, K Sigma and gamma N --> pi N, eta N, K Lambda, K Sigma up to W = 2.1 GeV. The pole positions and residues of nucleon resonances are extracted by analytically continuing the meson-baryon amplitudes T_{MB,MB}(W) to the complex Riemann energy surface. From the extracted residues, we have determined the N* --> pi N, gamma N, eta N, K Lambda, K Sigma transition amplitudes at resonance poles. We compare the resonance pole positions from our analysis with those given by Particle Data Group and the recent coupled-channels analyses by the Juelich and Bonn-Gatchina groups. Four results agree well only for the first N* in each spin-parity-isospin (J^P,I) channel. For higher mass states, the number of states and their resonance positions from four results do not agree well. We discuss the possible sources of the discrepancies and the need of additional data from new hadron facilities such as J-PARC.

\pi N

We develop a dynamical coupled-channels model of K^- p reactions, aiming at extracting the parameters associated with hyperon resonances and providing the elementary antikaon-nucleon scattering amplitudes that can be used for investigating various phenomena in the strangeness sector such as the production of hypernuclei from kaon-nucleus reactions. The model consists of (a) meson-baryon (MB) potentials v_{MB,MB} derived from the phenomenological SU(3) Lagrangian, and (b) vertex interactions Gamma_{MB,Y*} for describing the decays of the bare excited hyperon states (Y*) into MB states. The model is defined in a channel space spanned by the two-body barK N, pi Sigma, pi Lambda, eta Lambda, and K Xi states and also the three-body pi pi Lambda and pi barK N states that have the resonant pi Sigma* and barK* N components, respectively. The resulting coupled-channels scattering equations satisfy the multichannel unitarity conditions and account for the dynamical effects arising from the off-shell rescattering processes. The model parameters are determined by fitting the available data of the unpolarized and polarized observables of the K^- p --> barK N, pi Sigma, pi Lambda, eta Lambda, K Xi reactions in the energy region from the threshold to invariant mass W=2.1 GeV. Two models with equally good chi^2 fits to the data have been constructed. The partial-wave amplitudes obtained from the constructed models are compared with the results from a recent partial-wave analysis by the Kent State University group. We discuss the differences between these three analysis results. Our results at energies near the threshold suggest that the higher partial waves should be treated on the same footing as the S wave if one wants to understand the nature of Lambda(1405)1/2^- using the data below the barK N threshold, as will be provided by the J-PARC E31 experiment.

and

As a first step toward developing a reaction model that enables a comprehensive description of neutrino-nucleon reactions in the nucleon resonance region, we have applied for the first time a dynamical coupled-channels model, which successfully describes pi N, gamma N --> pi N, eta N, pi pi N, KLambda, KSigma reactions up to W = 2 GeV, to predict the neutrino-induced meson-production reactions with Delta S = 0 at the forward angle limit. This has been achieved by relating the divergence of the axial-current matrix elements at Q^2 = 0 to the pi N --> X reaction amplitudes through the PCAC hypothesis. We present the contributions from each of the pi N, eta N, pi pi N, KLambda, KSigma channels to the F_2 structure function at Q^2 --> 0 limit up to W = 2 GeV.

\gamma N

We have investigated the model dependence of meson resonance properties extracted from the Dalitz-plot analysis of the three-pions photoproduction reactions on the nucleon. Within a unitary model developed in Phys. Rev. D 84, 114019 (2011), we generate Dalitz-plot distributions as data to perform an isobar model fit that is similar to most of the previous analyses of three-pion production reactions. It is found that the resonance positions from the two models agree well when both fit the data accurately, except for the resonance poles near branch points. The residues of the resonant amplitudes extracted from the two models and by the usual Breit-Wigner procedure agree well only for the isolated resonances with narrow widths. For overlapping resonances, most of the extracted residues could be drastically different. Our results suggest that even with high precision data, the resonance extraction should be based on models within which the amplitude parametrization is constrained by three-particle unitarity condition.

reactions

We show that two P11 nucleon resonance poles near the pi Delta threshold, obtained in several analyses, are stable against large variations of parameters within a dynamical coupled-channels analysis based on meson-exchange mechanisms. By also performing an analysis based on a model with a bare nucleon state, we find that this two-pole structure is insensitive to the analytic structure of the amplitude in the region below pi N threshold. Our results are M_pole = (1363^{+9}_{-6} -i79^{+3}_{-5}) MeV and (1373^{+12}_{-10} -i114^{+14}_{-9}) MeV. We also demonstrate that the number of poles in the 1.5 GeV 1.6 GeV region for high precision resonance extractions.

Dynamical coupled-channels model of K − p reactions: Determination of partial-wave amplitudes

We show that two P11 nucleon resonance poles near the pi Delta threshold, obtained in several analyses, are stable against large variations of parameters within a dynamical coupled-channels analysis based on meson-exchange mechanisms. By also performing an analysis based on a model with a bare nucleon state, we find that this two-pole structure is insensitive to the analytic structure of the amplitude in the region below pi N threshold. Our results are M_pole = (1363^{+9}_{-6} -i79^{+3}_{-5}) MeV and (1373^{+12}_{-10} -i114^{+14}_{-9}) MeV. We also demonstrate that the number of poles in the 1.5 GeV 1.6 GeV region for high precision resonance extractions.

Neutrino-induced forward meson-production reactions in nucleon resonance region

We report our recent effort on the extraction of N*- and Delta*-resonance parameters (pole masses, coupling constants, etc.) through the comprehensive analysis of pion- and photon-induced pi N, eta N, K Lambda, and K Sigma production reactions. The analysis was performed with the ANL-Osaka dynamical coupled-channels approach, which satisfies the multichannel unitarity of the S-matrix in the channel space spanned by pi N, eta N, K Lambda, K Sigma, and also three-body pi pi N that contains rho N, pi Delta, and sigma N resonant components. Ongoing projects and future plans are also discussed.

Extraction of Meson Resonances from Three-pions Photo-production Reactions

The CC and NC coherent pion productions have been studied with PCAC-based models and microscopic models. Current status of the theoretical studies is reviewed.

On the extraction of P11 resonances from pi N data

We develop a model for describing excited mesons decay into three mesons. The properties of the excited mesons can be extracted with this model. The model maintains the three-body unitarity that has been missed in previous data analyses based on the conventional isobar models. We study an importance of the three-body unitarity in extracting hadron properties from data. For this purpose, we use the unitary and isobar models to analyze the same pseudo data of gamma p -> pi+pi+pi-n, and extract the properties of excited mesons. We find a significant difference between the unitary and isobar models in the extracted properties of excited mesons, such as the mass, width and coupling strength to decay channels.

Extraction of P11 resonances from pi N data

I explain the Sato-Lee (SL) model and its extension to the neutrino-induced pion production off the nucleon. Then I discuss applications of the SL model to incoherent and coherent pion productions in the neutrino-nucleus scattering. I mention a further extension of this approach with a dynamical coupled-channels model developed in Excited Baryon Analysis Center of JLab.