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Register a new userDynamical coupled-channel model of meson production reactions in the nucleon resonance region
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A dynamical coupled-channel model is presented for investigating the nucleon resonances in the meson production reactions induced by pions and photons. The model is based on an energy-independent Hamiltonian which is derived from a set of Lagrangians by using a unitary transformation method. By applying the projection operator techniques,we derive a set of coupled-channel equations which satisfy the unitarity conditions within the channel space spanned by the considered two-particle meson-baryon states and the three-particle $pipi N$ state. We present and explain in detail a numerical method based on a spline-function expansion for solving the resulting coupled-channel equations which contain logarithmically divergent one-particle-exchange driving terms resulted from the $pipi N$ unitarity cut. We show that this driving term can generate rapidly varying structure in the reaction amplitudes associated with the unstable particle channels. It also has large effects in determining the two-pion production cross sections. Our results indicate that cautions must be taken to interpret the $N^*$ parameters extracted from using models which do not include $pipi N$ cut effects.
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It is shown that most of the models for analyzing meson-baryon reactions in the nucleon resonance region can be derived from a Hamiltonian formulation of the problem. An extension of the coupled-channel approach to include $pipi N$ channel is briefly described and some preliminary results for the $N^*(1535)$ excitation are presented.
As a first step to analyze the electromagnetic meson production reactions in the nucleon resonance region, the parameters of the hadronic interactions of a dynamical coupled-channel model, developed in {it Physics Reports 439, 193 (2007)}, are determined by fitting the $pi N$ scattering data. The channels included in the calculations are $pi N$, $eta N$ and $pipi N$ which has $piDelta$, $rho N$, and $sigma N$ resonant components. The non-resonant meson-baryon interactions of the model are derived from a set of Lagrangians by using a unitary transformation method. One or two bare excited nucleon states in each of $S$, $P$, $D$, and $F$ partial waves are included to generate the resonant amplitudes in the fits. The parameters of the model are first determined by fitting as much as possible the empirical $pi N$ elastic scattering amplitudes of SAID up to 2 GeV. We then refine and confirm the resulting parameters by directly comparing the predicted differential cross section and target polarization asymmetry with the original data of the elastic $pi^{pm} p to pi^{pm} p$ and charge-exchange $pi^- p to pi^0 n$ processes. The predicted total cross sections of $pi N$ reactions and $pi Nto eta N$ reactions are also in good agreement with the data. Applications of the constructed model in analyzing the electromagnetic meson production data as well as the future developments are discussed.
In this report, we will briefly review the dynamical model of pion electroweak production reactions in the $Delta$ resonance region and report on our study of neutrino-nucleus reactions based on this model.
We perform an updated coupled-channel analysis of eta-meson production including all recent photoproduction data on the proton. The dip observed in the differential cross sections at c.m. energies W=1.68 GeV is explained by destructive interference between the $S_{11}(1535)$ and $S_{11}(1560)$ states. The effect from $P_{11}(1710)$ is found to be small but still important to reproduce the correct shape of the differential cross section. For the $pi^- N to eta N$ scattering we suggest a reaction mechanism in terms of the $S_{11}(1535)$, $S_{11}(1560)$, and $P_{11}(1710)$ states. Our conclusion on the importance of the $S_{11}(1535)$, $S_{11}(1560)$, and $P_{11}(1710)$ resonances in the eta-production reactions is in line with our previous results. No strong indication for a narrow state with a width of 15 MeV and the mass of 1680 MeV is found in the analysis. $eta N$ scattering length is extracted and discussed.
We present a coupled-channel Lagrangian approach (GiM) to describe the $pi N to pi N$, $2pi N$ scattering in the resonance energy region. The $2pi N$ production has been significantly improved by using the isobar approximation with $sigma N$ and $pi Delta(1232)$ in the intermediate state. The three-body unitarity is maintained up to interference pattern between the isobar subchannels. The scattering amplitudes are obtained as a solution of the Bethe-Salpeter equation in the $K$ matrix approximation. As a first application we perform a partial wave analysis of the $pi N to pi N$, $pi^0pi^0 N$ reactions in the Roper resonance region. We obtain $R_{sigma N}(1440)=27^{+4}_{-9}$,% and $R_{sigma N}(1440)=12^{+5}_{-3}$,% for the $sigma N$ and $pi Delta$ decay branching ratios of $N^*(1440)$ respectively. The extracted $pi N$ inelasticities and reaction amplitudes are consistent with the results from other groups.
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