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Register a new userDynamical Coupled-Channel Model of $pi N$ Scattering in the W $leq$ 2 GeV Nucleon Resonance Region
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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.
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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.
The exclusive electroproduction process $ep rightarrow eppi^{0}$ was measured in the range of photon virtualities $Q^{2} = 0.4 - 1.0$~GeV$^{2}$ and the invariant mass range of the $ppi^{0}$ system of $W = 1.1 - 1.8$~GeV. These kinematics are covered in exclusive $pi^{0}$ electroproduction off the proton with nearly complete angular coverage in the $ppi^{0}$ center-of-mass system and with high statistical accuracy. Nearly 36000 cross section points were measured, and the structure functions $sigma_T+epsilonsigma_L$, $sigma_{LT}$, and $sigma_{TT}$, were extracted via fitting the $phi_{pi^{0}}$ dependence of the cross section. A Legendre polynomial expansion analysis demonstrates the sensitivity of our data to high-lying $N^*$ and $Delta^{*}$ resonances with $M~>~1.6$ GeV. As part of a broad effort to determine the electrocouplings of the $N^{*}$ and $Delta^{*}$ resonances using both single- and double-pion electroproduction, this dataset is crucial for the reliable extraction of the high-lying resonance electrocouplings from the combined isospin analysis of the $N pi$ and $pi^{+}pi^{-} p$ channels.
As a step toward performing a complete coupled-channels analysis of the world data of pi N, gamma^* N --> pi N, eta N, pi pi N reactions, the pi N --> pi pi N reactions are investigated starting with the dynamical coupled-channels model developed in Phys. Rev. C76, 065201 (2007). The channels included are pi N, eta N, and pi pi N which has pi Delta, rho N, and sigma N resonant components. The non-resonant amplitudes are generated from solving a set of coupled-channels equations with the meson-baryon potentials defined by effective Lagrangians. The resonant amplitudes are generated from 16 bare excited nucleon (N^*) states which are dressed by the non-resonant interactions as constrained by the unitarity condition. The data of total cross sections and pi N and pi pi invariant mass distributions of pi^+ p --> pi^+ pi^+ n, pi^+ pi^0p and pi^- p --> pi^+ pi^- n, pi^- pi^0 n, pi^0 pi^0 n reactions from threshold to the invariant mass W = 2 GeV can be described to a very large extent. We show the importance of the coupled-channels effects and the strong interference between the contributions from the pi Delta, sigma N, and rho N channels. The large interference between the resonant and non-resonant amplitudes is also demonstrated. Possible future developements are discussed.
Within the previously developed Dubna-Mainz-Taipei meson-exchange model, the singularity structure of the pi N scattering amplitudes has been investigated. For all partial waves up to F waves and c.m. energies up to W = 2 GeV, the T-matrix poles have been calculated by three different techniques: analytic continuation into the complex energy plane, speed-plot and the regularization method. For all 4-star resonances, we find a perfect agreement between the analytic continuation and the regularization method. We also find resonance poles for resonances that are not so well established, but in these cases the pole positions and residues obtained by analytic continuation can substantially differ from the results predicted by the speed-plot and regularization methods.
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.
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