Abstract:
It is shown that the threshold productions of $\pi^0 pp$, $\pi^+ np$ and $\pi^+ d$ from $pp$ collisions can be consistently described by a model consisting of a pion s-wave rescattering and $N\bar N$ pair-terms of heavy-meson exchanges. The large difference between $\sigma^{tot} (pp\rightarrow\pi ^+ d)$ and $\sigma^{tot} (pp\rightarrow\pi ^+ np)$ is understood from the orthogonality of the deuteron and the $np$ scattering wave functions. In a calculation using the Paris potential to account for the initial and final $NN$ interactions, it is found that the data can be best reproduced by using a soft $\pi NN$ form factor with $\Lambda_{\pi} =650 $ MeV for a monopole form. This is consistent with an earlier study of pion production in the $\Delta$ excitation region.

Abstract:
To facilitate the relativistic heavy-ion calculations based on transport equations, the binary collisions involving a $\Delta$ resonance in either the entrance channel or the exit channel are investigated within a Hamiltonian formulation of $\pi NN$ interactions. An averaging procedure is developed to define a quasi-particle $\Delta^*$ and to express the experimentally measured $NN\rightarrow \pi NN$ cross section in terms of an effective $NN\rightarrow N\Delta^\ast$ cross section. In contrast to previous works, the main feature of the present approach is that the mass and the momentum of the produced $\Delta^*$'s are calculated dynamically from the bare $\Delta \leftrightarrow \pi N$ vertex interaction of the model Hamiltonian and are constrained by the unitarity condition. The procedure is then extended to define the effective cross sections for the experimentally inaccessible $N\Delta^\ast \rightarrow NN$ and $N\Delta^\ast \rightarrow N\Delta^\ast$ reactions. The predicted cross sections are significantly different from what are commonly assumed in relativistic heavy-ion calculations. The $\Delta$ potential in nuclear matter has been calculated by using a Bruckner-Hartree-Fock approximation. By including the mean-field effects on the $\Delta$ propagation, the effective cross sections of the $NN\rightarrow N\Delta^\ast$, $N\Delta^\ast \rightarrow NN$ and $N\Delta^\ast \rightarrow N\Delta^\ast$ reactions in nuclear matter are predicted. It is demonstrated that the density dependence is most dramatic in the energy region close to the pion production threshold.

Abstract:
By using the convolution formula derived within the framework of relativistic quantum mechanics, we have examined the Fermi Motion effects on the ratios R_{pd/pp}= sigma^{pd}/(2 sigma^{pp}) between the proton-proton (p-p) and proton-deuteron (p-d) Drell-Yan cross sections. We have found that in the small x_2 < 0.3 region, the Fermi Motion effect is less than 1% and our results for the ratios R_{pd/pp} = sigma^{pd}/(2 sigma^{pp}) agree well with the data at 800 GeV. In the large Bjorken x_2 > about 0.4 region, the p-d Drell-Yan cross sections can be influenced strongly by the Fermi motion effect. At 120 GeV the predicted Fermi Motion effect can enhance the ratios R_{pd/pp} by about 20% at x_2 \sim 0.6 and about a factor of 2.5 at x_2 -> 1.0. Our results suggest that the Fermi motion effect, along with other possible nuclear effects, must be included, in extracting the \bar{d}/\bar{u} ratios in the proton from the experiments on p-p and p-d Drell-Yan processes at large x_2.

Abstract:
The development and results of the Dynamical Coupled-Channels analysis by a collaboration at the Excited Baryon Analysis Center (EBAC) are reported.

Abstract:
An effective Hamiltonian consisting of bare $\Delta \leftrightarrow\pi N$, $\gamma N$ vertex interactions and energy-independent meson-exchange $\pi N \leftrightarrow \pi N, \gamma N$ transition operators is derived by applying a unitary transformation to a model Lagrangian with $N,\Delta,\pi$, $\rho$, $\omega$, and $\gamma$ fields. With appropraite phenomenological form factors and coupling constants for $\rho$ and $\Delta$, the model can give a good description of $\pi N$ scattering phase shifts up to the $\Delta$ excitation energy region. It is shown that the best reproduction of the recent LEGS data of the photon-asymmetry ratios in $\gamma p \rightarrow \pi ^0 p$ reactions provides rather restricted constraints on the coupling strengths $G_E$ of the electric $E2$ and $G_M$ of the magnetic $M1$ transitions of the bare $\Delta \leftrightarrow \gamma N$ vertex and the less well-determined coupling constant $g_{\omega NN}$ of $\omega$ meson. Within the ranges that $G_M = 1.9 \pm 0.05$, $G_E = 0.0 \pm 0.025$, and $7 \leq g_{\omega NN}\leq 10.5$, the predicted differential cross sections and photon-asymmetry ratios are in an overall good agreement with the data of $\gamma p \rightarrow \pi ^0 p$, $\gamma p \rightarrow \pi ^+ n$, and $\gamma n\rightarrow \pi ^- p$ reactions from 180 MeV to the $\Delta$ excitation region. The predicted $M_{1^+}$ and $E_{1^+}$ multipole amplitudes are also in good agreement with the empirical values determined by the amplitude analyses. The constructed effective Hamiltonian is free of the nucleon renormlization problem and hence is suitable for nuclear many-body calculations. We have also shown that the assumptions made in the $K$-matrix method, commonly used in extracting empirically the $\gamma N \rightarrow \Delta$ transition amplitudes from the data, are consistent with

Abstract:
The development of a dynamical model for investigating the nucleon resonances using the reactions of meson production from \pi N, \gamma N, N(e,e'), and N(\nu,{\it l}) reactions is reviewed. The results for the \Delta (1232) state are summarized and discussed. The progress in investigating higher mass nucleon resonances is reported.

Abstract:
We discuss the difficulties in testing the hadron models by using the N^* parameters extracted from the empirical amplitude analyses of the pi-N and gamma-N reaction data. As an alternative or perhaps a more advantageous approach, we present a Hamiltonian formulation that can relate the pion production dynamics and the constituent quark models of N^* structure. The application of the approach in investigating the Delta and N^*(S_{11}) excitations is reviewed. It is found that while the Delta excitation can be described satisfactory, the pi-N scattering in S_{11} channel can not be described by the constituent quark models based on either the one-gluon-exchange or one-meson-exchange mechanisms. A phenomenological quark-quark potential has been constructed to reproduce the S_{11} amplitude.

Abstract:
Pion electroproduction amplitudes predicted by three theoretical models in the $Q^2 \leq 0.5$ (GeV/c)$^2$ region are compared. The objective is to facilitate the analyses of the data from new experiments on investigating the pion cloud effects on the $\gamma N \to \Delta$ transition form factors.

Abstract:
The dynamical model developed in [Phys. Rev. C 54, 2660 (1996)] has been applied to investigate the pion electroproduction reactions on the nucleon. It is found that the model can describe to a very large extent the recent data of p(e,e' pi^0) reaction from Jefferson Laboratory and MIT-Bates. The extracted magnetic dipole(M1), electric dipole(E2), and Coulomb(C2) strengths of the gamma N -> Delta transition are presented. It is found that the C2/M1 ratio drops significantly with Q^2 and reaches about -13% at Q^2=4 (GeV/c)^2, while the E2/M1 ratio remains close to the value \sim -3 % at the Q^2=0 photon point. The determined M1 transition form factor drops faster than the usual dipole form factor of the proton. We also find that the non-resonant interactions can dress the gamma N -> Delta vertex to enhance strongly its strength at low Q^2, but much less at high Q^2. Predictions are presented for future experimental tests. Possible developments of the model are discussed.