#### Abstract

A dynamical approach is developed to predict the $\pi N$ scattering amplitudes starting with the constituent quark models. The first step is to apply a variational method to solve the three-quark bound state problem. The resulting wave functions are used to calculate the ${N}^{*}\to \pi N,\eta N,\pi \Delta $ vertex functions by assuming that the $\pi $ and $\eta $ mesons couple directly to quarks. These vertex functions and the predicted baryon bare masses then define a Hamiltonian for $\pi N$ reactions. We apply a unitary transformation method to derive from the constructed Hamiltonian a multichannel and multiresonance reaction model for predicting the $\pi N$ scattering amplitudes up to $W=2\mathrm{}$ GeV. With the parameters constrained by the $\Delta \mathrm{}\left(1232\right)\mathrm{}$ excitation, we have examined the extent to which the $\pi N$ scattering in the ${S}_{11}$ channel can be described by constituent quark models based on one-gluon-exchange or one-meson exchange mechanisms. It is found that the data seem to favor the spin-spin interaction due to one-meson exchange and the tensor interaction due to one-gluon exchange. A phenomenological quark-quark potential has been constructed to reproduce the ${S}_{11}$ amplitude.

DOI: http://dx.doi.org/10.1103/PhysRevC.61.065203

- Received 16 August 1999
- Revised 3 February 2000
- Published 17 May 2000

© 2000 The American Physical Society