Dynamical test of constituent quark models with πN reactions

A dynamical approach is developed to predict the πN 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*→πN,ηN,πΔ vertex functions by assuming that the π and η mesons couple directly to quarks. These vertex functions and the predicted baryon bare masses then define a Hamiltonian for πN reactions. We apply a unitary transformation method to derive from the constructed Hamiltonian a multichannel and multiresonance reaction model for predicting the πN scattering amplitudes up to $W=2$ GeV. With the parameters constrained by the Δ(1232) excitation, we have examined the extent to which the πN scattering in the S₁₁ 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 S₁₁ amplitude.