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Dynamical Test of Constituent Quark Models with $πN$ Reactions

T. Yoshimoto·T. Sato·M. Arima·T. -S. H. Lee
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Abstract

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 $N^* \to πN, ηN, πΔ$ 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 multi-channel and multi-resonance 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 $S_{11}$ channel can be described by the constituent quark models based on the 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.

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T. Yoshimoto, T. Sato, M. Arima, T. -S. H. Lee. 1999-08-16. Dynamical Test of Constituent Quark Models with $πN$ Reactions. https://doi.org/10.1103/physrevc.61.065203

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