dorsal/arxiv
View SchemaDynamical Test of Constituent Quark Models with $\pi N$ Reactions
| Authors | T. Yoshimoto, T. Sato, M. Arima, T. -S. H. Lee |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9908048 |
| URL | https://arxiv.org/abs/nucl-th/9908048 |
| DOI | 10.1103/PhysRevC.61.065203 |
| Journal | Phys.Rev. C61 (2000) 065203 |
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 multi-channel and multi-resonance reaction model for predicting the $\pi N$ scattering amplitudes up to $W = 2$ GeV. With the parameters constrained by the $\Delta(1232$) excitation, we have examined the extent to which the $\pi N$ 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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"abstract": "A dynamical approach is developed to predict the $\\pi N$ scattering\namplitudes starting with the constituent quark models. The first step is to\napply a variational method to solve the three-quark bound state problem. The\nresulting wave functions are used to calculate the $N^* \\to \\pi N, \\eta N,\n\\pi\\Delta$ vertex functions by assuming that the $\\pi$ and $\\eta$ mesons couple\ndirectly to quarks. These vertex functions and the predicted baryon bare masses\nthen define a Hamiltonian for $\\pi N$ reactions. We apply a unitary\ntransformation method to derive from the constructed Hamiltonian a\nmulti-channel and multi-resonance reaction model for predicting the $\\pi N$\nscattering amplitudes up to $W = 2$ GeV. With the parameters constrained by the\n$\\Delta(1232$) excitation, we have examined the extent to which the $\\pi N$\nscattering in $S_{11}$ channel can be described by the constituent quark models\nbased on the one-gluon-exchange or one-meson-exchange mechanisms. It is found\nthat the data seem to favor the spin-spin interaction due to one-meson-exchange\nand the tensor interaction due to one-gluon-exchange. A phenomenological\nquark-quark potential has been constructed to reproduce the $S_{11}$ amplitude.",
"arxiv_id": "nucl-th/9908048",
"authors": [
"T. Yoshimoto",
"T. Sato",
"M. Arima",
"T. -S. H. Lee"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.61.065203",
"journal_ref": "Phys.Rev. C61 (2000) 065203",
"title": "Dynamical Test of Constituent Quark Models with $\\pi N$ Reactions",
"url": "https://arxiv.org/abs/nucl-th/9908048"
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