Pion-Nucleon Scattering and the $\pi$NN Coupling Constant in the Chiral Color Dielectric Model

Abstract

We apply the chiral color dielectric model to low- and medium-energy scattering within the coupled $\pi$N and $\pi \Delta$ system. Dynamic baryon states in which quarks are confined by the scalar color-dielectric field are constructed in Fock space. Spurious motion of the center of mass is eliminated by constructing momentum eigenstates via a Peierls-Yoccoz projection. The relativistic Lippmann-Schwinger equation is solved for the complex energies of the T matrix poles, and the pole positions of the nucleon and delta are used to fix the few parameters of the model. The $S$- and $P$-wave phase shifts, the bare N and $\Delta$ masses, the renormalized $\pi$NN and $\pi$N$\Delta$ coupling constants, and the $\pi$NN and $\pi$N$\Delta$ vertex functions are predicted. nucleon and delta are used to fix the few parameters of the model. The $S$- and $P$-wave phase shifts, the bare N and $\Delta$ masses, the renormalized $\pi$NN and $\pi$N$\Delta$ coupling constants, and the $\pi$NN and $\pi$N$\Delta$ vertex functions are predicted.

25 pages, 5 figures

References in corpus (1)

• A Cloudy Bag Model for the S-D Wave $\Kbar-N$ System

Cited by in corpus (6)

• The new mechanism for intermediate- and short-range nucleon-nucleon interaction
• Solution of the Bethe-Salpeter equation for pion-nucleon scattering
• Microscopic derivation of pion-nucleon and pion-Delta scattering lengths
• Soft-core meson-baryon interactions. II. $\pi N$ and $K^{+}N$ scattering
• Meson-Baryon Form Factors in Chiral Colour Dielectric Model
• Dihyperon in Chiral Colour Dielectric Model