Pion-Nucleon Scattering and the $π$NN Coupling Constant in the Chiral Color Dielectric Model
We apply the chiral color dielectric model to low- and medium-energy scattering within the coupled $π$N and $πΔ$ 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 $Δ$ masses, the renormalized $π$NN and $π$N$Δ$ coupling constants, and the $π$NN and $π$N$Δ$ 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 $Δ$ masses, the renormalized $π$NN and $π$N$Δ$ coupling constants, and the $π$NN and $π$N$Δ$ vertex functions are predicted.