Meson-baryon form factors in the chiral color dielectric model

Abstract

The renormalized form factors for pseudoscalar meson-baryon coupling are computed in the chiral color dielectric model. This has been done by rearranging the Lippmann-Schwinger series for the meson-baryon scattering matrix so that it can be expressed as a baryon pole term with renormalized form factors and baryon masses and the rest of the terms which arise from the crossed diagrams. Thus we are able to obtain an integral equation for the renormalized meson-baryon form factors in terms of the bare form factors as well as an expression for the meson self-energy. This integral equation is solved, and renormalized meson baryon form factors and renormalized baryon masses are computed. The parameters of the model are adjusted to obtain a best fit to the physical baryon masses. The calculations show that the renormalized form factors are energy dependent and differ from the bare form factors primarily at momentum transfers smaller than 1 GeV. At nucleon mass, the change in the form factors is about 10% at zero momentum transfer. The computed form factors are soft with the equivalent monopole cutoff mass of about 500 MeV. The renormalized coupling constants are obtained by comparing the chiral color dielectric model interaction Hamiltonian with the standard form of the meson-nucleon interaction Hamiltonian. The ratio of $\ensuremath{\Delta}N\ensuremath{\pi}$ and $\mathrm{NN}\ensuremath{\pi}$ coupling constants is found to be about 2.15. This value is very close to the experimental value.