Chiral quark-meson model of<i>N</i>and<i>Δ</i>with vector mesons

Abstract

We consider a model of N and \ensuremath{\Delta} built on quarks interacting with \ensuremath{\sigma}, \ensuremath{\pi}, \ensuremath{\rho}, ${A}_{1}$, and \ensuremath{\omega} mesons. We solve the problem in the mean-field approximation. The Lagrangian is based on the chiral SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) symmetry and incorporates the idea of universal coupling. Accordingly, \ensuremath{\rho} is coupled to the conserved isospin current, A to the partially conserved axial-vector current, and \ensuremath{\omega} to the conserved baryon current. As a result the only parameter of the model not directly related to experiment is the quark-pion coupling constant. Using the solitonic solution of the Lagrangian we calculate the properties of N and \ensuremath{\Delta}. It is found that the vector mesons play a very important role in the system, contributing significantly to the values of physical observables. We analyze the classical stability of the system with respect to breathing modes, which contain the lowest excitations. It is found that stable solutions exist only for a limited range of the values of the coupling constants.