Faddeev Approach to the Nucleon in the NJL model

Abstract

The nucleon and the delta are described as solutions of the relativistic Faddeev equation in the NJL model. We discuss the dependence of the baryon masses on the particular form of the four-Fermi interaction Lagrangians. Using the quark–diquark wave function, we calculate some bound state matrix elements such as the axial coupling constants, magnetic moments of the nucleon, the pion-nucleon sigma term and the proton-neutron mass difference. We also try to compare two pictures of describing the baryons in the NJL model, i.e. the mean-field approximation and the relativistic Faddeev approach. As a first step, we discuss how to improve the mean-field approximation by introducing an effective interaction. We also discuss the perturbative estimate of the deformation of the `vacuum" in the Faddeev approach.