The Goldberger-Treiman relation and the chiral soliton model

Abstract

Abstract The linear chiral soliton model with explicit quark fields and elementary pion- and sigma-fields is solved in order to describes nucleon and delta properties. Special emphasis is put on the axial vector coupling constant g A and on the Goldberger-Treiman relation. To this end baryon Fock states are constructed in a mean field approximation with hedgehog-like configurations from which the physical states are obtained by projection techniques. It is shown that the Goldberger-Treiman relation is only fulfilled if the quark- and pion-hedgehog is generalized and the variation is performed with projected states. Under this condition no parameter set is found which yields a proper g A and a proper pion-nucleon coupling constant g π NN , if the polarization of the Dirac sea is neglected. Other observables are reproduced within 20% limits or less.