Solitons in the Nambu-Jona-Lasinio model with vector and axial mesons

Abstract

We study the effect of vector and axial isovector mesons in the soliton of the SU(2) NJL-model for static hedgehog configurations and on the chiral circle. The Lagrangian reproduces Sakurai's Universality and implements vector dominance through current-field identities. The parameters of the Lagrangian are fixed by means of a heat-kernel expansion up to second order taking the A-π mixing into account. For the corresponding set of parameters we find solitons for constituent quark masses between M∼265–345 MeV which are much lower than those found without vector mesons. For the value M=315 MeV which corresponds both to the KSFR relation 2 g 2 f π 2 =m 2 and the Weinberg sum rule m A 2 =m 2 the soliton has a clearly negative quark eigenvalue. The soliton mass is about 1100 MeV. For this choise of parameters the radius and axial coupling constant turn out to be too small.