Chiral Bag Model with Constituent Quarks: Topological and Nontopological Solutions

We consider a three-phase modification of the hybrid chiral bag model involving the intermediate constituent quark phase along with the asymptotic freedom and hadronization phases. We find self-consistent solutions of the equations of the model in $1+1$ dimensions with the fermion vacuum polarization effects taken into account. We study the renormalized total energy of the bag as a function of parameters characterizing the geometry of the bag and its topological (baryon) charge. We show that for a nonzero topological charge, there exists an entire series of configurations that are local minimums of the total energy of the bag and contain all the three phases, whereas in the nontopological case, the bag energy minimum corresponds to zero sizes of the domain of the asymptotic freedom phase.