Realization of chiral symmetry in the domain model of QCD

Abstract

The domain model for the QCD vacuum has previously been developed and shown to exhibit confinement of quarks, a strong correlation of the local chirality of quark modes, and a duality of the background domainlike gluon field. Quark fluctuations satisfy a chirality violating boundary condition parametrized by a random chiral angle αj on the jth domain. The free energy of an ensemble of N→∞ domains depends on {αj,j=1,…,N} through the logarithm of the quark determinant. Its parity odd part is given by the axial anomaly. The anomaly contribution to the free energy suppresses continuous axial U(1) degeneracy in the ground state, leaving only a residual axial Z(2) symmetry. This discrete symmetry and the flavor SU(Nf)L×SU(Nf)R chiral symmetry in turn are spontaneously broken with a quark condensate arising due to the asymmetry of the spectrum of the Dirac operator. In order to illustrate the splitting between the η′ from octet pseudoscalar mesons realized in the domain model, we estimate the masses of the light pseudoscalar and vector mesons.