QCD vacuum replicas may be metastable: A model study of the stability of QCD vacuum replicas

Abstract

A metastable phase has important physical implications, since it may form vacuum bubbles detectable experimentally, whereas an unstable vacuum instantly explodes. It is well known, due to chiral symmetry breaking, there are at least two very different QCD vacua. At T=0, and in the true vacuum, the scalar and pseudo-scalar, or the vector and axial vector are not degenerate, and in the chiral limit, m{q,q¯}=0, the pseudoscalar ground states are Goldstone bosons. At T=0, the chiral invariant vacuum is unstable, decaying through an infinite number of scalar and pseudo-scalar tachyons. Moreover, QCD vacuum replicas, an infinite tower of finite volume, excited vacuum-like solutions, with energy densities lying between the true vacuum and the chiral invariant vacuum energy densities, have been predicted due to the non-linearity of the mass gap equation with a confining interaction. It remained to show whether the QCD replicas are metastable or unstable. In this paper, the spectrum of quark-antiquark systems is studied both in the true vacuum and in the two first excited QCD replicas. The mass gap equation for the vacua and the Salpeter-RPA equation for the mesons are solved for a simple chiral invariant and confining quark model approximating QCD in the Coulomb gauge. We find no tachyons, thus showing the QCD replicas in our approach may be indeed metastable.