A model study of the stability of QCD vacuum replicas

Abstract
A metastable phase for QCD has important physical implications, since it may form vacuum bubbles that live enough so to be detectable experimentally, whereas an unstable vacuum instantly explodes.

As it is well known, due to chiral symmetry breaking, that 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, the pseudoscalar ground states become Goldstone bosons. As for the chiral invariant vacuum, it is unstable, decaying through an infinite number of scalar and pseudo-scalar tachyons.

On the contrary, 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, have been predicted due to the non-linearity of the mass gap equation with a confining interaction. They possess real masses. We show the spectrum of quark-antiquark systems, studied both for the true vacuum and for the two first excited QCD replicas. The mass gap equation for the vacua and the Salpeter-RPA equation for mesons are solved for a simple chiral invariant and confining quark model approximating QCD in the Coulomb gauge.

We find their masses to be real, thus showing the QCD replicas in our approach may be indeed metastable.

Based on the publication: https://doi.org/10.1016/j.physletb.2020.135730