QCD vacuum replicas are metastable

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 pseudoscalar, or the vector and axial vector are not degenerate, and in the chiral limit, the pseudoscalar ground states are Goldstone bosons. At T=0 the chiral invariant vacuum is an unstable vacuum, decaying through an infinite number of scalar and pseudoscalar tachyons. Moreover QCD vacuum replicas, an infinite tower of excited vacuum solutions, which energy density lies between the true vacuum and the chiral invariant vacuum, have been predicted in the Coulomb gauge, 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 in the true vacuum and in the 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 is indeed metastable. Moreover the energy spectra of the mesonic quark-antiquark systems in the first replicas are close to the one of the true vacuum.