QCD $\theta$-vacua from the chiral limit to the quenched limit

TL;DR

This paper explores how the QCD vacuum structure varies with the $ heta$-angle and quark mass using the Di-Vecchia--Veneziano model, revealing continuous ground state energies and explaining phase transitions at $ heta = \pi$ across different limits.

Contribution

It demonstrates that the ground state energies are continuous functions of quark mass from the chiral to the quenched limit within the Di-Vecchia--Veneziano model, elucidating the nature of phase transitions at $ heta = \pi$.

Findings

Ground state energies are continuous functions of quark mass across limits.

The phase transition at $ heta = \pi$ occurs in both chiral and quenched limits.

Chiral condensate varies with quark mass, influencing vacuum structure.

Abstract

We investigate the dependence of the QCD vacuum structure on the $\theta$-angle and quark mass, using the Di-Vecchia--Veneziano model. Although the Di-Vecchia--Veneziano model is a chiral effective model, it contains the topological properties of the pure Yang--Mills theory. It is shown that within this model, the ground state energies for all $\theta$ are continuous functions of quark mass from the chiral limit to the quenched limit, even including the first order phase transition at $\theta = \pi$. Based on this effective model, we discuss (i) how the ground state depends on quark mass, and (ii) why the phase transition at $\theta = \pi$ is present both in the chiral and quenched limit. In order to analyze the relation between quark mass and the $\theta$-vacua, we calculate the chiral condensate as a function of quark mass. Also, considering the presence of the innate metastable states included in the QCD $\theta$-vacuum, we also give a unified understanding of the phase transitions at $\theta = \pi$ in the chiral and quenched limit.