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

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.

18 pages, 8 figures

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Cited by in corpus (7)

• Polyakov loop modeling for hot QCD
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• Axial Ward identity and the Schwinger mechanism -- Applications to the real-time chiral magnetic effect and condensates
• Chirality Production with Mass Effects-Schwinger Pair Production and the Axial Ward Identity
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• First-order CP phase transition in two-flavor QCD at $\theta =\pi$ under electromagnetic scale anomaly via a Nambu-Jona-Lasinio description