New aspect of chiral and axial breaking in QCD

TL;DR

This paper explores the conditions under which chiral and axial symmetries in QCD are simultaneously restored, highlighting a nontrivial coincidence related to topological susceptibility and analyzing its implications using a Nambu-Jona-Lasinio model.

Contribution

It introduces the concept of a nontrivial axial-chiral coincidence in QCD with massive light quarks and a massless strange quark, and investigates its effects on symmetry restoration at high temperatures.

Findings

The nontrivial coincidence occurs even with nonzero QCD coupling due to flavor-singlet topological susceptibility.

High-temperature symmetry restoration can be independent of light quark mass, unaffected by the order of the phase transition.

Differences in symmetry restoration are influenced by the strange quark mass and topological susceptibility interference.

Abstract

Violation of the $U(1)$ axial symmetry in QCD is stricter than the chiral $SU(2)$ breaking, simply because of the presence of the quantum axial anomaly. If the QCD gauge coupling is sent to zero, the strength of the $U(1)$ axial breaking coincides with that of the chiral $SU(2)$ breaking, which we shall in short call an axial-chiral coincidence. This coincidence is trivial since QCD then becomes a non-interacting theory. Actually, there exists another limit in the QCD parameter space, where an axial-chiral coincidence occurs even with nonzero QCD gauge coupling, that can be dubbed a nontrivial coincidence: it is the case with the massive light quarks $(m_l\neq 0)$ and the massless strange quark ($m_s=0$), due to the flavor-singlet nature of the topological susceptibility. This coincidence is robust and tied to the anomalous chiral Ward-Takahashi identity, which is operative even at hot QCD. This implies that the chiral $SU(2)$ symmetry is restored simultaneously with the $U(1)$ axial symmetry at high temperatures. This simultaneous restoration is independent of $m_l (\neq 0)$, hence is irrespective to the order of the chiral phase transition. In this paper, we discuss how the real-life QCD can be evolved from the nontrivial chiral-axial coincidence limit, by working on a Nambu-Jona-Lasinio model with the $U(1)$ axial anomaly contribution properly incorporated. It is shown that at high temperatures the large differences between the restorations of the chiral $SU(2)$ symmetry and the $U(1)$ axial symmetry for two light quarks and a sufficiently large current mass for the strange quark is induced by a significant interference of the topological susceptibility. Thus the deviation from the nontrivial coincidence, which is monitored by the strange quark mass controlling the topological susceptibility, provides a new way of understanding the chiral $SU(2)$ and $U(1)$ axial breaking in QCD.