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- Title
New Aspect of Chiral SU (2) and U (1) Axial Breaking in QCD.
- Authors
Cui, Chuan-Xin; Li, Jin-Yang; Matsuzaki, Shinya; Kawaguchi, Mamiya; Tomiya, Akio
- Abstract
The violation of the U (1) axial symmetry in QCD is stricter than the chiral S U (2) breaking simply because of the presence of the quantum axial anomaly. If the QCD gauge coupling is sent to zero (the asymptotic free limit, where the U (1) axial anomaly does not exist), the strength of the U (1) axial breaking coincides with that of the chiral S U (2) breaking, which we, 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, which can be dubbed a nontrivial coincidence: it is the case with the massive light quarks (m l ≠ 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 S U (2) symmetry is restored simultaneously with the U (1) axial symmetry at high temperatures. This simultaneous restoration is independent of m l (≠ 0) and, hence, is irrespective of 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 S U (2) symmetry and the U (1) axial symmetry for two light quarks and a sufficiently large current mass for the strange quark are 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 S U (2) and U (1) axial breaking in QCD.
- Subjects
QUANTUM chromodynamics; CHIRALITY of nuclear particles; NAMBU-Jona-Lasinio model; PHASE transitions; QUARKS; HIGH temperatures
- Publication
Particles (2571-712X), 2024, Vol 7, Issue 1, p237
- ISSN
2571-712X
- Publication type
Article
- DOI
10.3390/particles7010014