New interpretation of chiral phase transition: Violation of trilemma in QCD

TL;DR

This paper proposes a new interpretation of the chiral phase transition in QCD, highlighting the violation of the QCD trilemma involving susceptibility functions, and demonstrates this violation through a three-flavor NJL model, with implications for lattice QCD and flavor dependence studies.

Contribution

It introduces the concept of the QCD trilemma and shows its violation at the physical point using a three-flavor NJL model, extending understanding of chiral transition dynamics.

Findings

Violation of the QCD trilemma occurs at the vacuum and across the temperature range including the chiral crossover.

Flavor symmetry breaking enhances the axial anomaly contribution in the chiral order parameter.

The imbalance among susceptibility functions is linked to flavor symmetry violation and can be tested in future lattice simulations.

Abstract

We find that the chiral phase transition (chiral crossover) in QCD at physical point is triggered by big imbalance among three fundamental quantities essential for the QCD vacuum structure: susceptibility functions for the chiral symmetry, axial symmetry, and the topological charge. The balance, dobbed the QCD trilemma, is unavoidably violated when one of the magnitudes among them is highly dominated, or suppressed. Based on a three-flavor Nambu-Jona-Lasinio model, we explicitly evaluate the amount of violation of the QCD trilemma at physical point, and show that the violation takes place not only at vacuum, but even in a whole temperature regime including the chiral crossover epoch. This work confirms and extends the suggestion recently reported from lattice QCD with 2 flavors on dominance of the axial and topological susceptibilities left in the chiral susceptibility at high temperatures. It turns out that the imbalance is essentially due to the flavor symmetry violation of the lightest three flavors, and the flavor breaking specifically brings enhancement of the axial anomaly contribution in the chiral order parameter, while the the strength of the axial breaking and the transition rate of the topological charge are fairly insensitive to the flavor symmetry. The violation of QCD trilemma and its flavor dependence can be tested by lattice simulations with 2 + 1 flavors in the future, and would also give a new guiding principle to explore the flavor dependence of the chiral phase transition, such as the Columbia plot, including possible extension with external fields.