Chiral anomaly: from vacuum to Columbia plot

TL;DR

This paper employs an extended linear sigma model to analyze the effects of various $U(1)_A$ anomaly operators on the Columbia plot, revealing how different anomaly terms influence the nature of the QCD phase transition.

Contribution

It introduces a novel extension of the 't Hooft determinant, called a polydeterminant, to incorporate interactions among excited mesonic states and explores their impact on chiral symmetry breaking.

Findings

The quadratic 't Hooft determinant favors a cross-over transition at small quark masses.

Different anomaly operators significantly influence the shape of the Columbia plot.

The polydeterminant extends the modeling of chiral anomalies to include excited mesonic states.

Abstract

We use a low-energy effective approach, the extended linear sigma model, to study realizations of the $U(1)_A$ anomaly with different operators, linear and quadratic in the 't Hooft determinant. After discussing the parameterization in agreement with vacuum's phenomenology, we investigate the influence of these different anomaly terms on the Columbia plot: the square of the 't Hooft determinant favors a cross-over for small quark masses. Finally, we also discuss the extension of the 't Hooft determinant to cases in which different mesonic multiplets interact with each other. Novel chiral anomalous interaction terms involving excited (pseudo)scalar states, pseudovector, and pseudotensor mesons are expressed via a mathematical extension of the determinant, denoted as a polydeterminant.