Determination of $U(1)_{\rm A}$ restoration from pion and $a_0$-meson screening masses: Toward the chiral regime

TL;DR

This study models the restoration of $U(1)_A$ symmetry at high temperatures using an extended NJL model, calibrated with lattice QCD data, revealing insights into the nature and critical point of the chiral transition.

Contribution

It introduces a temperature-dependent coupling in the EPNJL model based on lattice QCD data, providing a more accurate description of $U(1)_A$ restoration and chiral transition characteristics.

Findings

$K(T)$ is suppressed near the pseudocritical temperature.

The model reproduces lattice QCD meson susceptibilities.

Chiral transition is second order at the light-quark chiral limit.

Abstract

We incorporate the effective restoration of $U(1)_{\rm A}$ symmetry in the 2+1 flavor entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model by introducing a temperature-dependent strength $K(T)$ to the Kobayashi-Maskawa-'t Hooft (KMT) determinant interaction. $T$ dependence of $K(T)$ is well determined from pion and $a_0$-meson screening masses obtained by lattice QCD (LQCD) simulations with improved p4 staggered fermions. The strength is strongly suppressed in the vicinity of the pseudocritical temperature of chiral transition. The EPNJL model with the $K(T)$ well reproduces meson susceptibilities calculated by LQCD with domain-wall fermions. The model shows that the chiral transition is second order at the "light-quark chiral-limit" point where the light quark mass is zero and the strange quark mass is fixed at the physical value. This indicates that there exists a tricritical point. Hence the location is estimated.