Probing the chiral and $U(1)$ axial symmetry restoration via meson susceptibilities in holographic QCD

TL;DR

This paper uses a holographic QCD model to study how chiral and $U(1)$ axial symmetries are restored at finite temperature, revealing different restoration scales and providing insights into meson behavior near the transition.

Contribution

It introduces a holographic QCD approach with two parameter sets to analyze symmetry restoration patterns and compares the results with lattice QCD findings.

Findings

Chiral symmetry restoration occurs near $T_{pc} \,\sim\, 155$ MeV.

$U(1)$ axial symmetry restores at a higher temperature around 190 MeV.

Meson susceptibilities and screening masses confirm chiral symmetry restoration.

Abstract

We investigate the restoration patterns of chiral and $U(1)$ axial symmetries at finite temperature using a soft-wall holographic QCD model. The study employs two distinct parameter sets (Case I and Case II), both calibrated to reproduce a pseudocritical temperature $T_{\rm pc} \sim 155$ MeV and the physical pion mass. The temperature dependence of the light and strange quark condensates confirms a smooth chiral crossover transition, with pseudocritical temperatures of $T_{\rm pc}=0.157$ GeV and $T_{\rm pc}=0.154$ GeV for Cases I and II, respectively. The screening masses of chiral partner mesons ($\pi$-$\sigma$ and $\eta$-$a_0$) become degenerate near $T_{\rm pc}$, providing a clear signature of chiral symmetry restoration. Analysis of the corresponding meson susceptibilities further supports this conclusion. However, the indicator for $U(1)$ axial symmetry restoration, $\chi_\pi - \chi_{a_0}$, vanishes at a temperature $T \sim 0.190 $ GeV, which indicates a distinct restoration scale with chiral symmetry restoration scale within the present holographic framework. The temperature-dependent topological susceptibility $\chi_{\rm top}^{1/4}$ is also computed, showing a sharp drop near $T_{\rm pc}$ and a subsequent slight decrease. While the model qualitatively captures established features of the chiral transition, the results highlight a limitation in the qualitative description of the $U(1)$ axial anomaly compared to LQCD in our work.