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

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 $T_{\mathrm{pc}}\sim 155$ 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 $T_{\mathrm{pc}}=0.157$ GeV and $T_{\mathrm{pc}}=0.154$ GeV for Cases I and II, respectively. The screening masses of chiral partner mesons ($\pi$-$\sigma$ and $\eta$-$a_0$) become degenerate near $T_{\mathrm{pc}}$, 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 ${\chi }_{\mathrm{top}}^{1/4}$ is also computed, showing a sharp drop near $T_{\mathrm{pc}}$ 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.