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 $T_{\rm pc} \sim 155$ 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 ($π$-$σ$ and $η$-$a_0$) 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, $χ_π- χ_{a_0}$, 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 $χ_{\rm top}^{1/4}$ 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.

Figures (11)

• Figure 1: Left: The light quark condensate $\sigma_l$ and the strange quark condensate $\sigma_s$ as functions of temperature $T$. Right: Evaluating the pseudocritical temperature at $T_{pc}=0.157$ GeV from the peak of $d \sigma_l/dT$. These results are for case I with $m_l=7.5\,{ \rm MeV}$.
• Figure 2: The color online is similar to Fig. \ref{['condensateI']}. The evaluated pseudocritical temperature is $T_{pc}=0.154$ GeV with the case II parameter setup.
• Figure 3: Screening mass of the chiral symmetry partners ($\pi$ and $\sigma$, and $\eta$ and $a_0$) as a function of temperature for case I.
• Figure 4: The color online is similar to Fig. \ref{['screen']} for case II.
• Figure 5: Comparison of $\chi_{\sigma}$ in Eq. \ref{['chisig2']} with the normalized $\chi_{\sigma}$ in Eq. \ref{['chisig']}, with the normalization factor $N_{\sigma}=\zeta^2/4$.