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

Hiwa A. Ahmed ^1,*, Danning Li ^2,†, Mamiya Kawaguchi ^3,‡, and Mei Huang^4,§

¹Charmo Centre for Research, Training and Consultancy, Charmo University, 46023, Chamchamal, Sulaymaniyah, Iraq
²Department of Physics and Siyuan Laboratory, Jinan University, Guangzhou 510632, People’s Republic of China
³Centre for Fundamental Physics, School of Mechanics and Photoelectric Physics, Anhui University of Science and Technology, Huainan, Anhui 232001, People’s Republic of China
⁴School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China

^*Contact author: hiwa.ahmed@chu.edu.iq
^†Contact author: lidanning@jnu.edu.cn
^‡Contact author: mamiya@aust.edu.cn
^§Contact author: huangmei@ucas.ac.cn

Phys. Rev. D 114, 026032 – Published 27 July, 2026

DOI: https://doi.org/10.1103/qfmp-b7y3

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 (cases I and II), both calibrated to reproduce a pseudocritical temperature $T_{pc} \sim 155 MeV$ 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 $T_{pc} = 0.157$ and $T_{pc} = 0.154 GeV$ for cases I and II, respectively. The screening masses of chiral partner mesons ( $π - σ$ and $η - a_{0}$ ) become degenerate near $T_{pc}$ , providing a clear signature of chiral symmetry restoration. Analysis of the corresponding meson susceptibilities further supports this conclusion. However, the effective restoration of the $U (1)_{A}$ symmetry—probed via the susceptibility difference $χ_{π} - χ_{a_{0}}$ —occurs more slowly than that of chiral symmetry. This indicates a separation between the chiral and axial symmetry restoration scales within the present holographic framework. The temperature-dependent topological susceptibility $χ_{top}^{1 / 4}$ is also computed, showing a sharp drop near $T_{pc}$ and a subsequent slight decrease. While the model qualitatively captures established features of the chiral transition, the results highlight a limitation in the quantitative description of the $U (1)$ axial anomaly compared to lattice QCD in our work.

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Phys. Rev. D 114, 026032– Published 27 July, 2026

Vol. 114, Iss. 2 — 15 July 2026

Received 24 March 2026
Accepted 25 June 2026

DOI: https://doi.org/10.1103/qfmp-b7y3

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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

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

Abstract

Physics Subject Headings (PhySH)

Article Text

References (69)

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