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Columbia plot based on the symmetry-improved Cornwall-Jackiw-Tomboulis formalism in the linear sigma model

Yuepeng Guan1,*, Mamiya Kawaguchi2,†, Shinya Matsuzaki1,‡, and Akio Tomiya3,4,§

  • *Contact author: guanyp22@mails.jlu.edu.cn
  • †Contact author: mamiya@aust.edu.cn
  • ‡Contact author: synya@jlu.edu.cn
  • §Contact author: akio@yukawa.kyoto-u.ac.jp
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Phys. Rev. D 113, 014013 – Published 13 January, 2026

DOI: https://doi.org/10.1103/71r7-8b3p

Abstract

We study the Columbia plot for the chiral phase transition in the framework of a three-flavor linear sigma model based on the Cornwall-Jackiw-Tomboulis (CJT) formalism. The conventional CJT approach with the Hartree truncation suffers from artificial chiral breaking, leading to the violation of the Nambu-Goldstone theorem and the (anomalous) chiral Ward-Takahashi identities. We apply the symmetry-improved CJT formalism to resolve this issue. We observe a first-order phase transition and a tricritical point in the light-quark mass regime, which is relatively independent of the size of the sigma meson, in contrast to the conventional CJT approach. The tricritical point, found on the ms axis, is at mstri/msphys=0.175 with msphys being the physical strange quark mass in real-life QCD. The critical pion mass in the three-flavor symmetric limit, on the second-order boundary, is measured at mπ∼52.4  MeV, with the critical temperature Tc∼51.7  MeV.

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Phys. Rev. D 113, 014013– Published 13 January, 2026
  • Received 8 August 2025
  • Accepted 18 December 2025
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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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