Columbia plot based on symmetry-improved CJT formalism in linear sigma model
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| Format: | Preprint |
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2025
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| _version_ | 1866908764470247424 |
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| author | Guan, Yuepeng Kawaguchi, Mamiya Matsuzaki, Shinya Tomiya, Akio |
| author_facet | Guan, Yuepeng Kawaguchi, Mamiya Matsuzaki, Shinya Tomiya, Akio |
| contents | 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 fairly insensitive to the size of the sigma meson, in contrast to the conventional CJT approach. The tricritical point, found on the $m_s$ axis, is at $m_s^{\rm tri}/m_s^{\rm phys.} = 0.175$ with $m_s^{\rm phys.}$ 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 $m_π\sim 52.4$ MeV, with the critical temperature $T_c \sim 51.7$ MeV. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_02257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Columbia plot based on symmetry-improved CJT formalism in linear sigma model Guan, Yuepeng Kawaguchi, Mamiya Matsuzaki, Shinya Tomiya, Akio High Energy Physics - Phenomenology 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 fairly insensitive to the size of the sigma meson, in contrast to the conventional CJT approach. The tricritical point, found on the $m_s$ axis, is at $m_s^{\rm tri}/m_s^{\rm phys.} = 0.175$ with $m_s^{\rm phys.}$ 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 $m_π\sim 52.4$ MeV, with the critical temperature $T_c \sim 51.7$ MeV. |
| title | Columbia plot based on symmetry-improved CJT formalism in linear sigma model |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2508.02257 |