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arXiv 2402.19243hep-phhep-lathep-thnucl-th
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在非物理π介子质量和高温下重新审视$O(N)$ $σ$模型

Revisiting $O(N)$ $σ$ model at unphysical pion masses and high temperatures

Yuan-Lin Lyu, Qu-Zhi Li, Zhiguang Xiao, Han-Qing Zheng

备注：
13 pages, 5 figures, 1 table; to match the published version
发表信息：
Phys. Rev. D 109, 094026 (2024)
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AI总结：

该研究用$N/D$方法在$1/N$展开领头阶恢复$O(N)$ $σ$模型振幅的交叉对称性，重现了相关极点结构与轨迹，验证了最低$f_0$态在手征对称性破缺中的$σ$介子角色。

摘要：

对$m_π=391$MeV下的$ππ$散射相移格点数据开展的Roy方程（罗伊方程）分析表明，最低质量的$f_0$介子在该条件下会成为束缚态。此外，交叉对称性会在阈值下方产生一对复极点[X.-H. Cao等人，Phys. Rev. D 108, 034009 (2023)]。我们采用$N/D$方法，在$1/N$展开的领头阶部分恢复$O(N)$ $σ$模型振幅的交叉对称性，定性重现了Roy方程分析所揭示的、随π介子质量变化的极点结构与极点轨迹。我们还讨论了随温度变化的$σ$极点轨迹，发现其性质与随$m_π$变化时的性质相似。随着温度升高，复$σ$极点首先从第二黎曼面移动到实轴，成为两个虚态极点；随后其中一个虚态极点移动到第一黎曼面，转变为束缚态极点；最终在高温下趋近于π介子极点位置，这与手征对称性恢复的预期一致。我们的结果进一步提供了证据，表明从实验和格点数据中提取的最低$f_0$态，在手征对称性自发破缺中扮演着$σ$介子的角色。最后，我们还简要讨论了$m_π$和温度较大时的有效势问题。

英文摘要：

Roy-equation analyses on lattice data of $ππ$ scattering phase shifts at $m_π=391$MeV reveals that the lowest $f_0$ meson becomes a bound state under this condition. In addition, there is a pair of complex poles below threshold generated by crossing symmetry [X.-H. Cao et al., Phys. Rev. D 108, 034009 (2023)]. We use the $N/D$ method to partially recover crossing symmetry of the $O(N)$ $σ$ model amplitude at leading order of $1/N$ expansion, and qualitatively reproduce the pole structure and pole trajectories with varying pion masses as revealed by Roy-equation analyses. The $σ$ pole trajectory with varying temperature is also discussed and found to be similar to its properties when varying $m_π$. As the temperature increases, the complex $σ$ poles firstly move from the second Riemann sheet to the real axis becoming two virtual state poles, and then one virtual state pole moves to the first sheet turning into a bound state pole and finally tends to the pion pole position at high temperature which is as expected from the chiral symmetry restoration. Our results provide further evidences that the lowest $f_0$ state extracted from experiments and lattice data plays the role of $σ$ meson in the spontaneous breaking of chiral symmetry. Finally, we also briefly discuss the problems of the effective potential in the situation when $m_π$ and temperature get large.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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