Revisiting $O(N)$ $σ$ model at unphysical pion masses and high temperatures
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910453485010944 |
|---|---|
| author | Lyu, Yuan-Lin Li, Qu-Zhi Xiao, Zhiguang Zheng, Han-Qing |
| author_facet | Lyu, Yuan-Lin Li, Qu-Zhi Xiao, Zhiguang Zheng, Han-Qing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19243 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting $O(N)$ $σ$ model at unphysical pion masses and high temperatures Lyu, Yuan-Lin Li, Qu-Zhi Xiao, Zhiguang Zheng, Han-Qing High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory 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. |
| title | Revisiting $O(N)$ $σ$ model at unphysical pion masses and high temperatures |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2402.19243 |