Studies on quark-mass dependence of the $N^*(920)$ pole from $πN$ $χ$PT amplitudes
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917138034327552 |
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| author | Wang, Xu Kang, Kai-Ge Li, Qu-Zhi Xiao, Zhiguang Zheng, Han-Qing |
| author_facet | Wang, Xu Kang, Kai-Ge Li, Qu-Zhi Xiao, Zhiguang Zheng, Han-Qing |
| contents | The quark-mass dependence of the $N^*(920)$ pole is analyzed using $K$-matrix method, with the $πN$ scattering amplitude calculated up to $O(p^3)$ order in chiral perturbation theory. As the quark mass increases, the $N^*(920)$ pole gradually approaches the real axis in the complex $w$-plane (where $w=\sqrt{s}$). Eventually, in the $O(p^2)$ case, it crosses the $u$-cut on the real axis and enters the adjacent Riemann sheet when the pion mass reaches $526~{\rm MeV}$. At order $O(p^3)$, the rate at which it approaches the real axis slows down; however, we argue that it will ultimately cross the $u$-cut and enter the adjacent Riemann sheet as well. Additionally, the trajectory of the \(N^*(920)\) pole is in qualitative agreement with the results from the linear $σ$ model calculation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Studies on quark-mass dependence of the $N^*(920)$ pole from $πN$ $χ$PT amplitudes Wang, Xu Kang, Kai-Ge Li, Qu-Zhi Xiao, Zhiguang Zheng, Han-Qing High Energy Physics - Phenomenology High Energy Physics - Lattice The quark-mass dependence of the $N^*(920)$ pole is analyzed using $K$-matrix method, with the $πN$ scattering amplitude calculated up to $O(p^3)$ order in chiral perturbation theory. As the quark mass increases, the $N^*(920)$ pole gradually approaches the real axis in the complex $w$-plane (where $w=\sqrt{s}$). Eventually, in the $O(p^2)$ case, it crosses the $u$-cut on the real axis and enters the adjacent Riemann sheet when the pion mass reaches $526~{\rm MeV}$. At order $O(p^3)$, the rate at which it approaches the real axis slows down; however, we argue that it will ultimately cross the $u$-cut and enter the adjacent Riemann sheet as well. Additionally, the trajectory of the \(N^*(920)\) pole is in qualitative agreement with the results from the linear $σ$ model calculation. |
| title | Studies on quark-mass dependence of the $N^*(920)$ pole from $πN$ $χ$PT amplitudes |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2512.10241 |