Unitary model analysis of $f_0(500)$ pole positions by continuously varying $m_π$: comparison with discrete lattice predictions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910352258629632 |
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| author | Rupp, George |
| author_facet | Rupp, George |
| contents | Resonance, bound-state, and virtual-state pole positions of the $f_0(500)$ scalar meson are computed as a continuous function of pion mass in the framework of a unitarized and analytic coupled-channel model for scalar mesons, described as dynamical quark-antiquark states. The $f_0(500)$ is modeled with both light and strange $q\bar{q}$ seeds, mixing with each other through the common $S$-wave $ππ$, $K\bar{K}$, and $ηη$ meson-meson decay channels. The few model parameters are fitted to experimental $S$-wave $ππ$ phase shifts up to 1 GeV. In the case of the physical $π^\pm$ mass of 139.57 MeV, resonance poles at $(460-i222)$ MeV and $(978-i37.2)$ MeV are found for the $f_0(500)$ and $f_0(980)$, respectively. Resonance, bound-state, and virtual-state pole trajectories are computed and plotted as a function of pion masses up to 500 MeV, both in the complex-energy and complex-momentum planes. The results are discussed and compared to the most advanced lattice QCD computations employing interpolators that correspond to the $q\bar{q}$ and meson-meson channels in the present model, that is, for a few discrete values of the unphysical pion mass in those lattice calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitary model analysis of $f_0(500)$ pole positions by continuously varying $m_π$: comparison with discrete lattice predictions Rupp, George High Energy Physics - Phenomenology High Energy Physics - Lattice Resonance, bound-state, and virtual-state pole positions of the $f_0(500)$ scalar meson are computed as a continuous function of pion mass in the framework of a unitarized and analytic coupled-channel model for scalar mesons, described as dynamical quark-antiquark states. The $f_0(500)$ is modeled with both light and strange $q\bar{q}$ seeds, mixing with each other through the common $S$-wave $ππ$, $K\bar{K}$, and $ηη$ meson-meson decay channels. The few model parameters are fitted to experimental $S$-wave $ππ$ phase shifts up to 1 GeV. In the case of the physical $π^\pm$ mass of 139.57 MeV, resonance poles at $(460-i222)$ MeV and $(978-i37.2)$ MeV are found for the $f_0(500)$ and $f_0(980)$, respectively. Resonance, bound-state, and virtual-state pole trajectories are computed and plotted as a function of pion masses up to 500 MeV, both in the complex-energy and complex-momentum planes. The results are discussed and compared to the most advanced lattice QCD computations employing interpolators that correspond to the $q\bar{q}$ and meson-meson channels in the present model, that is, for a few discrete values of the unphysical pion mass in those lattice calculations. |
| title | Unitary model analysis of $f_0(500)$ pole positions by continuously varying $m_π$: comparison with discrete lattice predictions |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2401.08379 |