$σ(500)$ resonance pole positions as function of $m_π$: analysis with a unitary coupled-channel model
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913638398296064 |
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| author | Rupp, George |
| author_facet | Rupp, George |
| contents | Resonance pole positions of the $f_0(500)$ alias $σ(500)$ meson are computed and plotted as a continuous function of pion mass in the framework of a unitary and analytic coupled-channel model for scalar mesons as dynamical $q\bar{q}$ states. The $σ$ is described with a light and a strange $q\bar{q}$ seed, mixing with each other mainly through the common $ππ$, $K\bar{K}$, and $ηη$ meson-meson channels. The few model parameters are fitted to experimental $S$-wave $ππ$ phase shifts up to 1 GeV, yielding, in the case of the physical pion mass, resonance poles at $(460-i222)$ MeV for the $σ(500)$ and $(978-i37)$ MeV for the $f_0(980)$. Resonance, bound-state, and virtual-state pole trajectories are shown as a function of $m_π$ running from 139.57 MeV to 1 GeV. These are compared to recent lattice QCD computations that use interpolating fields corresponding to the model's channels, i.e., for a few discrete $m_π$values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $σ(500)$ resonance pole positions as function of $m_π$: analysis with a unitary coupled-channel model Rupp, George High Energy Physics - Phenomenology High Energy Physics - Lattice Resonance pole positions of the $f_0(500)$ alias $σ(500)$ meson are computed and plotted as a continuous function of pion mass in the framework of a unitary and analytic coupled-channel model for scalar mesons as dynamical $q\bar{q}$ states. The $σ$ is described with a light and a strange $q\bar{q}$ seed, mixing with each other mainly through the common $ππ$, $K\bar{K}$, and $ηη$ meson-meson channels. The few model parameters are fitted to experimental $S$-wave $ππ$ phase shifts up to 1 GeV, yielding, in the case of the physical pion mass, resonance poles at $(460-i222)$ MeV for the $σ(500)$ and $(978-i37)$ MeV for the $f_0(980)$. Resonance, bound-state, and virtual-state pole trajectories are shown as a function of $m_π$ running from 139.57 MeV to 1 GeV. These are compared to recent lattice QCD computations that use interpolating fields corresponding to the model's channels, i.e., for a few discrete $m_π$values. |
| title | $σ(500)$ resonance pole positions as function of $m_π$: analysis with a unitary coupled-channel model |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2402.07725 |