A unitary coupled-channel three-body amplitude with pions and kaons
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929490425282560 |
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| author | Feng, Yuchuan Gil, Fernando Döring, Michael Molina, Raquel Mai, Maxim Shastry, Vanamali Szczepaniak, Adam |
| author_facet | Feng, Yuchuan Gil, Fernando Döring, Michael Molina, Raquel Mai, Maxim Shastry, Vanamali Szczepaniak, Adam |
| contents | Three-body dynamics above threshold is required for the reliable extraction of many amplitudes and resonances from experiment and lattice QCD. The S-matrix principle of unitarity can be used to construct dynamical coupled-channel approaches in which three particles scatter off each other, re-arranging two-body subsystems by particle exchange. This paper reports the development of a three-body coupled-channel, amplitude including pions and kaons. The unequal-mass amplitude contains two-body S- and P-wave subsystems ("isobars") of all isospins, $I=0,\,1/2,\,1,\, 3/2, \, 2$, and it also allows for transitions within a given isobar. The $f_0(500)\, ("σ"),\,f_0(980),\,ρ(700), K_0^*(700)\,("κ")$, and $K^*(892)$ resonances are included, apart from repulsive isobars. Different methods to evaluate the amplitude for physical momenta are discussed. Production amplitudes for $a_1$ quantum numbers are shown as a proof of principle for the numerical implementation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08721 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A unitary coupled-channel three-body amplitude with pions and kaons Feng, Yuchuan Gil, Fernando Döring, Michael Molina, Raquel Mai, Maxim Shastry, Vanamali Szczepaniak, Adam Nuclear Theory High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Experiment Three-body dynamics above threshold is required for the reliable extraction of many amplitudes and resonances from experiment and lattice QCD. The S-matrix principle of unitarity can be used to construct dynamical coupled-channel approaches in which three particles scatter off each other, re-arranging two-body subsystems by particle exchange. This paper reports the development of a three-body coupled-channel, amplitude including pions and kaons. The unequal-mass amplitude contains two-body S- and P-wave subsystems ("isobars") of all isospins, $I=0,\,1/2,\,1,\, 3/2, \, 2$, and it also allows for transitions within a given isobar. The $f_0(500)\, ("σ"),\,f_0(980),\,ρ(700), K_0^*(700)\,("κ")$, and $K^*(892)$ resonances are included, apart from repulsive isobars. Different methods to evaluate the amplitude for physical momenta are discussed. Production amplitudes for $a_1$ quantum numbers are shown as a proof of principle for the numerical implementation. |
| title | A unitary coupled-channel three-body amplitude with pions and kaons |
| topic | Nuclear Theory High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Experiment |
| url | https://arxiv.org/abs/2407.08721 |