Electroweak three-body decays in the presence of two- and three-body bound states
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arXiv
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| Format: | Preprint |
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2024
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| author | Briceño, Raul A. Jackura, Andrew Pefkou, Dimitra A. Romero-López, Fernando |
| author_facet | Briceño, Raul A. Jackura, Andrew Pefkou, Dimitra A. Romero-López, Fernando |
| contents | Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_12167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Electroweak three-body decays in the presence of two- and three-body bound states Briceño, Raul A. Jackura, Andrew Pefkou, Dimitra A. Romero-López, Fernando High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors. |
| title | Electroweak three-body decays in the presence of two- and three-body bound states |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2402.12167 |