Lellouch-Lüscher factor for the $K\to 3π$ decays
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914770999836672 |
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| author | Pang, Jin-Yi Bubna, Rishabh Müller, Fabian Rusetsky, Akaki Wu, Jia-Jun |
| author_facet | Pang, Jin-Yi Bubna, Rishabh Müller, Fabian Rusetsky, Akaki Wu, Jia-Jun |
| contents | We derive an explicit expression for the Lellouch-Lüscher (LL) factor in the $K\to 3π$ decays at leading order (without derivative couplings). Several important technical details are addressed, like a proper decomposition into the isospin amplitudes, the choice of a minimal set of effective couplings and the renormalization, as well as the algorithm for the solution of the pertinent Faddeev equations in the infinite volume which is based on the contour deformation method. Most importantly, our numerical results demonstrate that the three-body force contributes very little to the LL factor. This result paves the way for the study of the $K\to 3π$ decays on the lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04391 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lellouch-Lüscher factor for the $K\to 3π$ decays Pang, Jin-Yi Bubna, Rishabh Müller, Fabian Rusetsky, Akaki Wu, Jia-Jun High Energy Physics - Lattice High Energy Physics - Phenomenology We derive an explicit expression for the Lellouch-Lüscher (LL) factor in the $K\to 3π$ decays at leading order (without derivative couplings). Several important technical details are addressed, like a proper decomposition into the isospin amplitudes, the choice of a minimal set of effective couplings and the renormalization, as well as the algorithm for the solution of the pertinent Faddeev equations in the infinite volume which is based on the contour deformation method. Most importantly, our numerical results demonstrate that the three-body force contributes very little to the LL factor. This result paves the way for the study of the $K\to 3π$ decays on the lattice. |
| title | Lellouch-Lüscher factor for the $K\to 3π$ decays |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2312.04391 |