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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.23609 |
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| _version_ | 1866914420163084288 |
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| author | Mukherjee, Rajnandini Hansen, Maxwell T. |
| author_facet | Mukherjee, Rajnandini Hansen, Maxwell T. |
| contents | The rigorous treatment of four-particle intermediate and final states poses a major challenge for lattice calculations of scattering and decay amplitudes, as well as long-distance matrix elements. As a step towards addressing these challenges, we present a new formalism that perturbatively relates two- and four-particle finite-volume energies and matrix elements to the couplings of the infinite-volume theory. Our method works at leading order in the two-to-two, four-to-four, and two-to-four couplings of the theory, while also capturing the leading finite-volume effects associated with two-to-two subprocess scattering in the four-particle sector. The result takes the form of a quantization condition which we implement numerically to produce a plot of volume-dependent energies for center-of-mass energies up to the six-particle threshold. The solutions exhibit a clear signature of two- and four-particle-like states and the avoided level crossings between them, which are particularly sensitive to the two-to-four coupling. We further discuss the implications of this formalism for quantifying the four-particle contributions in decay and transition amplitudes (e.g. for hadronic $D$ decays). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23609 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards four-pion effects in multi-hadron decays Mukherjee, Rajnandini Hansen, Maxwell T. High Energy Physics - Lattice The rigorous treatment of four-particle intermediate and final states poses a major challenge for lattice calculations of scattering and decay amplitudes, as well as long-distance matrix elements. As a step towards addressing these challenges, we present a new formalism that perturbatively relates two- and four-particle finite-volume energies and matrix elements to the couplings of the infinite-volume theory. Our method works at leading order in the two-to-two, four-to-four, and two-to-four couplings of the theory, while also capturing the leading finite-volume effects associated with two-to-two subprocess scattering in the four-particle sector. The result takes the form of a quantization condition which we implement numerically to produce a plot of volume-dependent energies for center-of-mass energies up to the six-particle threshold. The solutions exhibit a clear signature of two- and four-particle-like states and the avoided level crossings between them, which are particularly sensitive to the two-to-four coupling. We further discuss the implications of this formalism for quantifying the four-particle contributions in decay and transition amplitudes (e.g. for hadronic $D$ decays). |
| title | Towards four-pion effects in multi-hadron decays |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2603.23609 |