Partial-wave projection of relativistic three-body amplitudes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929512418115584 |
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| author | Briceño, Raúl A. Costa, Caroline S. R. Jackura, Andrew W. |
| author_facet | Briceño, Raúl A. Costa, Caroline S. R. Jackura, Andrew W. |
| contents | We derive the integral equations for partial-wave projected three-body scattering amplitudes, starting from the integral equations for three-body amplitudes developed for lattice QCD analyses. The results, which hold for generic three-body systems of spinless particles, build upon the recently derived partial-wave projected one-particle exchange, a primary component of the relativistic framework proven to satisfy S matrix unitarity. We derive simplified expressions for factorizable short-distance interactions, $\mathcal{K}_{3}$, in two equivalent formalisms - one symmetric under particle interchange and one asymmetric. For the asymmetric case, we offer parameterizations useful for amplitude analysis. Finally, we examine toy models for $3π$ systems at unphysically heavy pion masses with total isospins 0,1, and 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15577 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial-wave projection of relativistic three-body amplitudes Briceño, Raúl A. Costa, Caroline S. R. Jackura, Andrew W. High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory We derive the integral equations for partial-wave projected three-body scattering amplitudes, starting from the integral equations for three-body amplitudes developed for lattice QCD analyses. The results, which hold for generic three-body systems of spinless particles, build upon the recently derived partial-wave projected one-particle exchange, a primary component of the relativistic framework proven to satisfy S matrix unitarity. We derive simplified expressions for factorizable short-distance interactions, $\mathcal{K}_{3}$, in two equivalent formalisms - one symmetric under particle interchange and one asymmetric. For the asymmetric case, we offer parameterizations useful for amplitude analysis. Finally, we examine toy models for $3π$ systems at unphysically heavy pion masses with total isospins 0,1, and 2. |
| title | Partial-wave projection of relativistic three-body amplitudes |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2409.15577 |