All Loop Scattering For All Multiplicity
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914959334572032 |
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| author | Arkani-Hamed, Nima Frost, Hadleigh Salvatori, Giulio Plamondon, Pierre-Guy Thomas, Hugh |
| author_facet | Arkani-Hamed, Nima Frost, Hadleigh Salvatori, Giulio Plamondon, Pierre-Guy Thomas, Hugh |
| contents | This is part of a series of papers describing the new curve integral formalism for scattering amplitudes of the colored scalar tr$ϕ^3$ theory. We show that the curve integral manifests a very surprising fact about these amplitudes: the dependence on the number of particles, $n$, and the loop order, $L$, is effectively decoupled. We derive the curve integrals at tree-level for all $n$. We then show that, for higher loop-order, it suffices to study the curve integrals for $L$-loop tadpole-like amplitudes, which have just one particle per color trace-factor. By combining these tadpole-like formulas with the the tree-level result, we find formulas for the all $n$ amplitudes at $L$ loops. We illustrate this result by giving explicit curve integrals for all the amplitudes in the theory, including the non-planar amplitudes, through to two loops, for all $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09284 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | All Loop Scattering For All Multiplicity Arkani-Hamed, Nima Frost, Hadleigh Salvatori, Giulio Plamondon, Pierre-Guy Thomas, Hugh High Energy Physics - Theory This is part of a series of papers describing the new curve integral formalism for scattering amplitudes of the colored scalar tr$ϕ^3$ theory. We show that the curve integral manifests a very surprising fact about these amplitudes: the dependence on the number of particles, $n$, and the loop order, $L$, is effectively decoupled. We derive the curve integrals at tree-level for all $n$. We then show that, for higher loop-order, it suffices to study the curve integrals for $L$-loop tadpole-like amplitudes, which have just one particle per color trace-factor. By combining these tadpole-like formulas with the the tree-level result, we find formulas for the all $n$ amplitudes at $L$ loops. We illustrate this result by giving explicit curve integrals for all the amplitudes in the theory, including the non-planar amplitudes, through to two loops, for all $n$. |
| title | All Loop Scattering For All Multiplicity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2311.09284 |