{"paper":{"title":"Two-loop integrals for $t \\bar{t} +$jet production at hadron colliders in the leading colour approximation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Matteo Becchetti, Nicol\\`o Giraudo, Simon Badger, Simone Zoia","submitted_at":"2024-04-18T16:54:05Z","abstract_excerpt":"We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for $pp \\rightarrow t\\bar{t}j$. We derive differential equations for the master integrals by solving the integration-by-parts identities over finite fields. Of the two systems of differential equations, one is presented in canonical '${\\rm d} \\log$' form, while the other is found to have an elliptic sector. For the elliptic topology we identify the relevant elliptic curve, and present the differential equations in a more general form which depends quadratically"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.12325","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.12325/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}