{"paper":{"title":"The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"James M. Drummond, Johannes M. Henn, Lance J. Dixon","submitted_at":"2011-04-14T14:57:00Z","abstract_excerpt":"We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\\tilde\\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar $\\\\mathcal{N}=4$ super-Yang-Mills theory, $\\Omega^{(1)}$ and $\\Omega^{(2)}$. The derivative of $\\Omega^{(2)}$ with respect to one of the conformal invariants yields $\\tilde\\Phi_6$, while another first-order differential operator applied to $\\tilde\\Phi_6$ yields $\\Omega^{(1)}$. We also introduce some kinematic var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2787","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}