{"paper":{"title":"Characterizing the solutions to scattering equations that support tree-level $\\text{N}^{k}\\text{MHV}$ gauge/gravity amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Fei Teng, Yi-Jian Du, Yong-Shi Wu","submitted_at":"2016-08-22T03:09:12Z","abstract_excerpt":"In this paper we define, independent of theories, two discriminant matrices involving a solution to the scattering equations in four dimensions, the ranks of which are used to divide the solution set into a disjoint union of subsets. We further demonstrate, {entirely within the Cachazo-He-Yuan formalism,} that each subset of solutions gives nonzero contribution to tree-level $\\text{N}^{k}\\text{MHV}$ gauge/gravity amplitudes only for a specific value of $k$. Thus the solutions can be characterized by the rank of their discriminant matrices, which in turn determines the value of $k$ of the $\\tex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06040","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":""},"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"}