2016/08/31 by Yi-Jian Du, Fei Teng, Yong-Shi Wu
Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Discriminant #Disjoint sets #Gluon #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Rank (graph theory) #Scattering #Scattering amplitude #hep-th
paper · pdf · doi:10.1007/jhep11(2016)088
published as JHEP 11 (2016) 088 · 26 pages. v2: Introduction expanded, more references and one discussion section added. v3: an example added in section 5.2, matching published version
openalex created_date 2016/09/16 · openalex publication_date 2016/11/01 · arxiv created 2016/11/17 · arxiv updated 2016/11/18 · openalex updated_date 2026/08/05
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 N k 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 N k MHV amplitudes a solution can support. As another application of the technique developed, we show analytically that in Einstein-Yang-Mills theory, if all gluons have the same helicity, the tree-level single-trace amplitudes must vanish.