Cuts and coproducts of massive triangle diagrams

• Published in: The journal of high energy physics Vol. 2015; no. 7; pp. 1 - 60
• Main Authors: Abreu, Samuel, Britto, Ruth, Grönqvist, Hanna
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2015; Springer Nature B.V; Springer Verlag (Germany)
• Subjects: Channels; Classical and Quantum Gravitation; Discontinuity; Elementary Particles; High energy physics; High Energy Physics - Phenomenology; High Energy Physics - Theory; Integrals; Invariants; Physics; Physics and Astronomy; Placing; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Thresholds; Triangles; Scattering Amplitudes; QCD; Supersymmetric gauge theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2015)111

A bstract Relations between multiple unitarity cuts and coproducts of Feynman inte-grals are extended to allow for internal masses. These masses introduce new branch cuts, whose discontinuities can be derived by placing single propagators on shell and identified as particular entries of the coproduct. First entries of the coproduct are then seen to include mass invariants alone, as well as threshold corrections for external momentum channels. As in the massless case, the original integral can possibly be recovered from its cuts by starting with the known part of the coproduct and imposing integrability contraints. We formulate precise rules for cuts of diagrams, and we gather evidence for the relations to co-products through a detailed study of one-loop triangle integrals with various combinations of external and internal masses.