Cuts and coproducts of massive triangle diagrams

Samuel Abreu (1, 2) , Ruth Britto (2, 3) , Hanna Grönqvist (2)

1 University of Edinburgh
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 Trinity College Dublin

Relations between multiple unitarity cuts and coproducts of Feynman integrals 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 coproducts through a detailed study of one-loop triangle integrals with various combinations of external and internal masses.

Keywords: Scattering Amplitudes; Supersymmetric gauge theory; QCD

Domains: High Energy Physics - Theory [hep-th]; High Energy Physics - Phenomenology [hep-ph]

Samuel Abreu, Ruth Britto, Hanna Grönqvist. Cuts and coproducts of massive triangle diagrams. Journal of High Energy Physics, 2015, 2015 (7), pp.111. ⟨10.1007/JHEP07(2015)111⟩. ⟨cea-01201809⟩