Universal four-dimensional representation of H → γγ at two loops through the Loop-Tree Duality

• Published in: The journal of high energy physics Vol. 2019; no. 2; pp. 1 - 39
• Main Authors: Driencourt-Mangin, Félix, Rodrigo, Germán, Sborlini, Germán F. R., Torres Bobadilla, William J.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2019; Springer Nature B.V; SpringerOpen
• Subjects: Amplitudes; Classical and Quantum Gravitation; Economic models; Elementary Particles; Higgs Physics; High energy physics; Perturbative QCD; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; Singularities; String Theory; Scattering Amplitudes; Higgs Physics; Perturbative QCD
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2019)143

A bstract We extend useful properties of the H → γγ unintegrated dual amplitudes from one- to two-loop level, using the Loop-Tree Duality formalism. In particular, we show that the universality of the functional form — regardless of the nature of the internal particle — still holds at this order. We also present an algorithmic way to renormalise two-loop amplitudes, by locally cancelling the ultraviolet singularities at integrand level, thus allowing a full four-dimensional numerical implementation of the method. Our results are compared with analytic expressions already available in the literature, finding a perfect numerical agreement. The success of this computation plays a crucial role for the development of a fully local four-dimensional framework to compute physical observables at Next-to-Next-to Leading order and beyond.