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.
@article{arxiv.1901.09853,
title = {Universal four-dimensional representation of $H \to \gamma \gamma$ at two loops through the Loop-Tree Duality},
author = {Felix Driencourt-Mangin and German Rodrigo and German F. R. Sborlini and William J. Torres Bobadilla},
journal= {arXiv preprint arXiv:1901.09853},
year = {2019}
}