Showing papers by "Pierpaolo Mastrolia published in 2018"
TL;DR: In this article, the tools of intersection theory are introduced to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis, and the authors consider the Baikov representation of maximal cuts in arbitrary space-time dimension.
Abstract: We introduce the tools of intersection theory to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis. In order to illustrate this technique, we consider the Baikov representation of maximal cuts in arbitrary space-time dimension. We introduce a minimal basis of differential forms with logarithmic singularities on the boundaries of the corresponding integration cycles. We give an algorithm for computing a basis decomposition of an arbitrary maximal cut using so-called intersection numbers and describe two alternative ways of computing them. Furthermore, we show how to obtain Pfaffian systems of differential equations for the basis integrals using the same technique. All the steps are illustrated on the example of a two-loop non-planar triangle diagram with a massive loop.
93 citations
TL;DR: In this article, the current status of the analytic evaluation of the two-loop corrections to the μescattering in quantum electrodynamics is reported, along with state-of-the-art techniques which have been developed to address this challenging task.
Abstract: We report on the current status of the analytic evaluation of the two-loop corrections to the μescattering in Quantum Electrodynamics, presenting state-of-the art techniques which have been developed to address this challenging task.
5 citations