Function Theory for Multiloop Feynman Integrals

Abstract

Precise predictions for collider observables require the computation of higher orders in perturbation theory. This task usually involves the evaluation of complicated multiloop integrals, which typically give rise to complicated special functions. This article discusses recent progress in understanding the mathematics underlying multiloop Feynman integrals and discusses a class of functions that generalizes the logarithm and that often appears in multiloop computations. The same class of functions is an active area of research in modern mathematics, which has led to the development of new powerful tools to compute Feynman integrals. These tools are at the heart of some of the most complicated computations ever performed for a hadron collider.