Functions Beyond Multiple Polylogarithms for Precision Collider Physics

TL;DR

This paper reviews advanced Feynman diagram integrals involving special functions beyond multiple polylogarithms, emphasizing their importance for precision collider physics and outlining future research directions.

Contribution

It provides an overview of current research on complex Feynman integrals involving functions beyond multiple polylogarithms and highlights key future research directions.

Findings

Complex diagrams contribute at NNLO to key processes

Integrals involve algebraic manifolds beyond polylogarithms

Highlights need for new mathematical tools in collider physics

Abstract

Feynman diagrams constitute one of the essential ingredients for making precision predictions for collider experiments. Yet, while the simplest Feynman diagrams can be evaluated in terms of multiple polylogarithms -- whose properties as special functions are well understood -- more complex diagrams often involve integrals over complicated algebraic manifolds. Such diagrams already contribute at NNLO to the self-energy of the electron, $t \bar{t}$ production, $\gamma \gamma$ production, and Higgs decay, and appear at two loops in the planar limit of maximally supersymmetric Yang-Mills theory. This makes the study of these more complicated types of integrals of phenomenological as well as conceptual importance. In this white paper contribution to the Snowmass community planning exercise, we provide an overview of the state of research on Feynman diagrams that involve special functions beyond multiple polylogarithms, and highlight a number of research directions that constitute essential avenues for future investigation.