Analytic representations of two-loop scattering amplitudes with internal masses

TL;DR

This paper reviews recent advances in calculating two-loop scattering amplitudes with massive internal particles, focusing on complex functions like elliptic integrals and their role in precision predictions for particle physics processes.

Contribution

It discusses new methods and insights for analyzing two-loop amplitudes with internal masses, emphasizing the use of advanced mathematical functions and techniques for complex multi-scale integrals.

Findings

Enhanced understanding of elliptic functions in two-loop integrals

Progress towards NNLO corrections for five-point processes

Application to top-quark pair production amplitudes

Abstract

We highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with elliptic curves. With the presence of more scales in the amplitudes, it becomes imperative to have a better understanding of the contributing Feynman integrals and using current cutting-edge technologies to tackle the growth in analytic and algebraic complexities. In particular, we start with discussing two-loop scattering amplitudes for top-quark pair production and conclude with motivating important steps towards obtaining next-to-next-to leading-order corrections for five-point processes.