The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals

TL;DR

This review discusses recent algorithms and methods for analytically computing multi-loop Feynman integrals, crucial for high-precision predictions in particle physics, with implications for collider experiments and fundamental physics.

Contribution

It presents an overview of the latest computer algebra and special function algorithms used for multi-loop Feynman integral calculations in quantum field theories.

Findings

Highlights recent computational techniques for multi-loop integrals

Connects algorithms to precision calculations in the Standard Model

Emphasizes relevance for collider physics and fundamental constants

Abstract

The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the Standard Model of elementary particles. In this survey article the most recent and relevant computer algebra and special function algorithms are presented that are currently used or that may play an important role to perform such challenging precision calculations in the future. They are discussed in the context of analytic zero, single and double scale calculations in the Quantum Field Theories of the Standard Model and effective field theories, also with classical applications. These calculations play a central role in the analysis of precision measurements at present and future colliders to obtain ultimate information for fundamental physics.