Analytical Calculation of Two-Loop Feynman Diagrams

TL;DR

This paper reviews advanced analytical methods for calculating complex two-loop Feynman diagrams, focusing on integral reduction, differential equations, and special functions for precise results.

Contribution

It introduces a comprehensive review of the Laporta algorithm, differential equations technique, and the use of harmonic polylogarithms for two-loop Feynman diagram calculations.

Findings

Effective reduction of scalar integrals to master integrals

Analytical expressions using harmonic polylogarithms

Generalizations to wider classes of transcendental functions

Abstract

We review the Laporta algorithm for the reduction of scalar integrals to the master integrals and the differential equations technique for their evaluation. We discuss the use of the basis of harmonic polylogarithms for the analytical expression of the results and some generalization of this basis to wider sets of transcendental functions.