Three-loop on-shell Feynman integrals with two masses

TL;DR

This paper computes all three-loop on-shell QCD Feynman integrals with two masses by reducing them to 27 master integrals and providing their epsilon expansions, including exact and approximate forms.

Contribution

It presents the calculation of all relevant master integrals for three-loop on-shell two-mass Feynman diagrams, including their epsilon expansions and limiting case series.

Findings

Explicit expressions for master integrals obtained

Epsilon expansions provided for exact and approximate cases

Facilitates higher-order QCD calculations involving two masses

Abstract

All three-loop on-shell QCD Feynman integrals with two masses can be reduced to 27 master integrals. Here we calculate these master integrals, expanded in epsilon, both exactly in the mass ratio and as series in limiting cases.