Two-Loop Maximal Unitarity with External Masses

TL;DR

This paper extends the two-loop maximal unitarity method to include double-box integrals with up to three external masses, providing explicit formulas for their coefficients that can be used analytically or numerically.

Contribution

It introduces a novel extension of the maximal unitarity method to handle massive external legs at two loops, deriving unique coefficient formulas for master integrals.

Findings

Derived explicit formulas for double-box integral coefficients with external masses.

Validated the method's applicability for analytical and numerical computations.

Enhanced the precision of multi-loop amplitude calculations involving massive particles.

Abstract

We extend the maximal unitarity method at two loops to double-box basis integrals with up to three external massive legs. We use consistency equations based on the requirement that integrals of total derivatives vanish. We obtain unique formulae for the coefficients of the master double-box integrals. These formulae can be used either analytically or numerically.