$N^3LO$ calculations for $2 \to 2$ processes using Simplified Differential Equations

TL;DR

This paper introduces a novel application of the Simplified Differential Equations method to compute complex three-loop Feynman integrals for 2-to-2 scattering processes, advancing precision calculations in quantum field theory.

Contribution

It demonstrates the use of the SDE approach to evaluate three-loop ladder-box integrals with one off-shell leg, providing new tools for high-precision theoretical predictions.

Findings

Successful computation of massless three-loop ladder-box integrals.

Development of canonical differential equations for tennis-court families.

Application of SDE approach to complex multi-loop integrals.

Abstract

We present the computation of the massless three-loop ladder-box family with one external off-shell leg using the Simplified Differential Equations (SDE) approach. We also discuss the methods we used for finding a canonical differential equation for the two tennis-court families with one off-shell leg, and the application of the SDE approach on these two families.