An Integrand Reconstruction Method for Three-Loop Amplitudes

TL;DR

This paper introduces a novel integrand reconstruction method for three-loop amplitudes using algebraic geometry techniques, enabling the extraction of master integral coefficients for complex scattering processes.

Contribution

It develops a new approach combining Groebner bases and primary decomposition to efficiently compute master integrals in three-loop four-point functions.

Findings

Analytic results for three-loop triple-box contributions to gluon-gluon scattering.

Method applicable to arbitrary triple-box configurations.

Extraction of all ten propagator master integral coefficients.

Abstract

We consider the maximal cut of a three-loop four point function with massless kinematics. By applying Groebner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.