Towards numerical two-loop integrand reduction

TL;DR

This paper introduces a method for reducing two-loop helicity amplitudes at the integrand level, facilitating automated calculations of complex scattering processes in particle physics.

Contribution

It presents a novel integrand-level reduction technique applicable to two-loop amplitudes in various dimensions, advancing towards automation in amplitude computations.

Findings

Method enables reduction of two-loop helicity amplitudes

Supports calculations in both $d=4-2\epsilon$ and $d=4$ dimensions

Lays groundwork for automated two-loop amplitude software

Abstract

We present a method for the integrand-level reduction of two-loop helicity amplitudes in both $d=4-2\epsilon$ and $d=4$ dimensions. The amplitude is expressed in terms of a set of Feynman integrals and their coefficients that depend on the external kinematics. The analysis presented in this paper, in conjunction with the ongoing development of the computational framework $\text{HELAC-2LOOP}$, paves the road for the construction of an automated program for two-loop amplitude calculations for arbitrary scattering processes.