Maximal transcendental weight contribution of scattering amplitudes

TL;DR

This paper introduces a method to extract the maximal transcendental weight component of Feynman integrals in scattering amplitudes, using singularity structure insights, demonstrated on two-loop gluon fusion to Higgs processes.

Contribution

A novel approach to project Feynman integrals onto their maximal weight parts, complementing existing unitarity methods, with a proof-of-principle application to two-loop scattering amplitudes.

Findings

Successfully applied to two-loop $gg \to H$ amplitudes

Handles both planar and non-planar integrals

Provides insights into singularity structures and evanescent terms

Abstract

Feynman integrals in quantum field theory evaluate to special functions and numbers that are usefully described by the notion of transcendental weight. In this paper, we propose a way of projecting a given dimensionally-regularised Feynman integral, for example contributing to a scattering amplitudes, onto its maximal weight part. The method uses insights into the singularity structure of space-time loop integrands, and is complementary to usual generalised unitarity approaches. We describe the method and give a proof-of-principle application to the two-loop scattering amplitudes $gg \to H$ in the heavy top-quark mass limit, which involves both planar and non-planar Feynman integrals. We also comment on further possible applications and discuss subtleties related to evanescent integrand terms.