Constructing multi-loop scattering amplitudes with manifest singularity structure

TL;DR

This paper introduces a new integral basis for multi-loop scattering amplitudes that makes their infrared singularity structure manifest at the integrand level, simplifying the analysis of divergence properties.

Contribution

It presents a novel finite, uniform weight integral basis that reveals infrared exponentiation properties directly at the integrand level.

Findings

The new basis makes infrared poles explicit in the integrand.

Applied to QCD two-loop form factors, it clarifies the origin of divergence terms.

Simplifies the analysis of multi-loop amplitude singularities.

Abstract

The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by introducing an appropriate integral basis which is simultaneously finite and uniform weight. As an example, we cast the integrand for the QCD corrections to the two-loop massless quark electromagnetic form factor into a form where it is manifest that the $\epsilon^{-4}$ and $\epsilon^{-3}$ pole terms arise from the $\epsilon$ expansion of the square of our one-loop master integral.