Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism

TL;DR

This paper derives more compact and stable two-loop five-parton finite remainders in the spinor-helicity formalism, improving evaluation speed and numerical stability for high-energy physics calculations.

Contribution

It introduces a new spinor-helicity based reconstruction method that reduces sampling requirements and enhances the evaluation of two-loop five-parton finite remainders.

Findings

More compact expressions in spinor-helicity variables.

Faster and more stable numerical evaluations.

Requires fewer samples for analytical reconstruction.

Abstract

We present all two-loop five-parton leading-colour finite remainders in the spinor-helicity formalism by analysing numerical evaluations of their known expressions in terms of Mandelstam invariants. Recasting them in terms of spinor-helicity variables allows us to obtain expressions which are more compact, faster to evaluate, numerically more stable and manifestly free from poles of higher order than necessary. At the same time, due to the better scaling of our reconstruction strategy with the complexity of the input, we required one order of magnitude fewer numerical samples to complete the analytical reconstruction than were needed by the authors of Ref. \cite{Abreu:2019odu}, albeit using higher numerical working precision. This places our reconstruction technique as an alternative to the finite-field single-numerator reconstruction for future applications.