N$^3$LO Higgs and Drell-Yan production at threshold: the one-loop two-emission contribution

TL;DR

This paper computes the two-emission soft radiation contributions at N$^3$LO for Higgs and Drell-Yan processes, providing essential components for precise threshold corrections in QCD phenomenology.

Contribution

It presents a novel calculation of two soft parton emissions at N$^3$LO, crucial for accurate threshold corrections in Higgs and Drell-Yan production, with results consistent with existing predictions.

Findings

Results are valid to all orders in dimensional regularization.

Calculations are expressed in terms of pure functions.

Re-derivation of Drell-Yan threshold cross section confirms previous results.

Abstract

In this paper, we study phenomenologically interesting soft radiation distributions in massless QCD. Specifically, we consider the emission of two soft partons off of a pair of light-like Wilson lines, in either the fundamental or the adjoint representation, at next-to-leading order. Our results are an essential component of the next-to-next-to-next-to-leading order threshold corrections to both Higgs boson production in the gluon fusion channel and Drell-Yan lepton production. Our calculations are consistent with the recently published results for Higgs boson production. As a non-trivial cross-check on our analysis, we rederive a recent prediction for the Drell-Yan threshold cross section using a completely different strategy. Our results are compact, valid to all orders in the dimensional regularization parameter, and expressed in terms of pure functions.