Single-soft emissions for amplitudes with two colored particles at three loops

TL;DR

This paper calculates the three-loop correction to the single-soft emission current for scattering amplitudes with two color-charged particles, developing new techniques applicable to QCD and supersymmetric theories.

Contribution

It introduces a novel integrand expansion method for soft emissions and provides high-order corrections relevant for precision calculations in QCD and supersymmetric theories.

Findings

Three-loop correction to soft emission current computed

New integrand expansion technique developed

Contributions to Higgs and Drell-Yan cross sections at N$^4$LO

Abstract

We compute the three-loop correction to the universal single-soft emission current for the case of scattering amplitudes with two additional color-charged partons. We present results valid for QCD and $\mathcal{N}=4$ super-symmetric Yang-Mills theory. To achieve our results we develop a new integrand expansion technique for scattering amplitudes in the presence of soft emissions. Furthermore, we obtain contributions from single final-state parton matrix elements to the Higgs boson and Drell-Yan production cross section at next-to-next-to-next-to-next-to leading order (N$^4$LO) in perturbative QCD in the threshold limit.