Single soft gluon emission at two loops

TL;DR

This paper computes the two-loop single soft-gluon current in massless QCD and ${ m extbf{N=4}}$ Super-Yang-Mills theory, providing essential ingredients for high-order Higgs production calculations and revealing uniform transcendentality.

Contribution

It presents the analytical calculation of the two-loop soft-gluon current in QCD and ${ m extbf{N=4}}$ SYM, including expansions to order $oldsymbol{ extepsilon^2}$ and insights into three-loop predictions.

Findings

Analytical two-loop soft-gluon current in QCD and ${ m extbf{N=4}}$ SYM.

Expansion to order $oldsymbol{ extepsilon^2}$ for Higgs production.

Uniform transcendentality observed in ${ m extbf{N=4}}$ SYM results.

Abstract

We study the single soft-gluon current at two loops with two energetic partons in massless perturbative QCD, which describes, for example, the soft limit of the two-loop amplitude for $gg\to Hg$. The results are presented as Laurent expansions in $\epsilon$ in $D=4-2\epsilon$ spacetime dimension. We calculate the expansion to order $\epsilon^2$ analytically, which is a necessary ingredient for Higgs production at hadron colliders at next-to-next-to-next-to-leading order in the soft-virtual approximation. We also give two-loop results of the single soft-gluon current in ${\cal N}=4$ Super-Yang-Mills theory, and find that it has uniform transcendentality. By iteration relation of splitting amplitudes, our calculations can determine the three-loop single soft-gluon current to order $\epsilon^0$ in ${\cal N}=4$ Super-Yang-Mills theory in the limit of large $N_c$.