Single soft gluon emission at two loops

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 $\mathcal{N}=4$ 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 $\mathcal{N}=4$ Super-Yang-Mills theory in the limit of large $N_c$.

typos corrected; journal version

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