Single soft gluon emission at two loops

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 -> 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 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 N = 4 Super-Yang-Mills theory in the limit of large N-c.