One-loop transverse-momentum-dependent soft function at higher orders in the dimensional regulator

Abstract

The transverse-momentum-dependent (TMD) soft function for a generic hadroproduction process involving massive colored particles is analytically calculated at the one-loop level, extended to higher orders in the dimensional regulator $\hat{I}\mu$. We present both the azimuthal-angle-averaged and azimuthal-angle-dependent soft functions in impact-parameter space, making them suitable for small $q_T$ resummation calculations. Their analytic expressions are provided in terms of multiple polylogarithms. Our results offer essential ingredients for a complete higher-order perturbative calculation of the TMD soft function.

45 pages. v2: journal version (minor corrections wrt v1)