Integral of the double-emission eikonal function for a massive and a massless emitter at an arbitrary angle

Abstract

We present an analytic calculation of the integrated double-emission eikonal function of a massive and a massless emitter whose momenta are at an arbitrary angle to each other. This quantity provides one of the required ingredients for extending the nested soft-collinear subtraction scheme to processes with massive final-state particles. To calculate it, we use the standard methodology involving reverse unitarity and its extension to cases with Heaviside functions, integration-by-parts technology and reduction to master integrals, and differential equations. In addition, we also describe a semi-numerical method based on the subtraction of infra-red and collinear singularities from the eikonal function, allowing us to extract divergences of the integrated eikonal function analytically, and to derive a simple integral representation for the finite remainder.