Soft functions for generalised angularity event shapes at NNLO

Abstract

We consider a class of dijet event shapes which tend to angularity in the forward limit. The factorisation formula for this class of event shapes differs from angularity only in the soft function. The NNLO soft function of an event shape in this class is therefore the only missing ingredient required for NNLL' resummation. We describe a modular approach to the calculation of the soft function for any event shape in this class, at NLO and NNLO. Much of the structure of the soft function can be written in terms of a single rapidity integral. The remainder can be computed as a three-dimensional numerical integral for which we provide a code. To demonstrate the flexibility of our approach, we compute the NNLO soft function for three new families of event shapes in this class. Potential applications include the investigation of hadronisation effects at future $e^+ e^-$ colliders, or through the re-analysis of archived data.