Automated Calculation of $N$-jet Soft Functions

Abstract

We present a systematic framework for the calculation of soft functions that are defined in terms of $N\ge 2$ light-like Wilson lines. The formalism represents an extension of a method that we developed earlier for the calculation of dijet soft functions to the general $N$-jet case. We discuss the technical aspects of this generalisation, focussing on SCET-1 soft functions that obey the non-Abelian exponentiation theorem in this contribution. As a first application of our method, we consider the $N$-jettiness observable and present numerical results for the $1$-jettiness and $2$-jettiness hadron-collider soft functions to next-to-next-to-leading order in the perturbative expansion.

Comments: 10 pages, 3 figures, to appear in the proceedings of the Loops and Legs conference 2018, 29 April - 4 May 2018, St. Goar, Germany