The N-jettiness soft function at next-to-next-to-leading order

TL;DR

This paper develops a comprehensive method to calculate soft functions at NNLO in QCD, specifically applying it to the N-jettiness observable, with numerical results relevant for collider phenomenology.

Contribution

It introduces a general framework for NNLO soft function calculations in SCET and applies it to N-jettiness, providing the first complete NNLO results for this observable.

Findings

Complete NNLO soft function for N-jettiness obtained

Numerical results for one-jettiness in electron-proton and proton-proton collisions

Framework applicable to other SCET_I observables

Abstract

We present a general framework for the calculation of soft functions for SCET_I observables through next-to-next-to-leading order (NNLO) in the strong coupling constant. As an example of our formalism we show how it can be used to obtain the complete NNLO soft function for the $N$-jettiness event shape variable. We present numerical results for two examples with phenomenological impact: the one-jettiness soft function for both electron-proton and proton-proton collisions.