$N$-jettiness soft function at next-to-next-to-leading order in perturbative QCD

TL;DR

This paper derives a compact, divergence-free representation of the $N$-jettiness soft function at NNLO in perturbative QCD, facilitating precise calculations in collider physics.

Contribution

It provides the first compact, divergence-free formula for the $N$-jettiness soft function at NNLO, applicable for any number of hard partons.

Findings

Analytical demonstration of divergence cancellation

Explicit formula for the finite remainder of the soft function

Applicable to arbitrary number of hard partons N

Abstract

We derive a compact representation of the renormalized $N$-jettiness soft function that is free of infrared and collinear divergences through next-to-next-to-leading order in perturbative QCD. The number of hard partons $N$ is a parameter in the formula for the finite remainder. Cancellation of all infrared and collinear singularities between the bare soft function and its renormalization matrix in color space is demonstrated analytically.