Jet Regions from Event Shapes and the N-Jet Soft Function at Hadron Colliders

TL;DR

This paper develops a theoretical framework for analyzing jet regions in collider events using N-jettiness, providing a factorization theorem and NLO soft function calculations to enable advanced resummed predictions.

Contribution

It introduces a fully differential factorization theorem for N-jettiness and computes the soft function at NLO, enabling higher-order resummed predictions for jet cross sections.

Findings

Derived a factorization theorem for N-jettiness cross sections.

Computed the NLO soft function for N-jettiness.

Laid groundwork for NNLL resummation of jet observables.

Abstract

The N-jettiness event shape divides phase space into N+2 regions, each containing one jet or beam. These jet regions are insensitive to the distribution of soft radiation and, with a geometric measure for N-jettiness, have circular boundaries. We give a factorization theorem for the cross section which is fully differential in the mass of each jet, and compute the corresponding soft function at next-to-leading order (NLO). For N-jettiness, all ingredients are now available to extend NLO cross sections to resummed predictions at next-to-next-to-leading logarithmic order.