The Soft Function for Exclusive N-Jet Production at Hadron Colliders

TL;DR

This paper derives a factorization theorem for N-jettiness at hadron colliders, computes the soft function at NLO, and provides tools for advanced resummed predictions in N-jet processes.

Contribution

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

Findings

Derived a factorization theorem for N-jettiness cross sections.

Computed the NLO soft function with analytical UV divergence extraction.

Provided numerical integrals for extending predictions to NNLL accuracy.

Abstract

The N-jettiness event shape divides phase space into N+2 regions, each containing one jet or beam. Using a geometric measure these regions correspond to jets with circular boundaries. We give a factorization theorem for the cross section fully differential in the (transverse) mass of each jet, and compute the corresponding soft function at next-to-leading order (NLO). The ultraviolet divergences are analytically extracted by exploiting hemispheres for interactions between each pair of hard partons, leaving only convergent integrals that are sensitive to the precise boundaries. This method can be applied in general to N-jet soft functions, including other observables. For N-jettiness, the final result for the soft function involves stable one-dimensional numerical integrals, and all ingredients are now available to extend NLO cross sections to resummed predictions at next-to-next-to-leading logarithmic order.