Factorization of boosted multijet processes for threshold resummation

Abstract

Explicit applications of factorization theorems for processes at hadron colliders near the hadronic end point have largely focused on simple final states with either no jets (e.g., Drell-Yan) or one inclusive jet (e.g., deep-inelastic scattering and prompt photon production). Factorization for the former type of process gives rise to a soft function that depends on timelike momenta, whereas the soft function for the latter type depends on null momenta. We derive in soft-collinear effective theory a factorization theorem that allows for an arbitrary number of jets, where the jets are defined with respect to a jet algorithm, together with any number of nonstrongly interacting particles. We find the soft function in general depends on the null components of the soft momenta inside the jets and on a timelike component of the soft momentum outside of the jets. This generalizes and interpolates between the soft functions for the cases of no jets and one inclusive jet. We verify consistency of our factorization theorem to $\mathcal{O}({\ensuremath{\alpha}}_{s})$ for any number of jets. While in this paper we demonstrate consistency only near the hadronic end point, we keep the kinematics general enough (in particular allowing for nonzero boost) to allow for an extension to partonic threshold resummation away from the hadronic end point.