Factorization of Boosted Multijet Processes for Threshold Resummation

TL;DR

This paper develops a soft-collinear effective theory (SCET) based factorization theorem for hadron-collider processes producing an arbitrary number of jets near the hadronic threshold, with jets defined by a jet algorithm and any number of non-strongly interacting particles. The authors introduce a novel soft function that depends on the timelike soft momentum outside the jets and the null components of soft momentum inside each jet, enabling interpolation between the zero-jet and single-jet limits and facilitating threshold resummation. They derive the factorization formula, define the hard, jet, and soft functions, and compute their one-loop anomalous dimensions to demonstrate renormalization-group consistency at ${\cal O}(\alpha_s)$, paving the way for NLL (and potentially NNLL) resummations for multi-jet final states. The framework provides a path toward precision predictions for multijet processes at the LHC, including extensions away from hadronic endpoint guided by parton-luminosity steering.

Abstract

Explicit applications of factorization theorems for processes at hadron colliders near the hadronic endpoint 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 non-strongly 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 order alpha_s for any number of jets. While in this paper we demonstrate consistency only near the hadronic endpoint, 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 endpoint.