Non-Global Logarithms, Factorization, and the Soft Substructure of Jets

TL;DR

This paper develops a method to factorize and resum non-global logarithms in QCD jet physics through multiple measurements, achieving high accuracy and agreement with Monte Carlo simulations, enhancing understanding of soft jet dynamics.

Contribution

It introduces a novel factorization and resummation framework for non-global logarithms using multiple measurements, allowing arbitrary perturbative accuracy and connection to inclusive observables.

Findings

Resummation achieved via renormalization group evolution.

Agreement with Monte Carlo at sub-percent level for leading logs.

Framework applicable to soft jet dynamics and higher-order accuracy.

Abstract

An outstanding problem in QCD and jet physics is the factorization and resummation of logarithms that arise due to phase space constraints, so-called non-global logarithms (NGLs). In this paper, we show that NGLs can be factorized and resummed down to an unresolved infrared scale by making sufficiently many measurements on a jet or other restricted phase space region. Resummation is accomplished by renormalization group evolution of the objects in the factorization theorem and anomalous dimensions can be calculated to any perturbative accuracy and with any number of colors. To connect with the NGLs of more inclusive measurements, we present a novel perturbative expansion which is controlled by the volume of the allowed phase space for unresolved emissions. Arbitrary accuracy can be obtained by making more and more measurements so to resolve lower and lower scales. We find that even a minimal number of measurements produces agreement with Monte Carlo methods for leading-logarithmic resummation of NGLs at the sub-percent level over the full dynamical range relevant for the Large Hadron Collider. We also discuss other applications of our factorization theorem to soft jet dynamics and how to extend to higher-order accuracy.