Generalized resummation of QCD final-state observables

TL;DR

This work introduces a general master formula for next-to-leading logarithmic (NLL) resummation of a broad class of infrared- and collinear-safe QCD final-state observables in the n-jet limit, along with applicability conditions (rIRC safety, continuous globalness, etc.). It enables automatic extraction of observable-specific parameters from a simple subroutine, removing the need for fully manual resummations. The authors demonstrate the approach by producing the first NLL resummed prediction for an event shape in hadronic dijets (tau_perp), decomposed by underlying hard subprocesses and showing sensitivity to color structure and beam radiation. The results are semi-analytical and readily matchable to fixed-order calculations, signaling a path toward automated, cross-process resummations in QCD.

Abstract

The resummation of logarithmically-enhanced terms to all perturbative orders is a prerequisite for many studies of QCD final-states. Until now such resummations have always been performed by hand, for a single observable at a time. In this letter we present a general `master' resummation formula (and applicability conditions), suitable for a large class of observables. This makes it possible for next-to-leading logarithmic resummations to be carried out automatically given only a computer routine for the observable. To illustrate the method we present the first next-to-leading logarithmic resummed prediction for an event shape in hadronic dijet production.

Figures (1)

• Figure 1: NLL resummed differential distribution $D(\tau_\perp) \equiv d\Sigma(\tau_\perp)/d \ln \tau_\perp$ for different underlying hard subprocesses.