The First Calculation of Fractional Jets

TL;DR

This paper introduces the first analytic study of fractional jet multiplicity in $e^+e^-$ collisions, revealing unique factorization properties and divergences, and suggests future collider measurements.

Contribution

It provides the first fixed-order QCD analysis and a candidate factorization theorem for fractional jet multiplicity, highlighting its novel features and deviations from standard jet observables.

Findings

Distributions match parton shower Monte Carlo results.

Absence of collinear logarithms in the cross section.

Presence of non-global soft logarithms and novel divergences.

Abstract

In collider physics, jet algorithms are a ubiquitous tool for clustering particles into discrete jet objects. Event shapes offer an alternative way to characterize jets, and one can define a jet multiplicity event shape, which can take on fractional values, using the framework of "jets without jets". In this paper, we perform the first analytic studies of fractional jet multiplicity $\tilde{N}_{\rm jet}$ in the context of $e^+e^-$ collisions. We use fixed-order QCD to understand the $\tilde{N}_{\rm jet}$ cross section at order $\alpha_s^2$, and we introduce a candidate factorization theorem to capture certain higher-order effects. The resulting distributions have a hybrid jet algorithm/event shape behavior which agrees with parton shower Monte Carlo generators. The $\tilde{N}_{\rm jet}$ observable does not satisfy ordinary soft-collinear factorization, and the $\tilde{N}_{\rm jet}$ cross section exhibits a number of unique features, including the absence of collinear logarithms and the presence of soft logarithms that are purely non-global. Additionally, we find novel divergences connected to the energy sharing between emissions, which are reminiscent of rapidity divergences encountered in other applications. Given these interesting properties of fractional jet multiplicity, we advocate for future measurements and calculations of $\tilde{N}_{\rm jet}$ at hadron colliders like the LHC.