New and Old Jet Clustering Algorithms for Electron-Positron Events

TL;DR

This paper surveys and compares a wide range of jet clustering algorithms for $e^+e^-$ annihilations, tracing their historical development and assessing their theoretical and experimental performance. By contrasting distance measures, preclustering/reassignment strategies, and coherence with QCD cascades, it highlights how different schemes impact perturbative calculations, particularly the fixed-order and resummed behavior of jet observables such as the three-jet rate and $f_3(y)$. A key finding is that no single algorithm is best in all contexts; algorithms with angular ordering and soft-freezing (e.g., Cambridge, DL, CL) tend to exhibit reduced scale dependence and improved perturbative stability, aiding precise extractions of $\alpha_s$ and robust interpretations of soft-gluon dynamics. The study also clarifies how perturbative sensitivity, hadronization effects, and flavor dependence influence the choice of jet finder for specific analyses.

Abstract

Over the years, many jet clustering algorithms have been proposed for the analysis of hadronic final states in $e^+e^-$ annihilations. These have somewhat different emphasis and are therefore more or less suited for various applications. We here review some of the most used and compare them from a theoretical and experimental point of view.

Figures (8)

• Figure 1: The ordering of emissions in Ariadne, HERWIG, and Jetset QCD showers in the plane of $\kappa$ and $y$ (logarithm of transverse momentum and rapidity of emitted gluons).
• Figure 2: The seagull diagram with $E_3,E_4\ll E_1,E_2$ and $\theta_{14},\theta_{23}\ll\theta_{34}$.
• Figure 3: Parton branching with 'unresolved', soft, large-angle gluon emission $g_4$. Here, one has the following configuration: $E_2\gg E_3\gg E_4$, and $\theta_{23}\ll \theta_{24}\approx\theta_{34}$.
• Figure 4: Parton branching with 'resolved', soft, large-angle gluon emission $g_4$. In this case, $\theta_{45}>\theta_{4\hat{23}}$, where $\hat{23}$ symbolizes the cluster formed by the merging of $\bar{q}_2$ and $g_3$.
• Figure 5: The parton level $A(y)$ function entering in the three-jet fraction (\ref{['f3']}) at LO and NLO in the D, A and C schemes (solid line), DL and CL schemes (dashed line), AR0 and AR1 schemes (dotted line).