Structure of non-global logarithms with Cambridge/Aachen clustering

TL;DR

This paper analyzes the structure of non-global logarithms in QCD for $e^+e^-$ processes with jets clustered by Cambridge--Aachen, revealing its advantages over other algorithms in minimizing non-global effects.

Contribution

It provides the first detailed calculation of non-global logarithms up to four loops for C/A clustering, including full color and jet-radius dependence.

Findings

C/A clustering minimizes non-global logarithms compared to anti-$k_t$ and $k_t$ algorithms.

Expressions include full color and jet-radius dependence.

C/A is the preferred clustering algorithm for reducing non-global effects.

Abstract

We determine the structure of both Abelian and non-Abelian non-global logarithms up to four loops for $e^+e^-$ processes in perturbative QCD, where final-state jets are defined using the Cambridge--Aachen (C/A) clustering algorithm. The calculations are performed within the soft (eikonal) approximation using strong-energy ordering of the final-state partons for the case of the dijet invariant mass. The resulting expressions include full colour and complete jet-radius dependence. Compared to the anti-$k_t$ and $k_t$ clustering algorithms, the C/A distribution minimises the impact of these non-global logarithms, making it the preferred choice among the three algorithms.