Structure of non-global logarithms with Cambridge/Aachen clustering

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. 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.