On the resummation of clustering logarithms for non-global observables

Clustering logs have been the subject of much study in recent literature. They are a class of large logs which arise for non-global jet-shape observables where final-state particles are clustered by a non-cone-like jet algorithm. Their resummation to all orders is highly non-trivial due to the role of clustering amongst soft gluons which results in the phase-space being non-factorisable. This may therefore significantly impact the accuracy of analytical estimations of many of such observables. Nonetheless, in this paper we address this very issue for jet shapes defined using the k(t) and C/A algorithms, taking the jet mass as our explicit example. We calculate the coefficients of the Abelian a(s)(2)L(2), a(s)(3)L(3) and a(s)(4)L(4) NLL terms in the exponent of the resummed distribution and show that the impact of these logs is small which gives confidence on the perturbative estimate without the neglected higher-order terms. Furthermore we numerically resum the non-global logs of the jet mass distribution in the k(t) algorithm in the large-N-c limit.