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 non-trivial 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 $\alpha_s^2 L^2$, $\alpha_s^3 L^3$ and $\alpha_s^4 L^4$ 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.