On the resummation of clustering logarithms for non-global observables

TL;DR

This paper investigates the resummation of clustering logarithms for non-global jet observables, specifically for jet mass distributions using $k_t$ and C/A algorithms, demonstrating that their impact is small and providing numerical resummation results.

Contribution

It calculates the coefficients of NLL terms for clustering logs in jet mass distributions and performs numerical resummation in the large-$N_c$ limit, addressing a complex resummation challenge.

Findings

Clustering logs have a small impact on jet mass distributions.

Calculated NLL coefficients for $ ext{α}_s^2$, $ ext{α}_s^3$, and $ ext{α}_s^4$ terms.

Numerically resummed non-global logs in the large-$N_c$ limit.

Abstract

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.