Abelian Non-Global Logarithms from Soft Gluon Clustering

TL;DR

This paper investigates the impact of soft gluon clustering algorithms on jet cross sections, revealing that clustering logarithms are complex, likely non-resummable at NLL, and relate to non-global logarithms, with calculations for specific algorithms.

Contribution

It introduces the calculation of Abelian clustering logarithms at two loops for various jet algorithms, extending previous results and clarifying their relation to non-global logarithms.

Findings

Clustering logarithms appear at least at NLL in jet distributions.

Clustering effects can be viewed as a class of non-global logarithms.

Anti-kT algorithm suppresses clustering logarithms, making it theoretically preferred.

Abstract

Most recombination-style jet algorithms cluster soft gluons in a complex way. This leads to correlations in the soft gluon phase space and introduces logarithmic corrections to jet cross sections. The leading Abelian clustering logarithms occur at least at next-to leading logarithm (NLL) in the exponent of the distribution, and we show that new clustering effects contributing at NLL likely arise at each order. Therefore we find that it is unlikely that clustering logs can be resummed to NLL. Clustering logarithms make the anti-kT algorithm theoretically preferred, for which they are power suppressed. They can arise in Abelian and non-Abelian terms, and we calculate the Abelian clustering logarithms at two loops for the jet mass distribution using the Cambridge/Aachen and kT algorithms, including jet radius dependence, which extends previous results. We find that previously identified logarithms from clustering effects can be naturally thought of as a class of non-global logarithms (NGLs), which have traditionally been tied to non-Abelian correlations in soft gluon emission.