Abstract
Charged track multiplicity is among the most powerful observables for discriminating quark- from gluon-initiated jets. Despite its utility, it is not infrared and collinear (IRC) safe, so perturbative calculations are limited to studying the energy evolution of multiplicity moments. While IRC-safe observables, like jet mass, are perturbatively calculable, their distributions often exhibit Casimir scaling, such that their quark/gluon discrimination power is limited by the ratio of quark to gluon color factors. In this paper, we introduce new IRC-safe counting observables whose discrimination performance exceeds that of jet mass and approaches that of track multiplicity. The key observation is that track multiplicity is approximately Poisson distributed, with more suppressed tails than the Sudakov peak structure from jet mass. By using an iterated version of the soft drop jet grooming algorithm, we can define a “soft drop multiplicity” which is Poisson distributed at leading-logarithmic accuracy. In addition, we calculate the next-to-leading-logarithmic corrections to this Poisson structure. If we allow the soft drop groomer to proceed to the end of the jet branching history, we can define a collinear-unsafe (but still infrared-safe) counting observable. Exploiting the universality of the collinear limit, we define generalized fragmentation functions to study the perturbative energy evolution of collinear-unsafe multiplicity.
Highlights
Color charges, CF = 4/3 versus CA = 3, such that gluon jets emit more soft gluon radiation than quark jets
The quark/gluon performance of counting observables still depends on the color factors CA and CF, but instead of being described by Sudakov form factors, these observables are described by Poisson distributions; this allows their discrimination power to improve as more emissions are included
We introduced an infrared and collinear (IRC)-safe counting observable which approaches the quark/gluon discrimination performance of IRC-unsafe track multiplicity
Summary
Our counting observables are defined using an iterated variant of the soft drop declustering algorithm. Our analysis is based on ISD where the soft drop algorithm is iterated In this case, the procedure does not terminate when a hard branching is found, but is instead iteratively applied to the harder of the two subjets. While ISD could be used as a grooming procedure in its own right, the primary purpose of ISD in this paper is to determine which set of (zij, θij) branchings contribute to the observables we define below For this purpose, the ISD algorithm proceeds as follows:. We recluster and measure our observables on the hardest jet from each event using FastJet. Because ISD is sufficiently different from ordinary soft drop, we do not use the RecursiveTools fjcontrib [51], but rather directly traverse the C/A tree in our analysis. We plan to make our code available publicly in a future release of fjcontrib
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