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.Comment: 38+10 pages, 21 figures; v2: discussions added to match JHEP versio