  Jet grooming has emerged as a necessary and powerful tool in a precision jet
physics program. In this paper, we present three results on jet grooming in
perturbation theory, focusing on heavy jet mass in $e^+e^-\to$ hadrons
collisions, groomed with the modified mass drop tagger. First, we calculate the
analytic cross section at leading-order. Second, using the leading-order result
and numerical results through next-to-next-to-leading order, we show that cusps
in the distribution on the interior of phase space at leading-order are
softened at higher orders. Finally, using analytic and numerical results, we
show that terms that violate the assumptions of the factorization theorem for
groomed jet mass are numerically much smaller than expected from power
counting. These results provide important information regarding the convergence
of perturbation theory for groomed jet observables and reliable estimates for
residual uncertainties in a precision calculation.
