  The measurement of the top quark mass has large systematic uncertainties
coming from the Monte Carlo simulations that are used to match theory and
experiment. We explore how much that uncertainty can be reduced by using jet
grooming procedures. We estimate the inherent ambiguity in what is meant by
Monte Carlo mass to be around 530 MeV without any corrections. This uncertainty
can be reduced by 60% to 200 MeV by calibrating to the W mass and a further 33%
to 140 MeV by applying soft-drop jet grooming (or by 20% more to 170 MeV with
trimming). At e+e- colliders, the associated uncertainty is around 110 MeV,
reducing to 50 MeV after calibrating to the W mass. By analyzing the tuning
parameters, we conclude that the importance of jet grooming after calibrating
to the W mass is to reduce sensitivity to the underlying event.
