  We show that the presence of an infrared cutoff $Q_0$ in the parton shower
(PS) evolution for massive quarks implies that the generator quark mass
corresponds to a $Q_0$-dependent short-distance mass scheme and is therefore
not the pole mass. Our analysis considers an angular ordered parton shower
based on the coherent branching formalism for quasi-collinear stable heavy
quarks and splitting functions at next-to-leading logarithmic (NLL) order, and
it is based on the analysis of the peak of hemisphere jet mass distributions.
We show that NLL shower evolution is sufficient to describe the peak jet mass
at full next-to-leading order (NLO). We determine the relation of this
short-distance mass to the pole mass at NLO. We also show that the shower cut
$Q_0$ affects soft radiation in a universal way for massless and
quasi-collinear massive quark production. The basis of our analysis is (i) an
analytic solution of the PS evolution based on the coherent branching
formalism, (ii) an implementation of the infrared cut $Q_0$ of the angular
ordered shower into factorized analytic calculations in the framework of
Soft-Collinear-Effective-Theory (SCET) and (iii) the dependence of the peak of
the jet mass distribution on the shower cut. Numerical comparisons to
simulations with the HERWIG 7 event generator confirm our findings. Our
analysis provides an important step towards a full understanding concerning the
interpretation of top quark mass measurements based on direct reconstruction.
