  We present results for the 2-jettiness differential distribution for boosted
top quark pairs produced in $e^+e^-$ collisions in the peak region accounting
for QCD large-logarithm resummation at next-to-next-to-next-to-leading
logarithmic (N$^3$LL) order and fixed-order corrections to matrix elements at
next-to-next-to-leading order (NNLO) calculated in the framework of
soft-collinear effective theory and boosted heavy quark effective theory.
Electroweak and finite-width effects are included at leading order. We study
the perturbative convergence of the cross section in the pole and MSR mass
schemes, with and without soft gap subtractions. We find that there is a
partial cancellation between the pole mass and soft function renormalons. When
renormalon subtractions concerning the top mass and the soft function are
implemented, the perturbative uncertainties are, however, systematically
smaller and an improvement in the stability of the peak position is observed.
We find that the top MSR mass may be determined with perturbative uncertainties
well below $100$\,MeV from the peak position of the 2-jettiness distribution.
This result has important applications for Monte Carlo top quark mass
calibrations.
