  The most precise top quark mass measurements use kinematic reconstruction
methods, determining the top mass parameter of a Monte Carlo event generator,
$m_t^{\rm MC}$. Due to the complicated interplay of hadronization and parton
shower dynamics in Monte Carlo event generators relevant for kinematic
reconstruction, relating $m_t^{\rm MC}$ to field theory masses is a non-trivial
task. In this talk we report on a calibration procedure to determine this
relation using hadron level QCD predictions for 2-Jettiness in $e^+e^-$
annihilation, an observable which has kinematic top mass sensitivity and a
close relation to the invariant mass of the particles coming from the top
decay. The theoretical ingredients of the QCD prediction are reviewed. Fitting
$e^+e^-$ 2-Jettiness calculations at NLL/NNLL order to PYTHIA 8.205, we find
that $m_t^{\rm MC}$ agrees with the MSR mass $m_{t,1\,{\rm GeV}}^{\rm MSR}$
within uncertainties. At NNLL we find $m_t^{\rm MC} = m_{t,1\,{\rm GeV}}^{\rm
MSR} + (0.18 \pm 0.22)\,{\rm GeV}$. $m_t^{\rm MC}$ can differ from the pole
mass $m_t^{\rm pole}$ by up to $600\,{\rm MeV}$, and using the pole mass
generally leads to larger uncertainties. At NNLL we find $m_t^{\rm MC} =
m_t^{\rm pole} + (0.57 \pm 0.28)\,{\rm GeV}$ as the fit result. In contrast,
converting $m_{t,1\,{\rm GeV}}^{\rm MSR}$ obtained at NNLL to the pole mass
gives a result for $m_t^{\rm pole}$ that is substantially larger and
incompatible with the fit result. We also explain some theoretical aspects
relevant for employing the C-parameter as an alternative calibration
observable.
