  Currently the most precise LHC measurements of the top quark mass are
determinations of the top quark mass parameter of Monte-Carlo (MC) event
generators reaching uncertainties of well below $1$ GeV. However, there is an
additional theoretical problem when using the MC top mass $m_t^{\rm MC}$ as an
input for theoretical predictions, because a rigorous relation of $m_t^{\rm
MC}$ to a renormalized field theory mass is, at the very strict level, absent.
In this talk I show how - nevertheless - some concrete statements on $m_t^{\rm
MC}$ can be deduced assuming that the MC generator behaves like a rigorous
first principles QCD calculator for the observables that are used for the
analyses. I give simple conceptual arguments showing that in this context
$m_t^{\rm MC}$ can be interpreted like the mass of a heavy-light top meson, and
that there is a conversion relation to field theory top quark masses that
requires a non-perturbative input. The situation is in analogy to B physics
where a similar relation exists between experimental B meson masses and field
theory bottom masses. The relation gives a prescription how to use $m_t^{\rm
MC}$ as an input for theoretical predictions in perturbative QCD. The outcome
is that at this time an additional uncertainty of about $1$ GeV has to be
accounted for. I discuss limitations of the arguments I give and possible ways
to test them, or even to improve the current situation.
