  In this paper we study the theoretical uncertainties in the determination of
the top-quark mass using next-to-leading-order (NLO) generators interfaced to
parton showers (PS) that have different levels of accuracy. Specifically we
consider three generators: one that implements NLO corrections in the
production dynamics, one that includes also NLO corrections in top decay in the
narrow width approximation, and one that implements NLO corrections for both
production and decay including finite-width and interference effects. Since our
aim is to provide an assessment of the uncertainties of purely theoretical
origin, we consider simplified top-mass related observables that are broadly
related to those effectively used by experiments, eventually modelling
experimental resolution effects with simple smearing procedures. We estimate
the differences in the value of the extracted top mass that would occur due to
the use of the three different NLO generators, to the variation of scales, to
the choice of parton distribution functions and to the matching procedure.
Furthermore, we also consider differences due to the shower and to the
modelling of non-perturbative effects by interfacing our NLO generators to both
Pythia8.2 and Herwig7.1, with various settings. We find very different results
depending upon the adopted shower model. While with Pythia8.2 we find moderate
differences between the different NLO+PS generators, with Herwig7.1 we find
very large ones. Furthermore, the differences between Pythia8.2 and Herwig7.1
generators are also remarkably large.
