  In 2004 the matrix element method was used in a pioneering work by the
Tevatron experiment D0 to determine the top-quark mass from a handful of
events. Since then the method has been matured into a powerful analysis tool.
While the first applications were restricted to leading-order accuracy, in the
meantime also the extension to next-to-leading order (NLO) accuracy has been
studied. In this article we explore the potential of the matrix element method
at NLO to determine the top-quark mass using events with pair-produced top
quarks. We simulate a toy experiment by generating unweighted events with a
fixed input mass and apply the matrix element method to construct an estimator
for the top-quark mass. Two different setups are investigated: unweighted
events obtained from the fixed-order cross section at NLO accuracy as well as
events obtained using POWHEG matched to a parton shower. The latter lead to a
more realistic simulation and allow to study the impact of higher-order
corrections as well as the robustness of the approach. We find that the matrix
element method in NLO accuracy leads to a significant reduction of the
theoretical uncertainties compared to leading order. In view of the high
luminosity phase of the LHC, this observation is especially relevant in
analyses which are no longer dominated by statistical uncertainties.
