  This paper explores the effects of finite width in processes of pair
production of an extra heavy quark with charge 2/3 (top partner) and its
subsequent decay into a bosonic Dark Matter (DM) candidate -- either scalar or
vector -- and SM up-type quarks at the Large Hadron Collider (LHC). This
dynamics has been ignored so far in standard experimental searches of heavy
quarks decaying to DM and we assess herein the regions of validity of current
approaches, based on the assumption that the extra quarks have a narrow width.
Further, we discuss the configurations of masses, widths and couplings where
the latter breaks down.
