  Based on a simplified model including a singlet vector-like top quark $T$
with charge $|Q|=2/3$, we analyze the prospects of observing $T$ via the single
$T$ production in the $tZ$ channel with $Z$ decaying to neutrinos at the
hadron-hadron colliders. This simplified model only includes two free
parameters, the coupling constant $g^*$ and the $T$ quark mass $m_T$. To
investigate the observability of the single $T$ production, we perform a
detailed background analysis and detector simulation for the collision energies
14~TeV, 27~TeV, and 100~TeV. We scan the $g^*-m_T$ parameter space and show the
exclusion and discovery capabilities on the $T$ quark with the highest
integrated luminosity designed at these colliders. Moreover, the limits from
the narrow-width approximation and electroweak precision observables are
considered.
