  A search is presented for single production of a vector-like T quark with
charge 2/3 $e$, in the decay channel featuring a top quark and a Z boson, with
the top quark decaying hadronically and the Z boson decaying to neutrinos. The
search uses data collected by the CMS experiment in proton-proton collisions at
a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of
137 fb$^{-1}$ recorded at the CERN LHC in 2016-2018. The search is sensitive to
a T quark mass between 0.6 and 1.8 TeV with decay widths ranging from
negligibly small up to 30% of the T quark mass. Reconstruction strategies for
the top quark are based on the degree of Lorentz boosting of its final state.
At 95% confidence level, the upper limit on the product of the cross section
and branching fraction for a T quark of small decay width varies between 15 and
602 fb, depending on its mass. For a T quark with decay widths between 10 and
30% of its mass, this upper limit ranges between 16 and 836 fb. For most of the
studied range, the results provide the best limits to date. This is the first
search for single T quark production based on the full Run 2 data set of the
LHC.
