Search for single production of a vector-like quark T decaying to a top quark and a Z boson with the Z boson decaying to neutrinos

A search is presented for single production of a vector-like quark T of electric charge $+2/3$ 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 $13~\mathrm{TeV}$ recorded at the CERN LHC in 2016-2018, corresponding to an integrated luminosity of $136~\mathrm{fb}^{-1}$. The search is sensitive to a T quark mass between $0.6$ and $1.8~\mathrm{TeV}$ with decay widths ranging from narrow up to $30\%$ of the T quark mass. Reconstruction strategies for the top quark are optimized for boosted and non-boosted regimes. At the $95\%$ confidence level, in the studied T quark mass range the product of the cross section and branching fraction is excluded above values in the range $15$-$602~\mathrm{fb}$ for a T quark of narrow decay width, and above values in the range $16$-$836~\mathrm{fb}$ for decay widths from $10\%$ to $30\%$ of the T quark mass. $$\textit{This document has been revised with respect to the version dated March 3, 2021.}$$