\begin{document}$ 2/3 $\end{document}, we analyze the prospects of observing T via the single T production in the \begin{document}$ tZ $\end{document} channel with Z decaying to neutrinos at the hadron-hadron colliders. This simplified model only includes two free parameters, the coupling constant \begin{document}$ g^* $\end{document} and the T quark mass \begin{document}$ m_T $\end{document}. To investigate the observability of the single T production, we perform a detailed background analysis and detector simulation for the collision energies 14 TeV, 27 TeV, and 100 TeV. We scan the \begin{document}$ g^*-m_T $\end{document} parameter space and show the exclusion and discovery capabilities on the T quark with the highest integrated luminosity designed at these colliders. Moreover, the limits from the narrow-width approximation and electroweak precision observables are considered."> Search for the singlet vector-like top quark in the <inline-formula><tex-math id="M1">\begin{document}$ {\boldsymbol T\boldsymbol\to{\boldsymbol {tZ}}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/93f17cf6-4e5d-4027-a359-24b356a0d02d/CPC-2022-0579_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/93f17cf6-4e5d-4027-a359-24b356a0d02d/CPC-2022-0579_M1.png"/></alternatives></inline-formula> channel with <inline-formula><tex-math id="M2">\begin{document}$ {{\boldsymbol Z}{\bf\to} \boldsymbol\nu\bar{\boldsymbol\nu}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/93f17cf6-4e5d-4027-a359-24b356a0d02d/CPC-2022-0579_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/93f17cf6-4e5d-4027-a359-24b356a0d02d/CPC-2022-0579_M2.png"/></alternatives></inline-formula> at hadron colliders -
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