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A search is presented for single production of a vector-like quark (T)decaying to a Z boson and a top quark, with the Z boson decaying leptonicallyand the top quark decaying hadronically. The search uses data collected by theCMS experiment in proton-proton collisions at a center-of-mass energy of 13 TeVin 2016, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Thepresence of forward jets is a particular characteristic of single production ofvector-like quarks that is used in the analysis. For the first time, differentT quark width hypotheses are studied, from negligibly small to 30% of the newparticle mass. At the 95% confidence level, the product of cross section andbranching fraction is excluded above values in the range 0.26-0.04 pb for Tquark masses in the range 0.7-1.7 TeV, assuming a negligible width. A similarsensitivity is observed for widths of up to 30% of the T quark mass. Theproduction of a heavy Z' boson decaying to Tt, with T $\rightarrow$ tZ, is alsosearched for, and limits on the product of cross section and branchingfractions for this process are set between 0.13 and 0.06 pb for Z' boson massesin the range from 1.5 to 2.5 TeV.

Search for single production of a vector-like T quark decaying to a Z boson and a top quark in proton-proton collisions at $\sqrt{s} = $13 TeV