Search for a heavy resonance decaying to a top quark and a vector-like top quark in the lepton+jets final state

A search is presented for a heavy spin-1 resonance $\mathrm{Z}^\prime$ decaying to a top quark and a vector-like top quark T in the lepton+jets final state. The search is performed using a data set of proton-proton collisions at a centre-of-mass energy of $13~\mathrm{TeV}$ corresponding to an integrated luminosity of $35.9~\mathrm{fb}^{-1}$ as recorded by the CMS experiment at the CERN LHC in the year 2016. The analysis is optimised for final states arising from the T decay modes to a top quark and a Higgs or a Z boson ($\mathrm{T} \to \mathrm{Ht},\,\mathrm{Zt}$). The event selection makes use of resolved and boosted top quark decays, as well as boosted decays of H bosons and heavy gauge bosons using jet substructure techniques. No signficant deviation from the standard model background expectation is observed. Model-independent exclusion limits on the product of the cross section and branching fraction are presented for various combinations of the $\mathrm{Z}^\prime$ resonance mass and the vector-like T quark mass. In a benchmark model with extra dimensions, masses of the $\mathrm{Z}^\prime$ resonance less than $2.4~\mathrm{TeV}$ are excluded. These limits represent the most stringent limits to date for the decay mode $\mathrm{Z}^\prime \to \mathrm{tT} \to \mathrm{tHt}$.