Search for a heavy resonance decaying to a top quark and a vector-like top quark in the lepton + jets final state in pp collisions at $$sqrts=13,extTeV$$ s = 13 TeV

A search is presented for a heavy spin-1 resonance $${\mathrm{Z}}^{\prime }$$ decaying to a top quark and a vector-like top quark partner $$\text{T}$$ in the lepton + jets final state. The search is performed using a data set of $$\mathrm{p}$$ $$\mathrm{p}$$ collisions at a centre-of-mass energy of 13 $$\text{TeV}$$ corresponding to an integrated luminosity of $$35.9{\text{fb}}^{-1}$$ as recorded by the CMS experiment at the CERN LHC in the year 2016. The analysis is optimised for final states arising from the $$\text{T}$$ decay modes to a top quark and a Higgs or $$\mathrm{Z}$$ boson ( $$\text{T}\to \mathrm{H}\mathrm{t},\mathrm{Z}\mathrm{t}$$ ). The event selection makes use of resolved and merged top quark decay products, as well as decays of boosted Higgs bosons and $$\mathrm{Z}$$ and $$\mathrm{W}$$ bosons using jet substructure techniques. No significant deviation from the standard model background expectation is observed. Exclusion limits on the product of the cross section and branching fraction for $${\mathrm{Z}}^{\prime }\to \mathrm{t}\text{T},\text{T}\to \mathrm{H}\mathrm{t},\mathrm{Z}\mathrm{t},\mathrm{W}\mathrm{b}$$ are presented for various combinations of the $${\mathrm{Z}}^{\prime }$$ resonance mass and the vector-like $$\text{T}$$ quark mass. These results represent the most stringent limits to date for the decay mode $${\mathrm{Z}}^{\prime }\to \mathrm{t}\text{T}\to \mathrm{t}\mathrm{H}\mathrm{t}$$ . In a benchmark model with extra dimensions, invoking a heavy spin-1 resonance $${\mathrm{G}}^{\ast }$$ , masses of the $${\mathrm{G}}^{\ast }$$ between 1.5 and 2.3 $$\text{TeV}$$ and between 2.0 and 2.4 $$\text{TeV}$$ are excluded for $$\text{T}$$ masses of 1.2 and 1.5 $$\text{TeV}$$ , respectively.