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 $$\sqrt{s} = 13\,\text {TeV} $$ s = 13 TeV

A search is presented for a heavy spin-1 resonance $$\mathrm {Z}'$$ 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 ( $$\text {T} \rightarrow \mathrm {H} \mathrm {t}, \mathrm {Z} \mathrm {t}$$ ). 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 $$\mathrm {Z}'\rightarrow \mathrm {t}\text {T}, \text {T} \rightarrow \mathrm {H} \mathrm {t}, \mathrm {Z} \mathrm {t}, \mathrm {W}\mathrm {b}$$ are presented for various combinations of the $$\mathrm {Z}'$$ resonance mass and the vector-like $$\text {T} $$ quark mass. These results represent the most stringent limits to date for the decay mode $$\mathrm {Z}'\rightarrow \mathrm {t}\text {T} \rightarrow \mathrm {t}\mathrm {H} \mathrm {t}$$ . In a benchmark model with extra dimensions, invoking a heavy spin-1 resonance $$\mathrm {G}^* $$ , masses of the $$\mathrm {G}^* $$ 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.