We extend and improve upon our previous calculation of electroweak top-quark pair hadroproduction in extensions of the Standard Model with extra heavy neutral and charged spin-1 resonances. In particular, we allow for flavour-non-diagonal $Z$ couplings and take into account non-resonant production in the SM and beyond including the contributions with $t$-channel $W$ and $W$ bosons. All amplitudes are generated using the Recola2 package. As in our previous work, we include NLO QCD corrections and consistently match to parton showers with the POWHEG method fully taking into account the interference effects between SM and new physics amplitudes. We consider the Sequential Standard Model, the Topcolour model, as well as the Third Family Hypercharge Model featuring non-flavour-diagonal $Z$ couplings which has been proposed recently to explain the anomalies in $B$ decays. We present numerical results for $t bar t$ cross sections at hadron colliders with a centre-of-mass energy up to 100 TeV.
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