We present theoretical results with soft-gluon corrections for two separate processes: (1) the production of a single top quark in association with a $W$ boson in the Standard Model; and (2) the production of a single top quark in association with a heavy $Z$ boson in new physics models with or without anomalous couplings. We show that the higher-order corrections from soft-gluon emission are dominant for a wide range of collider energies. Results are shown for the total cross sections and top-quark transverse-momentum and rapidity distributions for $tW$ and $tZ$ production at LHC and future collider energies up to 100 TeV. The uncertainties from scale dependence and parton distribution functions are also analyzed.
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