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At the LHC, top quarks can be produced singly with a sizeable rate viaelectroweak interactions. This process probes a limited set of top-quarkelectroweak couplings, i.e. , the same entering the top-quark decay, yet athigher scales and with a different sensitivity. Requiring the production of a$Z$ or $H$ boson in association with single-top significantly extends thesensitivity of this process to new physics, opening up the unique possibilityof testing top-Higgs, top-gauge, triple gauge, gauge-Higgs interactions withoutbeing dominated by QCD interactions. We consider $tZj$ and $tHj$ production atthe LHC, providing predictions at next-to-leading accuracy in QCD in theframework of the standard model effective field theory, including all relevantoperators up to dimension six. We perform the first complete study of thesensitivity to new interactions of these processes, highlighting the interplayand complementarity among $tj$, $tZj$ and $tHj$ in simultaneously constrainingtop-quark, triple gauge, and gauge-Higgs interactions in the current and futureruns at the LHC.

Single-top associated production with a $Z$ or $H$ boson at the LHC: the SMEFT interpretation