Searching for vectorlike $T$ quarks in the $T\to tZ$ channel at a future muon-proton collider

We investigate the discovery potential of a singly produced vector-like top quark $T$ in the $T\to tZ$ decay channel at future muon-proton ($μp$) colliders, considering three benchmark center-of-mass energies: $\sqrt{s}=5.29$, $6.48$, and $9.16$~TeV. The baseline signal final state consists of a sem