  We describe the computation of the $\mathcal{O}(\alpha^3)$ corrections for
single top (and single anti-top) production in the $t$-channel at hadron
colliders. We show also The genuine one loop SUSY contribution to these
processes. Such contributions are generally quite modest in the mSUGRA
scenario. The experimental observables would therefore only practically depend,
in this framework, on the CKM $Wtb$ coupling.
