Single-top $t$-channel production with off-shell and non-resonant effects

This letter details and discusses the next-to-leading order QCD corrections to $t$-channel electro-weak $W^+ b j$ production, where finite top-width effects are consistently taken into account. The computation is done within the aMC@NLO framework and includes both resonant and non-resonant contributions as well as interferences between the two. Results are presented for the LHC and compared to those of the narrow-width approximation and effective theory approaches.