{The unitarity condition of the Cabibbo-Kobayashi-Maskawa provides an important precision test of the Standard Model. This test requires a good control of different theoretical contributions. In this talk, we discuss the short-distance corrections to the weak effective theory as well as the lattice-to-continuum matching for the semi-leptonic four-fermi operator. We compare different renormalisation schemes used in the computation of these radiative corrections, namely the \wmass scheme and the $\overline{\rm MS}$ scheme. We also discuss the calculation of the two-loop $\mathcal{O}(\alpha \alpha_s)$ electroweak corrections and the corresponding three-loop $\mathcal{O}(\alpha\alpha_s^2)$ anomalous dimension for the effective theory Wilson coefficient. We also present numerical results for the $\mathcal{O}(\alpha \alpha_s)$ conversion factor to the regularisation independent scheme, which is used in Lattice calculations.