The Semi-Leptonic Weak Hamiltonian: Going Beyond Two-Loops

Abstract

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-fermion operator. We compare different renormalisation schemes used in the computation of these radiative corrections, namely the 𝑊-Mass scheme and the MS scheme. We also discuss the calculation of the two-loop O (𝛼𝛼 𝑠 ) electroweak corrections and the corresponding three-loop O (𝛼𝛼 2 𝑠 ) anomalous dimension for the effective theory Wilson coefficient. We also present numerical results for the O (𝛼𝛼 𝑠 ) conversion factor to the regularisation independent scheme, which is used in Lattice calculations.