CPviolation and family mixing in the effective electroweak Lagrangian

Abstract

We construct the most general effective Lagrangian of the matter sector of the standard model, including mixing and $\mathrm{CP}$ violating terms. The Lagrangian contains the effective operators that give the leading contribution in theories where the physics beyond the standard model shows at a scale $\ensuremath{\Lambda}\ensuremath{\gg}{M}_{W}.$ We perform the diagonalization and passage to the physical basis in full generality. We determine the contribution to the different observables and discuss the possible new sources of $\mathrm{CP}$ violation, the idea being to be able to gain some knowledge about new physics beyond the standard model from general considerations, without having to compute model by model. The values of the coefficients of the effective Lagrangian in some theories, including the standard model, are presented and we try to draw some general conclusions about the general pattern exhibited by physics beyond the standard model in what concerns $\mathrm{CP}$ violation. In the process we have had to deal with two theoretical problems which are very interesting in their own: the renormalization of the CKM matrix elements and the wave function renormalization in the on-shell scheme when mixing is present.