We clarify some aspects of the LSZ formalism and wave-function renormalization for unstable particles in the presence of electroweak interactions when mixing and CP violation are considered. We also analyze the renormalization of the Cabibbo-Kobayashi-Maskawa ͑CKM͒ mixing matrix which is closely related to wavefunction renormalization. We critically review earlier attempts to define a set of ''on-shell'' wave-function renormalization constants. With the aid of extensive use of the Nielsen identities complemented by explicit calculations we corroborate that the counterterm for the CKM mixing matrix must be explicitly gauge independent and demonstrate that the commonly used prescription for the wave-function renormalization constants leads to gauge parameter dependent amplitudes, even if the CKM counterterm is gauge invariant as required. We show that a proper LSZ-compliant prescription leads to gauge independent amplitudes. The resulting wave-function renormalization constants necessarily possess absorptive parts, but we verify that they comply with the expected requirements concerning CP and CPT. The results obtained using this prescription are different ͑even at the level of the modulus squared of the amplitude͒ from the ones neglecting the absorptive parts in the case of top decay. The difference is numerically relevant.

We parametrize in a model-independent way possible departures from the minimal standard model predictions in the matter sector. We only assume the symmetry breaking pattern of the standard model and that new particles are sufficiently heavy so that the symmetry is nonlinearly realized. Models with dynamical symmetry breaking are generically of this type. We review in effective theory language to what extent the simplest models of dynamical breaking are actually constrained and the assumptions going into the comparison with experiment. Dynamical symmetry breaking models can be approximated at intermediate energies by fourfermion operators. We present a complete classification of the latter when new particles appear in the usual representations of the SU(2) L ϫSU(3) c group as well as a partial classification in the general case. We discuss the accuracy of the four-fermion description by matching to a simple ''fundamental'' theory. The coefficients of the effective Lagrangian in the matter sector for dynamical symmetry breaking models ͑expressed in terms of the coefficients of the four-quark operators͒ are then compared to those of models with elementary scalars ͑such as the minimal standard model͒. Contrary to a somewhat widespread belief, we see that the sign of the vertex corrections is not fixed in dynamical symmetry breaking models. This work provides the theoretical tools required to analyze, in a rather general setting, constraints on the matter sector of the standard model.

We construct the most general effective Lagrangian of the matter sector of the standard model, including mixing and 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 ⌳ӷM 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 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 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.