Current densities in a space-time-dependent and CP-violating Higgs background in the adiabatic limit

Motivated by cosmological applications such as electroweak baryogenesis, we develop a field theoretic approach to the computation of particle currents on a space-time-dependent and CP-violating Higgs back-ground in the adiabatic limit. We consider the standard model with two Higgs doublets and CP violation in the scalar sector, and compute both fermionic and Higgs currents by means of an expansion in the background fields describing the profile of the bubble wall. We discuss the gauge dependence of the results and the renormalization of the current operators, showing that in the limit of local equilibrium, no extra renormalization conditions are needed in order to specify the system completely.