Electroweak standard model at finite temperature in presence of a bosonic chemical potential

We study the electroweak standard model at finite temperature in presence of a bosonic chemical potential associated with the conserved electromagnetic current. To preserve the thermodynamic equilibrium of the system, the thermal medium is neutralized by the introduction of four background charges related to the four gauge bosons of this model. Using the mean-field approximation, in the high temperature limit, we find that there exists a difference between the effective mass of the spatial and temporal components of the W boson. A W boson condensation induced via the background charges allows to vanish this difference.