Computing the temperature dependence of effective CP violation in the standard model

CP violation in the standard model originates from the Cabibbo-Kobayashi-Maskawa mixing matrix. Upon integrating all fermions out of the theory, its effects are captured by a series of effective nonrenormalizable operators for the bosonic gauge and Higgs fields. We compute the CP-violating part of the effective action to the leading nontrivial, sixth order in the covariant gradient expansion as a function of temperature. In the limit of zero temperature, our result addresses the discrepancy between two independent calculations existing in the literature [1, 2]. We find that CP violation in the standard model is strongly suppressed at high temperature, but that at T less than or similar to 1 GeV it may be relevant for certain scenarios of baryogenesis. We also identify a selected class of operators at the next, eighth order and discuss the convergence of the covariant gradient expansion.