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

TL;DR

This paper calculates how CP violation in the standard model varies with temperature, showing suppression at high temperatures and potential relevance for baryogenesis at lower temperatures, using a covariant gradient expansion approach.

Contribution

It provides the first detailed computation of the temperature-dependent CP-violating effective action in the standard model at sixth order in the gradient expansion.

Findings

CP violation is suppressed at high temperatures.

Potential relevance for baryogenesis below 1 GeV.

Addresses discrepancies in previous zero-temperature calculations.

Abstract

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<1GeV 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.