Temperature Dependence of Standard Model CP Violation

TL;DR

This paper investigates how CP violation effects in the Standard Model vary with temperature, finding that they diminish rapidly at high temperatures, which impacts theories of matter-antimatter asymmetry in the early Universe.

Contribution

It provides a detailed calculation of the temperature dependence of CP violation in the Standard Model, highlighting effects starting at sixth order in the gradient expansion.

Findings

CP violation terms appear at sixth order in the effective action.

CP violating effects decrease rapidly with increasing temperature.

Potential viability of cold electroweak baryogenesis within the Standard Model.

Abstract

We analyze the temperature dependence of CP violation effects in the Standard Model by determining the effective action of its bosonic fields, obtained after integrating out the fermions from the theory and performing a covariant gradient expansion. We find non-vanishing CP violating terms starting at the sixth order of the expansion, albeit only in the C odd/P even sector, with coefficients that depend on quark masses, CKM matrix elements, temperature and the magnitude of the Higgs field. The CP violating effects are observed to decrease rapidly with temperature, which has important implications for the generation of a matter-antimatter asymmetry in the early Universe. Our results suggest that the cold electroweak baryogenesis scenario may be viable within the Standard Model, provided the electroweak transition temperature is at most of order 1 GeV.