CP violation in the effective action of the Standard Model

TL;DR

This paper calculates CP-violating terms in the Standard Model's effective action using a covariant derivative expansion, finding non-zero contributions in specific sectors that are significantly larger than previous estimates.

Contribution

It provides a comprehensive sixth-order calculation of CP-odd terms in the Standard Model's effective action without approximations, revealing new CP-violating effects.

Findings

All parity-violating contributions are zero at this order.

Non-zero CP-violating terms are found in the C-odd P-even sector.

Results are several orders of magnitude larger than perturbative estimates.

Abstract

Following a suggestion by Smit, the CP odd terms of the effective action of the Standard Model, obtained by integration of quarks and leptons, are computed to sixth order within a strict covariant derivative expansion approach. No other approximations are made. The final result so derived includes all Standard Model gauge fields and Higgs. Remarkably, at the order considered in this work, all parity violating contributions turn out to be zero. Non vanishing CP violating terms are obtained in the C-odd P-even sector. These are several orders of magnitude larger than perturbative estimates. Various unexpected regularities in the final result are noted.