Landscape of Spontaneous CP Violation

TL;DR

This paper reviews how spontaneous CP violation can be realized in supersymmetric models, addressing naturalness, stability, and phenomenological implications such as baryogenesis and neutron EDM.

Contribution

It demonstrates the realization of SCPV along flat directions stabilized by supersymmetry-breaking effects and non-perturbative dynamics, with implications for baryon asymmetry and EDM experiments.

Findings

SCPV is realized along flat directions stabilized by supersymmetry-breaking.

The framework predicts a neutron EDM within near-future experimental reach.

The Affleck-Dine mechanism can generate the observed baryon asymmetry at low reheating temperatures.

Abstract

Spontaneous CP violation (SCPV) provides a promising solution to the strong CP problem, explaining the smallness of the QCD $\theta$-angle while generating the Cabibbo-Kobayashi-Maskawa (CKM) phase. In the present work, we review and discuss the realization of SCPV in the supersymmetric framework, which addresses critical issues such as the naturalness of the scale of SCPV and the presence of problematic higher dimensional operators and radiative corrections spoiling the mechanism. It is explicitly shown that SCPV is realized along flat directions and stabilized through supersymmetry-breaking effects and a non-perturbative dynamics, predicting light SCPV sector particles feebly coupled to the Standard Model particles. Furthermore, we discuss the issue of baryon asymmetric Universe in the SCPV framework and point out that the Affleck-Dine mechanism can successfully generate the observed baryon asymmetry with a low reheating temperature compatible with the gravitino dark matter. Our framework predicts a nonzero neutron electric dipole moment which is within the reach of near-future experiments.