Exploring the Landscape of Spontaneous CP Violation in Supersymmetric Theories

TL;DR

This paper investigates how spontaneous CP violation can be realized within supersymmetric theories, addressing the strong CP problem by exploring models that stabilize CP-violating phases through SUSY mechanisms.

Contribution

It presents two distinct SUSY-based models for spontaneous CP violation, including an extension of the spurion formalism and a model with intermediate-scale CP breaking stabilized by SUSY effects.

Findings

SCPV can be stabilized in exact SUSY using R-symmetry constraints.

A model with intermediate-scale CP breaking predicts light scalars linked to SUSY breaking.

Supersymmetry helps suppress problematic operators that could reintroduce the strong CP problem.

Abstract

The strong CP problem remains one of the most important unresolved issues in the Standard Model. Spontaneous CP violation (SCPV) is a promising approach to the problem by assuming that CP is an exact symmetry of the Lagrangian but broken spontaneously at the vacuum, which enables the generation of the observed Cabibbo-Kobayashi-Maskawa (CKM) phase without reintroducing a nonzero strong CP phase. Supersymmetry (SUSY) provides a natural framework to accommodate such a mechanism, as SUSY can not only protect the scale of SCPV from radiative corrections but also suppress problematic higher-dimensional operators generating a strong CP phase. In the present study, we explore the realization of SCPV in two distinct SUSY scenarios. First, we investigate SCPV in the exact SUSY limit by extending the spurion formalism developed in non-supersymmetric theories to identify the necessary condition for stabilizing CP-violating phases, and by analyzing the stabilization of radial vacuum expectation values through R-symmetry constraints on the superpotential. Second, we construct a model in which CP is spontaneously broken at an intermediate scale along pseudo-flat directions, stabilized by soft SUSY breaking and non-perturbative effects of a gauge theory. The latter setup predicts light scalars in the SCPV sector whose masses are determined by the SUSY breaking scale.