The EDM inverse problem: Identifying the sources of CP violation and PQ breaking with electric dipole moments

TL;DR

This paper explores how electric dipole moment measurements can identify the underlying sources of CP violation in physics beyond the Standard Model, focusing on six key operator classes and their distinct experimental signatures.

Contribution

It classifies six main CP-violating operators relevant for EDMs and demonstrates how their unique patterns can distinguish their origins in experimental data.

Findings

Distinct EDM patterns correspond to different CP-violating operators.

EDM measurements can differentiate between high-scale and low-scale CP violation.

The work links EDM observations to the origin of the QCD axion's vacuum expectation value.

Abstract

Many extensions of the Standard Model (SM) generically introduce new sources of CP violation, which can induce observable $P$-odd and $T$-odd permanent electric dipole moments (EDMs) of nuclei, atoms, and molecules. A future observation of nonvanishing EDMs would therefore provide a sensitive probe of physics beyond the SM, while also posing a nontrivial inverse problem: identifying their underlying ultraviolet origin. In this work, we identify six representative classes of CP-violating effective operators near the QCD scale, including the QCD $\theta$-term, that are particularly relevant for low-energy EDMs and can arise in a broad range of SM extensions. We show that these operator classes lead to distinct EDM patterns across different systems, thereby enabling discrimination among them through experimentally measured EDMs. We further emphasize that EDM measurements can shed light on the origin of the vacuum expectation value of the QCD axion. In particular, they may help distinguish whether a nonzero axion vacuum expectation value is predominantly induced by high-scale Peccei--Quinn symmetry-breaking effects, such as those associated with quantum gravity, or by the interplay between beyond-the-SM CP violation and the QCD anomaly.