Electric Dipole Moments of the Atoms, Molecules, Nuclei and Particles

Abstract: A permanent electric dipole moment (EDM) of a particle or system is a separation of charge along its angular-momentum axis and is a direct signal of T-violation and, assuming CPT symmetry, CP violation. For over sixty years EDMs have been studied, first as a signal of a parity-symmetry violation and then as a signal of CP violation that would clarify its role in nature and in theory. Contemporary motivations include the role that CP violation plays in explaining the cosmological matter-antimatter asymmetry and the search for new physics. Experiments on a variety of systems have become ever-more sensitive, but provide only upper limits on EDMs, and theory at several scales is crucial to interpret these limits. Nuclear theory provides connections from Standard-Model and Beyond-Standard-Model physics to the observable EDMs, and atomic and molecular theory reveal how CP-violation is manifest in these systems. EDM results in hadronic systems require that the Standard Model QCD parameter of $\bar\theta$ must be exceptionally small, which could be explained by the existence of axions - also a candidate dark-matter particle. Theoretical results on electroweak baryogenesis show that new physics is needed to explain the dominance of matter in the universe. Experimental and theoretical efforts continue to expand with new ideas and new questions, and this review provides a broad overview of theoretical motivations and interpretations as well as details about experimental techniques, experiments, and prospects. The intent is to provide specifics and context as this exciting field moves forward.

• The paper demonstrates that EDMs serve as a precision probe for CP violation beyond the Standard Model through both CKM contributions and BSM effects.
• It details advanced experimental techniques, including magnetic shielding and comagnetometry, to enhance sensitivity in diverse measurement systems.
• The review emphasizes the need for refined nuclear theory calculations to better interpret EDM constraints and inform new physics models.

Review of "Electric Dipole Moments of Atoms, Molecules, Nuclei and Particles"

The paper "Electric Dipole Moments of Atoms, Molecules, Nuclei and Particles," authored by T.E. Chupp, P. Fierlinger, M.J. Ramsey-Musolf, and J.T. Singh, provides a comprehensive examination of the theoretical and experimental landscape of electric dipole moments (EDMs). The exploration of EDMs serves as a critical avenue for probing CP violation beyond the predictions of the Standard Model (SM), thereby offering insights into unresolved phenomena such as the matter-antimatter asymmetry observed in the universe.

Theoretical Framework and Motivation

The theoretical framework presented in the document elaborates on the intrinsic connection between EDMs and CP violation. It systematically addresses the contributions from the SM, specifically the CKM matrix, and expands into Beyond-Standard-Model (BSM) territories through effective field theory (EFT). The paper highlights the intricacies of CP-violating sources at different scales, delineating Wilson coefficients associated with dimension-six operators. This exposition is crucial in appreciating the suppression mechanisms in the SM that necessitate BSM physics to account for observable CP violation competent enough to explain the baryon asymmetry.

Experimental Techniques and Current Results

The review details a range of experimental methodologies, underscoring the advances in sensitivity across various systems: neutrons, paramagnetic and diamagnetic atoms, and molecular beams. Notably, paramagnetic systems such as ThO and HfF$^+$ provide stringent constraints on the electron EDM due to the large internal electric fields in polar molecules. The refinement of experimental setups, including magnetic shielding and comagnetometry, is meticulously discussed, showcasing the evolution in tackling systematic errors that plague EDM measurements.

For diamagnetic atoms like $^{199}$Hg, the paper provides an updated synthesis of experimental records, notably highlighting the inherent difficulties in extracting EDM constraints due to nuclear theory uncertainties. These discussions reveal the criticality of both experimental precision and theoretical interpretation in unraveling EDM signals.

Implications for BSM Physics

The paper presents a compelling narrative on the implications of current EDM bounds for new physics. The constraints imposed by EDMs on BSM models, such as supersymmetry and Left-Right Symmetric Models, are elucidated with clarity. It underscores the tension between observed experimental limits and theoretically predicted CP-violating phases, suggesting either unexpectedly small phase values or high new physics scales.

Future Directions

The document points to future prospects in the EDM field, noting the potential of upcoming experiments to probe deeper into CP-violating phenomena. It calls for advancements in both the experimental domain, through novel techniques and increased sensitivities, and theoretical integrations, particularly targeting nuclear calculations to reduce uncertainties.

Conclusion

The paper serves as an in-depth resource that synthesizes both theoretical and experimental landscapes of EDM research. It captures the essence of EDMs as a pivotal scientific tool in exploring CP violation and its cosmological consequences. The insights and comprehensive overview presented affirm the necessity of continued pursuit in multiple systems and interdisciplinary collaborations to achieve breakthroughs in our understanding of CP violation and BSM physics. Moreover, it accentuates the need for refined nuclear theory calculations to complement the experimental efforts and enable precise interpretation of future findings.