Electric Dipole Moments and New Physics

Abstract

Searches for intrinsic electric dipole moments (EDMs) of nucleons, atoms and molecules are precision flavor-diagonal probes of new $CP$-odd physics, as motivated by the need to explain the matter-antimatter asymmetry in the universe. We review and summarise the effective field theory analysis of the observable EDMs in terms of a general set of $CP$-odd operators at 1~GeV, and the ensuing model-independent constraints on new physics. We also review and discuss the EDMs induced by $CP$-violation in the Standard Model, and the implications of EDM limits for various models of physics beyond the Standard Model.

Figures (6)

• Figure 1: A schematic representation of the hierarchy of effective field theory operators that link fundamental sources of $CP$-violation with observable EDMs. The color-coding reflacts the inheritance patterns for leptonic, semi-leptonic and hadronic $CP$-odd sources respectively. Observables highlighted in red have existing direct measurements that impact the network of constraints.
• Figure 2: Observable EDMs and the various enhancement and suppression factors that relate measurements to fundamental sources of $CP$-violation.
• Figure 3: Contribution of the SM CKM phase to the semileptonic Wilson coefficient $C_S$. On the left is the hadronic representation of $O(m_s^{-1})$ diagrams leading to $C_S$, and on the right the effective vertices are resolved as penguin diagrams. The top circle corresponds to an electroweak penguin and scales as $O(G_F^2m_t^2)$. Figure reproduced from Ema:2022yra.
• Figure 4: Evolution of precision EDM measurements, from the limits (in gray) circa 1985 through to today (in blue). The SM CKM background contributions are shown for comparison.
• Figure 5: The $\bar{\theta}$ parameter of QCD induces a $CP$-odd vertex between a pion and the nucleon represented by a black dot in the second diagram from the left. If the $U(1)_A$ symmetry is restored, then the first (singlet $\eta_s$ meson re-scattering) diagram exactly cancels the second. In the real world with $U(1)_A$ violated nonperturbatively, the second diagram dominates, and contributes to all three classes of observable EDMs, represented schamatically on the right. White dots and the triangle denote the conventional coupling of pions to nucleons and photons.