The theory of electric dipole moments: the view from below

Permanent electric dipole moments (EDMs) of nucleons, nuclei, atoms, and molecules are among the most sensitive probes of CP violation beyond the Standard Model and are intimately connected to the strong CP problem and the origin of the matter-antimatter asymmetry of the universe.

This review presents the theory of EDMs from the bottom up, tracing the chain of connections that links CP-violating interactions at level of elementary particles to observable EDMs across a wide range of systems.

Starting from a general CP-odd effective Lagrangian at the quark-gluon level comprising the QCD theta term, quark EDMs and chromo-EDMs, the Weinberg operator, and CP-odd four-fermion interactions, I show how chiral perturbation theory organizes the nonperturbative QCD dynamics into a small set of hadronic low-energy constants, whose relative sizes are determined by the chiral representation of the underlying source.

These hadronic interactions feed into calculations of nuclear EDMs and Schiff moments, which in turn enter atomic and molecular structure calculations that connect to experimentally accessible observables in diamagnetic and paramagnetic systems.

Special attention is given to the recently identified sensitivity of paramagnetic systems to hadronic CP violation, which opens a new and relatively unexplored window on the quark-gluon sector.

The complementarity of the full EDM portfolio including the neutron, light nuclei, atoms, and molecules, and the role of theory in disentangling the underlying source of CP violation is discussed throughout.