  We show that the proposed measurements of the electric dipole moments of
light nuclei in storage rings would put strong constraints on models of
flavor-diagonal CP violation. Our analysis is exemplified by a comparison of
the Standard Model including the QCD theta term, the minimal left-right
symmetric model, a specific version of the so-called aligned two-Higgs doublet
model, and briefly the minimal supersymmetric extension of the Standard Model.
By using effective field theory techniques we demonstrate to what extend
measurements of the electric dipole moments of the nucleons, the deuteron, and
helion could discriminate between these scenarios. We discuss how measurements
of electric dipole moments of other systems relate to the light-nuclear
measurements.
