CP-odd phase correlations and electric dipole moments

We revisit the constraints imposed by electric dipole moments (EDMs) of nucleons and heavy atoms on new $CP$-violating sources within supersymmetric theories. We point out that certain two-loop renormalization group corrections induce significant mixing between the basis-invariant $CP$-odd phases. In the framework of the constrained minimal supersymmetric standard model, the $CP$-odd invariant related to the soft trilinear $A$-phase at the grand unified theory (GUT) scale, ${\theta }_A$, induces nontrivial and distinct $CP$-odd phases for the three gaugino masses at the weak scale. The latter give one-loop contributions to EDMs enhanced by $\tan \beta$, and can provide the dominant contribution to the electron EDM induced by ${\theta }_A$. We perform a detailed analysis of the EDM constraints within the constrained minimal supersymmetric standard model, exhibiting the reach, in terms of sparticle spectra, which may be obtained assuming generic phases, as well as the limits on the $CP$-odd phases for some specific parameter points where detailed phenomenological studies are available. We also illustrate how this reach will expand with results from the next generation of experiments which are currently in development.