CPviolation and the scale of supersymmetry breaking

Supersymmetric models with a high supersymmetry breaking scale give, in general, large contributions to ${\varepsilon }_K$ and/or to various electric dipole moments, even when contributions to $\mathrm{CP}$ conserving, flavor changing processes are sufficiently suppressed. Some examples are models of dilaton dominance, alignment, non-Abelian flavor symmetries, heavy first two generation sfermions, anomaly mediation and gaugino mediation. There is then strong motivation for “approximate $CP,”$ that is, a situation where all $\mathrm{CP}$ violating phases are small. In contrast, in supersymmetric models with a low breaking scale it is quite plausible that the CKM matrix is the only source of flavor and $\mathrm{CP}$ violation. Gauge mediation provides a concrete example. Approximate $\mathrm{CP}$ is then unacceptable. Upcoming measurements of the $\mathrm{CP}$ asymmetry in $\overrightarrow{B}\psi K_S$ might exclude or support the idea of approximate $\mathrm{CP}$ and consequently probe the scale of supersymmetry breaking.