Large $\mathrm{CP}$ phases and the cancellation mechanism in EDMs in SUSY, string, and brane models

We show that EDMs obey a simple approximate scaling under the transformation $m_0\to \lambda m_0{,m}_{1/2}\to \lambda m_{1/2}$ in the large $\mu$ region when $\mu$ itself obeys the same scaling, i.e., $\overrightarrow{\mu }\lambda \mu .$ In the scaling region knowledge of a single point in the MSSM parameter space where the cancellation in the EDMs occurs allows one to generate a trajectory in the $m_0{-m}_{1/2}$ plane where the cancellation mechanism holds and the EDMs are small. We illustrate these results for the MSSM with radiative electroweak symmetry breaking constraints. We also discuss a class of D-brane models based on type IIB superstring compactifications which have non-universal phases in the gaugino mass sector and allow large $\mathrm{CP}$ violating phases consistent with the EDM constraints through the cancellation mechanism. The scaling in these D-brane models and in a heterotic string model is also discussed.