Constraints on Phases of Supersymmetric Flavour Conserving Couplings

In the unconstrained MSSM, we reanalyze the constraints on the phases of supersymmetric flavour conserving couplings that follow from the electron and neutron electric dipole moments (EDM). We find that the constraints become weak if at least one exchanged superpartner mass is >O(1 TeV) or if we accept large cancellations among different contributions. However, such cancellations have no evident underlying symmetry principle. For light superpartners, models with small phases look like the easiest solution to the experimental EDM constraints. This conclusion becomes stronger the larger is the value of $\tan\beta$. We discuss also the dependence of $\epsilon_K$, $\Delta m_B$ and $b\to s\gamma$ decay on those phases.