  We analyze the low energy implications of a flavor blind supersymmetric
scenario (where the CKM matrix is the only source of flavor violation) in the
presence of new CP violating but flavor conserving phases in the soft sector.
We find that the best probes of this rather restricted scenario are i) the
electric dipole moments (EDMs) of the electron (d_e) and the neutron (d_n) and
ii) flavor changing and CP violating processes in B systems, like the CP
asymmetries in b->s gamma and B->phi(eta^')K_S, i.e. A_CP(b->s gamma) and
S_phi(eta^')K_S, respectively. The non-standard values for S_phi(eta^')K_S,
measured at the B factories, can find a natural explanation within our scenario
and this would unambiguously imply i) positive and often large (non-standard)
values for A_CP(b->s gamma) and ii) a lower bound for the electron and neutron
EDMs at the level of d_e,n > 10^-28 e cm. Moreover, we predict positive New
Physics (NP) contributions to epsilon_K which could be welcomed in view of the
recently lowered Standard Model value for epsilon_K. Interestingly, an
explanation for the non-standard values for S_phi(eta^')K_S can also naturally
lead to an explanation for the anomaly of the muon anomalous magnetic moment.
Finally, we outline the role and the interplay of the direct NP searches at the
LHC with the indirect searches performed by low energy flavor physics
observables.
