EDMs vs. CPV in Bs,d mixing in two Higgs doublet models with MFV

We analyze the correlations between electric dipole moments (EDMs) of the neutron and heavy atoms and CP violation in Bs,d mixing in two Higgs doublet models respecting the Minimal Flavour Violation hypothesis, with flavour-blind CP-violating (CPV) phases. In particular, we consider the case of flavour-blind CPV phases from (i) the Yukawa interactions and (ii) the Higgs potential. We show that in both cases the upper bounds on the above EDMs do not forbid sizable non-standard CPV effects in Bs mixing. However, if a large CPV phase in Bs mixing will be confirmed, this will imply EDMs very close to their present experimental bounds, within the reach of the next generation of experiments, as well as BR(Bs,d→μ+μ−) typically largely enhanced over its SM expectation. The two flavour-blind CPV mechanisms can be distinguished through the correlation between SψKS and Sψϕ that is strikingly different if only one of them is relevant. Which of these two CPV mechanisms dominates depends on the precise values of Sψϕ and SψKS, as well as on the CKM phase (as determined by tree-level processes). Current data seems to show a mild preference for a hybrid scenario where both these mechanisms are at work.