Large loop effects of extra SUSY Higgs doublets to CP violation in B⁰ mixing

We consider more than one pair of SU(2)_L doublet Higgs supermultiplets in a generic supersymmetric extension of the standard model, and calculate their one-loop contributions to the soft mass insertions delta_{LL} etc. We find that if large supersymmetry breaking in this sector is realized, the loop effects can give rise to large contributions to the soft mass insertions, meaning that they We apply our result to a recently proposed model based on the discrete Q_6 family group, and calculate the non-diagonal matrix element M_{12} of the neutral meson systems. We focus our attention on the extra phases phi_{d,s}^Delta in B_{d,s}-mixing and flavor-specific CP-asymmetries a_{sl}^{d,s} in neutral B decays and obtain values that can be about one order of magnitude larger than the standard model predictions. Our final results are comparable with the recent experimental observations at D0 and CDF, but they are still about a factor of 5 smaller than the recently measured dimuon asymmetry from D0.