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Implications of large CP Violation in B mixing for Supersymmetric Standard Models

Following the anomalous like-sign dimuon charge asymmetry measured by the D0 collaboration at the Tevatron collider we discuss the implications of large CP violation in $B_{d,s}$ mixing for Supersymmetric (SUSY) Standard Models, focussing on those models which allow a family symmetry and unification. For the Minimal Supersymmetric Standard Model (MSSM) we show that it is only possible to account for $B_{s}$ mixing and CP violation at the expense of large squark mixing which would require a new approach to family symmetry models. In order to describe both $B_{s}$ and $B_{d}$ mixing and CP violation we are led to consider SUSY models with Higgs fields transforming as triplets under a family symmetry. We describe a realistic such model based on $Δ_{27}$ family symmetry in which tree-level exchange of the second Higgs family predicts $B_{s}$ and $B_{d}$ mixing and CP violation in good agreement with a recent global fit, while naturally suppressing flavour and CP violation involving the first and second quark and lepton families.