Supersymmetric Models with Approximate CP

Abstract

Supersymmetric models with an approximate CP, $10^{-3} \lsim ϕ_{CP} \ll 1$, are a viable framework for the description of nature. The full high energy theory has exact CP and horizontal symmetries that are spontaneously broken with a naturally induced hierarchy of scales, $Λ_{CP} \ll Λ_{H}$. Consequently, the effective low energy theory, that is the supersymmetric Standard Model, has CP broken explicitly but by a small parameter. The $ε_{K}$ parameter is accounted for by supersymmetric contributions. The predictions for other CP violating observables are very different from the Standard Model. In particular, CP violating effects in neutral B decays into final CP eigenstates such as $B \to ψK_{S}$ and in $K \to πν\barν$ decays are very small. This framework, though, is strongly disfavored by the recent measurements of $ε^\prime_{K}/ε_{K}$.