Solving the supersymmetricCPproblem with flavor breakingFterms

Supersymmetric flavor models for the radiative generation of fermion masses offer an alternative way to solve the SUSY-$CP$ problem. We assume that the supersymmetric theory is flavor and $CP$ conserving. $CP$ violating phases are associated to the vacuum expectation values of flavor violating SUSY-breaking fields. As a consequence, phases appear at tree level only in the soft supersymmetry-breaking matrices. Using a U(2) flavor model as an example we show that it is possible to generate radiatively the first and second generation of quark masses and mixings as well as the Cabibbo-Kobayashi-Maskawa (CKM) $CP$ phase. The one-loop supersymmetric contributions to electric dipole moments are automatically zero since all the relevant parameters in the Lagrangian are flavor conserving and as a consequence real. The size of the flavor and $CP$ mixing in the SUSY-breaking sector is mostly determined by the fermion mass ratios and CKM elements. We calculate the contributions to $ϵ$, ${ϵ}^{\prime }$ and to the $CP$ asymmetries in the $B$ decays to $\psi K_s$, $\varphi K_s$, ${\eta }^{\prime }{K}_s$ and $X_s\gamma$. We analyze a case study with maximal predictivity in the fermion sector. For this worst case scenario the measurements of $\Delta m_K$, $\Delta m_B$ and $ϵ$ constrain the model requiring extremely heavy squark spectra.