Flavor Problem, Proton Decay And Neutrino Oscillations In SUSY Models With Anomalous $\mathcal{U}(1)$

We discuss how realistic supersymmetric models can be constructed by employing an anomalous $\mathcal{U}(1)$ flavor symmetry which also mediates supersymmetry breaking. A judicious choice of $\mathcal{U}(1)$ charges enables the first two squark families to be sufficiently heavy ($10$ TeV), so that flavor changing neutral currents as well as dimension five nucleon decay are adequately suppressed. Using the SU(5) example, the charged fermion mass hierarchies, magnitudes of the CKM matrix elements, as well as the observed neutrino oscillations are simultaneously accommodated. We estimate the proton lifetime to be ${\tau }_p\sim {10}^3\cdot {\tau }_p[\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{l}SU(5)]$, with the decay mode $p\to K\mu$ being comparable to $p\to K{\nu }_{\mu ,\tau }$.