A Supersymmetric Theory of Flavor and R Parity

We construct a renormalizable, supersymmetric theory of flavor and $R$ parity based on the discrete flavor group $(S_3)^3$. The model can account for all the masses and mixing angles of the Standard Model, while maintaining sufficient squark degeneracy to circumvent the supersymmetric flavor problem. By starting with a simpler set of flavor symmetry breaking fields than we have suggested previously, we construct an economical Froggatt-Nielsen sector that generates the desired elements of the fermion Yukawa matrices. With the particle content above the flavor scale completely specified, we show that all renormalizable $R$-parity-violating interactions involving the ordinary matter fields are forbidden by the flavor symmetry. Thus, $R$ parity arises as an accidental symmetry in our model. Planck-suppressed operators that violate $R$ parity, if present, can be rendered harmless by taking the flavor scale to be $\lesssim 8 \times 10^{10}$ GeV.