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Natural, R-parity violating supersymmetry and horizontal flavor symmetries

The absence so far of any supersymmetric signals at the LHC pushes towards a rethinking of the assumptions underlying the MSSM. Because the large missing $E_T$ searches are inadequate to detect a LSP decaying within the detector, R-parity violating supersymmetry is still a good candidate for low energy, natural supersymmetry. We show that, in Froggatt-Nielsen-like models of horizontal symmetries, specific textures for the R-parity violating couplings are dictated by the symmetry, with the largest coupling involving the third generation fields. Lepton number can be an accidental symmetry of the renormalizable superpotential and barion number violation is given by a $\bar u\bar d\bar d$ operator. The collider phenomenology then mimics the main features of MFV R-parity violating supersymmetry. The LSP can evade current LHC supersymmetry searches, is allowed to be well below 1 TeV and at the same time all the constraints from proton decay and other low energy decays can be satisfied; in particular, dimension five operators allowed by R-parity but dangerous for the proton are under control, while neutrino masses are generated by the Weinberg operator. Assuming sub TeV ({\it natural}) superpartners, we obtain both upper and lower limits on the magnitude of the dominant R-parity violating coupling: a lower limit of order $10^{-9}$ arises from null LHC searches on R-hadrons and heavy stable charged particles, while a upper limit of order $10^{-3}$ follows from constraints on low-energy flavor changing neutral currents. Displaced vertices are predicted in the lower end of this range.