Natural supersymmetry's last hope: R-parity violation via UDD operators

Here we give a broad overview of the more natural spectra allowed by the LHC when UDD R-parity violation is allowed. Because R-parity violation removes the missing energy signals in colliders, the experimental constraints on the gluino, stops, sbottoms, and Higgsinos are relatively mild. We also show that UDD R-parity violation and lepton number conservation can be made consistent with grand unification. This feat is achieved through the product unification, SU(5)×U(3). In this model, mixing of the standard model quarks with additional quarklike particles charged under the U(3) generate a UDD R-parity violating operator. Furthermore, these models are also capable of generating a "natural" spectra. The emergence of these more natural low-scale spectra relies heavily on the fact that the gaugino masses are nonuniversal, a natural consequence of product unification.