R-parity violating anomaly mediated supersymmetry breaking
  We propose a new scenario that solves the slepton negative mass squared problem of the minimal supersymmetric standard model with anomaly mediated supersymmetry breaking. The solution is achieved by including three trilinear R-parity violating operators in the superpotential. The soft supersymmetry breaking terms satisfy renormalisation group invariant relations in terms of supersymmetric couplings and the overall supersymmetry breaking mass scale. Flavour changing neutral currents can be naturally highly suppressed. A specific model predicts tan beta=4.2+/-1.0. Excluding sleptons, the supersymmetric particle spectrum then depends upon two remaining free parameters. In the case of the R-parity violating couplings set at their quasi-fixed points at a supersymmetric GUT scale, the whole sparticle spectrum approximately depends upon only one free parameter. Imposing experimental limits leads to a constrained and distinctive phenomenology. The lightest CP-even Higgs of mass m_h=118 GeV would be seen at the Tevatron. All sparticles and heavy Higgs would evade detection except for the lightest charginos and neutralinos, whose distinctive leptonic decays would be seen at the LHC. 
B.C. Allanach, A. Dedes