Small neutrino masses due to R-symmetry breaking for a small   cosmological constant
  We describe a class of supersymmetric models in which neutrinos are kept light by an R-symmetry. In supergravity, R-symmetry must be broken to allow for a small cosmological constant after supersymmetry breaking. In the class of models described here, this R-symmetry breaking results in the generation of Dirac neutrino masses, connecting the tuning of the cosmological constant to the puzzle of neutrino masses. Surprisingly, under the assumption of low-scale supersymmetry breaking and superpartner masses close to a TeV, these masses are independent of the fundamental supersymmetry-breaking scale, and accommodate the correct magnitude. This offers a novel explanation for the vastly different scales of neutrino and charged fermion masses. These models require that R-symmetric supersymmetry exists at the TeV scale, and predict that neutrino masses are purely Dirac, implying the absence of neutrino-less double beta-decay. Interesting collider signals can arise due to charged scalars which decay leptonically, with branching ratios determined by the neutrino mixing matrix. 
Rhys Davies and Matthew McCullough
hep-ph