  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.
