We study the feasibility of a sterile neutrino search at the China Advanced Research Reactor by measuring $bar { u}_e$ survival probability with a baseline of less than 15 m. Both hydrogen and deuteron have been considered as potential targets. The s
ensitivity to sterile-to-regular neutrino mixing is investigated under the 3(active)+1(sterile) framework. We find that the mixing parameter $sin^2(2theta_{14})$ can be severely constrained by such measurement if the mass square difference $Delta m_{14}^2$ is of the order of $sim$1 eV$^2$.
An unstable gravitino with lifetime longer than $10^{26}$ sec or so has been proposed as a possible dark matter candidate in supergravity models with R-parity breaking. We find a natural realization of this idea in the minimal supersymmetric left-rig
ht models where left-right symmetry breaking scale in the few TeV range. It is known that in these models, R-parity must break in order to have parity breaking as required by low energy weak interactions. The sub-eV neutrino masses imply that R-parity breaking effects in this model must be highly suppressed. This in turn makes the gravitino LSP long lived enough, so that it becomes the dark matter of the Universe. It also allows detectable displaced vertices at the LHC from NLSP decays. We present a detailed analysis of the model and some aspects of its rich phenomenology.
