  We consider the proposal that dark matter (DM) is composed of a spin-3/2
particle that is a singlet of the standard model (SM). Its leading effective
interactions with ordinary matter involve a pair of their fields and a pair of
SM fermions, in the form of products of chiral currents. We make a
comprehensive analysis on possible phenomenological effects of the interactions
in various experiments and observations. These include collider searches for
monojet plus missing transverse energy events, direct detections of DM
scattering off nuclei, possible impacts on the gamma rays and
antiproton-to-proton flux ratio in cosmic rays, and the observed relic density.
The current data already set strong constraints on the effective interactions
in a complementary manner. The constraint from collider searches is most
effective at a relatively low mass of DM, and the antiproton-to-proton flux
ratio offers the best bound for a heavy DM, while the spin-independent direct
detection is the best in between. For DM mass of order 10 GeV to 1 TeV, the
effective interaction scale is constrained to be typically above a few tens
TeV.
