  Scenarios where left- and right-handed sneutrinos mix and the lightest mixed
one act as a thermal dark matter candidate can solve the dark matter, neutrino
mass, and hierarchy problems simultaneously. We focus on the dark matter mass
region of the order of 1 GeV, where dark matter direct detections are
insensitive. We calculate the decay rate of a false vacuum induced by a large
sneutrino trilinear coupling as well as other observables constrained by
experiments. As a result, we show that there is an allowed region where the
mass of the lightest neutralino is around 1 GeV. The allowed region can be
tested by the search for the Higgs boson invisible decay at future colliders.
