  It is well-known that in addition to the standard LMA solution to solar
anomaly, there is another solution called LMA-Dark which requires Non-Standard
Interactions (NSI) with effective couplings as large as the Fermi coupling.
Although this solution satisfies all the bounds from various neutrino
oscillation observations and even provides a better fit to low energy solar
neutrino spectrum, it is not as popular as the LMA solution mainly because no
model compatible with the existing bounds has been so far constructed to give
rise to this solution. We introduce a model that provides a foundation for such
large NSI with strength and flavor structure required for the LMA-Dark
solution. This model is based on a new $U(1)^\prime$ gauge interaction with a
gauge boson of mass $\sim 10$ MeV under which quarks as well as the second and
third generations of leptons are charged. We show that observable effects can
appear in the spectrum of supernova and high energy cosmic neutrinos. Our model
predicts a new contribution to the muon magnetic dipole moment and new rare
meson decay modes.
