A model for large non-standard interactions of neutrinos leading to the LMA-Dark solution

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.