Viable models for large non-standard neutrino interactions

Thanks to high precision long baseline neutrino experiments such as NO$\nu$A and DUNE, possible effects of Non-Standard neutrino Interactions (NSI) on neutrino oscillation data have received renewed interest in the last two years. It is however challenging to build models that can give rise to NSI with sizeable couplings discernible at neutrino oscillation experiments without violating the various existing experimental bounds. We introduce two viable models that can lead to neutral current NSI with sizable couplings. Both models are based on a new $U(1)^\prime$ gauge symmetry with $Z^\prime$ gauge boson of mass $O(10~{\rm MeV})$. We will highlight the common phenomenological features of these models and suggest ways to test them.