A model for Axial Non-Standard Interactions of neutrinos with quarks

The neutrino oscillation experiments are setting increasingly strong upper bounds on the vector Non-Standard neutrino Interactions (NSI) with matter fields. However, the bounds on the axial NSI are more relaxed, raising the hope that studying the neutral current events at an experiment such as DUNE can give a glimpse on new physics. We build a model that gives rise to axial NSI with large couplings leading to observable deviation from the standard prediction at DUNE. The model is based on a $U(1)$ gauge symmetry with a gauge boson of mass $\sim 30$~GeV which can be discovered at the high luminosity LHC. Combining the LHC and DUNE discoveries, we can unravel the axial form of interaction. The cancellation of anomalies of the gauge group suggests new heavy quarks as well as a dark matter candidate. The new quarks mixed with the first generation quarks can also be discovered at the LHC. Moreover, they provide a seesaw mechanism that explains the smallness of the $u$ and $d$ quark masses. The dark matter has an axial coupling to the quarks which makes its discovery via spin dependent direct dark matter search experiments possible.