Constraining axial non-standard interactions of neutrinos with long baseline experiments

Thanks to a number of neutrino oscillation and Coherent Elastic neutrino Nucleus Scattering (CE$ν$NS) experiments, the vector Non-Standard Interactions (NSI) of neutrinos have been well studied and constrained. We show that the long-sought-after new physics may hide in the ``axial" non-standard interactions rather than in the vector NSI. We then show how by studying neutral current scattering events in the detectors of long baseline experiments, MINOS, MINOS$+$ and DUNE, the impact of the axial NSI can be discovered.