Non-standard neutrino interactions and low energy experiments

We formulate an Effective Field Theory (EFT) for Non Standard neutrino Interactions (NSI) in elastic scattering with light quarks, leptons, gluons and photons, including all possible operators of dimension 5, 6 and 7. We provide the expressions for the cross sections in coherent neutrino-nucleus scattering and in deep inelastic scattering. Assuming single operator dominance we constrain the respective Wilson coefficient using the measurements by the COHERENT and CHARM collaborations. We also point out the constraining power of future elastic neutrino-nucleus scattering experiments. Finally, we explore the implications of the bounds for SMEFT operators above the electroweak breaking scale.