Probing lepton non-universality in tau neutrino Scattering

Recently hints of lepton flavor non-universality emerged in the BaBar and LHCb experiments. In this paper we propose tests of lepton universality in $\nu_{\tau}$ scattering. To parametrize the new physics we adopt an effective Lagrangian approach and consider the neutrino deep inelastic scattering processes $\nu_{\tau}+ N \to \tau + X$ and $\nu_{\mu}+ N \to \mu + X$ where we assume the largest new physics effects are in the $\tau$ sector. We also consider an explicit leptoquark model in our calculations. In order to make comparison with the standard model and also in order to cancel out the uncertainties of the parton distribution functions, we consider the ratio of total and differential cross sections of tau-neutrino to muon-neutrino scattering. We find new physics effects that can possibly be observed at the proposed Search for Hidden Particles (SHiP) experiment at CERN.