Neutral Current Neutrino Interactions at FASER$\nu$

In detecting neutrinos from the Large Hadron Collider, FASER$\nu$ will record the most energetic laboratory neutrinos ever studied. While charged current neutrino scattering events can be cleanly identified by an energetic lepton exiting the interaction vertex, neutral current interactions are more difficult to detect. We explore the potential of FASER$\nu$ to observe neutrino neutral current scattering $\nu N \to \nu N$, demonstrating techniques to discriminate neutrino scattering events from neutral hadron backgrounds as well as to estimate the incoming neutrino energy given the deep inelastic scattering final state. We find that deep neural networks trained on kinematic observables allow for the measurement of the neutral current scattering cross section over neutrino energies from 100 GeV to several TeV. Such a measurement can be interpreted as a probe of neutrino non-standard interactions that is complementary to limits from other tests such as oscillations and coherent neutrino-nucleus scattering.