Investigating nuclear effects in lepton-ion DIS at the LHC

Recent studies have demonstrated that the far-forward physics program of the Large Hadron Collider (LHC) can be useful to probe the hadron structure with GeV-TeV neutrinos and muons. In particular, these studies indicate that the measurement of the muon-ion and neutrino-ion cross-sections by the same experiment is feasible. In this paper, we investigate the impact of nuclear effects on the muon-tungsten ($\mu W$) and neutrino-tungsten ($\nu W$) deep inelastic scattering (DIS) events at FASER$\nu$ and its proposed upgrade FASER$\nu 2$. We estimate the rates associated with the inclusive cross-sections and for events with a charm tagged in the final state considering different parameterizations for the nuclear parton distribution functions. These results point out that muon and neutrino-induced interactions probe complementary kinematical ranges and that a simultaneous analysis of associated events will allow to test the universality (or not) of the nuclear effects. Moreover, we propose the study of the ratio between the charm tagged and inclusive events in order to discriminate between the distinct modeling of the nuclear effects at small-$x$. Our results indicate that a future experimental reconstruction of $\mu W$ and $\nu W$ DIS events at the LHC is a promising way to improve our understanding of nuclear effects and decrease the current uncertainties in parton distribution functions.