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 ($μW$) and neutrino-tungsten ($νW$) deep inelastic scattering (DIS) events at FASER$ν$ and its proposed upgrade FASER$ν2$. 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 $μW$ and $νW$ 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.

💡 Research Summary

The paper investigates how nuclear effects influence deep‑inelastic scattering (DIS) of muons and neutrinos on a tungsten target at the far‑forward LHC experiments FASER ν and its proposed high‑luminosity upgrade FASER ν2. Using FLUKA‑based simulations, the authors obtain realistic muon and neutrino fluxes in the forward direction and encode them as LHAPDF PDFs. The lepton‑tungsten differential cross sections are computed at next‑to‑leading order with the POWHEG‑BOX‑RES generator, interfaced to PYTHIA 8 for hadronisation. Three modern nuclear parton distribution function (nPDF) sets—EPPS21, nCTEQ15HQ, and nNNPDF 3.0(W)—are employed, together with a baseline free‑nucleon set (CT18ANLO) and the free‑nucleon version of nNNPDF 3.0(p) for comparison.

Event yields are obtained by integrating the product of the lepton flux, the differential cross section, and an acceptance function that requires the outgoing lepton to have energy > 100 GeV and at least two charged tracks with p > 1 GeV in the hadronic final state. For charm‑tagged events a tagging efficiency of 70 % is assumed, and a cut Q ≥ 1.65 GeV, M_X > 2 GeV is applied. The detector configurations are modelled after the real FASER ν (1.1 t tungsten, 250 fb⁻¹) and the proposed FASER ν2 (≈20 t tungsten, 3 ab⁻¹).

The authors first illustrate the size of nuclear modifications by plotting the ratios R_i = f_A^i/(A f_p^i) for up, strange and gluon PDFs at Q = 2 GeV and Q = 80 GeV. At low x (x ≲ 10⁻³) shadowing reaches 20‑30 % for the up quark, with nCTEQ15HQ giving the strongest suppression and nNNPDF 3.0(W) the weakest. Gluon shadowing and antishadowing differ markedly among the three sets, especially in the position and magnitude of the antishadowing peak. The strange distribution shows the largest spread, underscoring the current lack of constraints.

Table I presents inclusive event counts. Muon‑tungsten DIS yields between 1.5 × 10⁵ and 2.6 × 10⁷ events for FASER ν (and roughly 100‑times more for FASER ν2), while neutrino‑tungsten DIS yields are an order of magnitude smaller (≈5 × 10³‑8 × 10⁵). Table II shows charm‑tagged events: about 6 × 10³‑1 × 10⁴ muon‑induced charm events and a few hundred neutrino‑induced charm events for FASER ν, scaling up similarly for the upgraded detector. The charm sample is particularly sensitive to the gluon (for muons) and strange (for neutrinos) PDFs, which are the least constrained components of the nPDFs.

Differential distributions in Bjorken‑x are displayed in Fig. 3. Inclusive muon events dominate the mid‑ to high‑x region (x ≈ 10⁻³‑10⁻¹), whereas charm‑tagged events populate lower x (10⁻⁴‑10⁻³). Ratios of predictions with nuclear modifications to those without are shown; they reach 10‑30 % deviations at low x, providing a measurable signal of nuclear effects. Importantly, the ratio of charm‑tagged to inclusive events, R = N_charm/N_inclusive, largely cancels experimental systematics and magnifies the sensitivity to the underlying nPDF set. The authors demonstrate that this observable can discriminate between EPPS21, nCTEQ15HQ and nNNPDF 3.0(W) at the 20‑30 % level in the low‑x region.

The key insight is that muon‑ and neutrino‑induced DIS probe complementary kinematic regimes: muons access higher x and Q², while neutrinos reach the very low‑x, low‑Q² domain where shadowing is strongest. Simultaneous measurement of both processes with the same tungsten target thus offers a direct test of the universality of nuclear PDFs—whether a single set of nPDFs can describe both charged‑current (neutrino) and neutral‑current (muon) scattering.

In the concluding discussion, the authors argue that the forthcoming high‑luminosity FASER ν2 experiment will dramatically increase statistics, reducing the current large uncertainties on the strange and gluon nuclear PDFs. The proposed charm‑tagged to inclusive ratio provides a robust, experimentally accessible observable to distinguish between competing theoretical models of low‑x nuclear shadowing and antishadowing. Consequently, the study establishes a clear physics case for exploiting far‑forward LHC detectors as a novel laboratory for precision nuclear QCD, complementing traditional fixed‑target and electron‑ion collider programs.