Investigating nuclear effects in lepton-ion DIS at the LHC

This paper investigates the impact of nuclear effects on muon- and neutrino-tungsten deep inelastic scattering events at the LHC's FASER$\nu$ and FASER$\nu2$ experiments, demonstrating that a simultaneous analysis of inclusive and charm-tagged events can test the universality of nuclear effects and reduce uncertainties in parton distribution functions.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed particle accelerator that smashes protons together. Usually, scientists look at the debris flying out in all directions. But this paper focuses on a very specific, quiet corner of the experiment: the "far-forward" direction. Think of this as looking straight down the barrel of the gun, where only the fastest, most elusive particles—neutrinos and muons—manage to escape the chaos and travel hundreds of meters to a special detector called FASER.

Here is the core story of the paper, broken down with simple analogies:

The Mystery of the "Shadowy" Nucleus

Inside the atoms of the heavy tungsten blocks used in the detector, the tiny building blocks (quarks and gluons) don't just sit there like a pile of marbles. When they are packed tightly inside a nucleus, they behave differently than when they are alone. Scientists call these changes "nuclear effects."

Think of a nucleus like a crowded dance floor.

• Shadowing: At low energies, the dancers (quarks) huddle together so much that they hide each other, making it look like there are fewer dancers than there actually are.
• EMC Effect: At higher energies, the dancers move in a way that changes the rhythm of the whole floor.
• Antishadowing: In the middle, they might actually seem to pop out more clearly.

For years, scientists have tried to map this "dance floor" using different mathematical models (called PDFs). But there's a problem: the models disagree. It's like having three different maps of the same city, and they show different street layouts. Worse, data from neutrinos seems to contradict data from other particles, creating a "tension" in the scientific community.

The Experiment: Two Types of Messengers

The authors of this paper propose using two different "messengers" to probe this crowded dance floor:

1. Muons: Charged particles that interact via the electromagnetic force.
2. Neutrinos: Ghostly particles that interact via the weak force.

They plan to shoot these messengers at a block of tungsten (a heavy metal) and see how they scatter. This is called "Deep Inelastic Scattering" (DIS).

• The Analogy: Imagine throwing two different types of balls at a dense forest. One type of ball (muons) bounces off the trees in a way that tells you about the leaves. The other type (neutrinos) passes through the leaves but gets caught by the trunks. By comparing how both balls bounce, you can get a complete picture of the forest.

What They Found

The researchers ran simulations to predict how many times these particles would hit the tungsten and create specific results. They looked at two types of outcomes:

1. Inclusive Events: Just a general "splash" of debris. This is like counting how many trees were hit in total.
2. Charm-Tagged Events: Specific events where a heavy "charm" particle is created. This is like looking for a specific, rare type of fruit that only falls when a very specific branch is hit.

Key Discoveries:

• Different Maps, Different Results: When they used the different mathematical models (the "maps"), they got different predictions for how many hits they would see. This proves that the current models are still uncertain, especially regarding the "glue" (gluons) and "strange" particles inside the nucleus.
• The Power of the Ratio: The authors suggest a clever trick. Instead of just counting the total hits, they propose looking at the ratio of "Charm-Tagged" hits to "Inclusive" hits.
  • Analogy: If you want to know if a forest is dense, counting every tree is hard. But if you count how many rare apples fall compared to total leaves, the ratio might reveal the truth about the forest's density much faster.
  • This ratio acts as a "litmus test" to see which mathematical model is actually correct.
• FASER vs. FASER2:
  • FASER (Current): They predict they will see enough events to start testing these ideas, but the data will be a bit "fuzzy" (statistical uncertainty).
  • FASER2 (Future Upgrade): This is the big upgrade. With a much larger detector and more time, they predict they will see 100 times more events. This will turn the "fuzzy" picture into a crystal-clear high-definition image, allowing them to pin down exactly how the nuclear effects work.

The Bottom Line

The paper argues that by using the LHC's far-forward detectors to study how muons and neutrinos bounce off heavy tungsten, we can finally solve the mystery of how quarks behave inside a nucleus.

Specifically, by comparing the "Charm-Tagged" events to the "Inclusive" events, scientists can:

1. Test if the rules of physics (universality) are the same for neutrinos and muons.
2. Decide which of the conflicting mathematical models is actually right.
3. Reduce the uncertainty in our understanding of the fundamental building blocks of matter.

The authors conclude that this is a promising new window into nuclear physics that doesn't require building a whole new collider, but rather using the existing LHC in a new, clever way.

Technical Summary

Technical Summary: Investigating Nuclear Effects in Lepton-Ion DIS at the LHC

Problem Statement
The systematic determination of nuclear parton distribution functions (nPDFs) remains a critical challenge in understanding nuclear structure and the initial conditions of the Quark-Gluon Plasma. Despite decades of data from fixed-target and collider experiments, significant discrepancies persist between global analyses performed by different groups (e.g., EPPS21, nCTEQ15HQ, nNNPDF 3.0), particularly at small Bjorken-$x$ and in the strange and gluon distributions. Furthermore, a known tension exists between charged-lepton ion Deep Inelastic Scattering (DIS) data and the bulk of neutrino-ion DIS data, raising questions regarding the universality of nPDFs. While future Electron-Ion Colliders are designed to address these issues, the far-forward physics program at the Large Hadron Collider (LHC) offers a unique, immediate opportunity to probe these effects using high-energy neutrinos and muons produced in proton-proton collisions.

Methodology
The authors investigate the impact of nuclear effects on muon-tungsten ($\mu$W) and neutrino-tungsten ($\nu$W) DIS events at the FASER$\nu$ detector and its proposed upgrade, FASER$\nu2$, located in the far-forward region of the LHC. The study focuses on two classes of events: inclusive DIS and charm-tagged DIS.

• Theoretical Framework: The calculation of event rates utilizes the POWHEG-BOX-RES event generator for Next-to-Leading Order (NLO) perturbative QCD corrections, interfaced with PYTHIA8 for hadronization.
• Flux and Acceptance: The analysis incorporates simulated muon and neutrino fluxes in the far-forward direction (derived from FLUKA simulations and light/heavy meson decays) and applies specific detector acceptance cuts: final lepton energy $> 100$ GeV, at least two charged tracks with momentum $> 1$ GeV, $Q^2 \geq 1.65$ GeV$^2$, and a hadronic invariant mass $> 2$ GeV. A charm tagging efficiency of $\epsilon = 0.7$ is assumed.
• nPDF Parameterizations: The study compares predictions using three distinct nPDF sets: EPPS21, nCTEQ15HQ, and nNNPDF 3.0(W). These are contrasted with baseline free-nucleon parameterizations (CT18ANLO and nNNPDF 3.0(p)) to isolate nuclear effects.
• Scenarios: Predictions are generated for FASER$\nu$ (Run 3, $250 \text{ fb}^{-1}$, 1.1 tons of tungsten) and FASER$\nu2$ (HL-LHC era, $3 \text{ ab}^{-1}$, $\approx 20$ tons of tungsten).

Key Contributions and Results

1. Event Rate Estimates:

   • The study provides detailed predictions for the number of inclusive and charm-tagged events. Inclusive $\mu$W events are predicted to be approximately two orders of magnitude more frequent than $\nu$W events.
   • FASER$\nu2$ is expected to yield event rates roughly 100 times higher than FASER$\nu$, with statistical uncertainties becoming significantly smaller than current PDF uncertainties across the entire $x$ range.
   • Different nPDF parameterizations yield distinct event counts. For instance, in inclusive $\mu$W interactions, CT18ANLO (no nuclear effects) and nNNPDF 3.0(W) provide the highest and lowest event counts respectively, while for charm-tagged events, nCTEQ15HQ and nNNPDF 3.0(p) generate the highest rates.

2. Kinematic Sensitivity and Nuclear Effects:

   • Inclusive Events: At small $x$ (shadowing region), the difference between predictions with and without nuclear effects is significant for CTEQ-based models (nCTEQ15HQ, EPPS21) but smaller for nNNPDF 3.0. At large $x$ (EMC region), differences are observed but are generally smaller.
   • Charm-Tagged Events: These events are highly sensitive to the gluon distribution in $\mu$W interactions and the strange distribution in $\nu$W interactions. The study finds that charm-tagged event rates are reduced by an order of magnitude compared to inclusive rates. The predictions for charm-tagged events show strong dependence on the nPDF framework, particularly at small $x$, where CTEQ and NNPDF frameworks differ by a factor of $\approx 2$ due to different treatments of perturbative charm contributions.

3. Proposed Observable: The Charm-to-Inclusive Ratio:

   • The authors propose analyzing the ratio of charm-tagged to inclusive events as a discriminator for nuclear effect modeling. Since inclusive events are dominated by valence and sea quarks while charm-tagged events probe gluons (for muons) or strange quarks (for neutrinos), this ratio can isolate specific nuclear modifications.
   • FASER$\nu$ (Run 3): For $\mu$W interactions, the ratio varies significantly between nPDF sets (nCTEQ15HQ predicts higher values, NNPDF lower), suggesting this observable could distinguish models even with current statistics. For $\nu$W interactions, statistical uncertainties at FASER$\nu$ are currently too large to draw strong conclusions.
   • FASER$\nu2$ (HL-LHC): With the increased luminosity and target mass, statistical uncertainties will decrease substantially. The study predicts that the differences between nPDF parameterizations (e.g., EPPS21 vs. others for $\nu$W) will become larger than the statistical errors, allowing for a precise test of nuclear effect models.

Significance and Claims
The paper argues that the simultaneous measurement of $\mu$W and $\nu$W DIS events at the LHC offers a unique capability to test the universality of nPDFs, as the same detector and nuclear target are used for both lepton types. The authors claim that:

• Current uncertainties in nPDFs, particularly for strange and gluon distributions at small $x$, can be significantly reduced by data from FASER$\nu$ and FASER$\nu2$.
• The proposed ratio of charm-tagged to inclusive events is a powerful tool to discriminate between distinct nPDF parameterizations and resolve tensions between datasets.
• A precise understanding of nuclear cross-sections is not only fundamental for QCD but also essential for background estimation in Beyond the Standard Model (BSM) searches at far-forward detectors.
• The results motivate extending this analysis to the Future Circular Collider (FCC) in future work.

The authors maintain a modest tone regarding immediate conclusions, noting that while FASER$\nu$ data may already constrain models, the definitive precision required to fully resolve nPDF universality and specific nuclear effect modeling is expected to be achieved with the FASER$\nu2$ dataset during the HL-LHC era.