Measurement of Inclusive Charged-Current $\bar{\nu}_{\mu}$ Scattering on C, CH, Fe, and Pb at $\langle E_{\bar{\nu}}\rangle \sim$ 6 GeV with MINERvA

The MINERvA collaboration reports the first measurement of inclusive charged-current $\bar{\nu}_\mu$ cross sections on carbon, hydrocarbon, iron, and lead at a mean energy of $\sim 6$ GeV, revealing significant discrepancies between experimental data and current neutrino interaction models, particularly regarding nuclear effects at low antimuon transverse momentum.

The Gist

Imagine you are trying to understand how a specific type of invisible bullet (an antineutrino) behaves when it smashes into different kinds of walls.

In this paper, the MINERvA team at Fermilab acted like a team of forensic scientists. They fired a massive stream of these "ghost bullets" at four different types of targets:

1. Carbon (C): Like a light, porous sponge.
2. Hydrocarbon (CH): Like a slightly denser plastic foam.
3. Iron (Fe): Like a solid, heavy steel beam.
4. Lead (Pb): Like a massive, dense brick wall.

Their goal? To measure exactly how often these bullets hit the targets and how they bounce off, specifically looking at the angle and speed of the "shrapnel" (a particle called an antimuon) that flies out after the crash.

The Big Mystery: The "Heavy Wall" Problem

The scientists had a set of rulebooks (computer models) that predicted exactly how these collisions should happen. They thought, "If we know the rules for the light sponge, we can just scale them up for the heavy brick wall."

But the data told a different story.

When the bullets hit the heavy walls (Iron and Lead), the real-world results were very different from the rulebooks.

• The Analogy: Imagine throwing a tennis ball at a stack of pillows (Carbon). It bounces off easily. Now, imagine throwing the same ball at a stack of lead bricks (Lead). The rulebook says, "It should bounce off just like the pillows, just a bit slower."
• The Reality: The ball actually gets stuck, bounces weirdly, or explodes in a way the rulebook never predicted. The heavy walls were "swallowing" or "smearing" the collision in ways the scientists didn't expect.

What They Found

The team measured the "transverse momentum" ($p_T$). Think of this as measuring how much the shrapnel flies sideways after the hit.

• Low Sideways Speed: When the shrapnel didn't fly much sideways, the heavy walls caused a huge drop in collisions compared to what the models predicted. The models thought there would be more hits; the reality had fewer.
• High Sideways Speed: Even when the shrapnel flew fast and far, the models still got the numbers wrong for the heavy targets.

Why Does This Matter?

You might ask, "Who cares about antineutrinos hitting lead?"

These particles are the key to unlocking the biggest mysteries of the universe, like why the universe is made of matter instead of antimatter. To solve this, giant experiments (like DUNE in the US and Hyper-Kamiokande in Japan) are building massive detectors filled with different materials (like liquid Argon, which is heavy, like Iron).

If the "rulebooks" (computer models) used to interpret the data from these giant detectors are wrong, then the scientists might draw the wrong conclusions about the universe. It's like trying to navigate a ship using a map that has the wrong depth markings for the ocean floor; you might think you're safe, but you could hit a hidden reef.

The Takeaway

This paper is a "check engine light" for the physics world.

1. We measured it: They took incredibly precise measurements of how antineutrinos hit different materials.
2. The models failed: The current computer simulations are missing some crucial physics, especially when it comes to heavy atoms. They are underestimating how much the "nuclear crowd" messes with the collision.
3. The fix is needed: Before we can trust the results of future experiments that will tell us about the origins of the universe, we need to rewrite the rulebooks to account for these "heavy wall" effects.

In short: The universe is playing by rules we haven't fully written down yet, and this paper is a major step toward finding the missing pages.

Technical Summary

1. Problem Statement

Precision neutrino oscillation experiments (such as DUNE and Hyper-Kamiokande) rely on accurate reconstruction of neutrino energy to determine mass ordering and measure CP violation. However, current interaction models suffer from significant uncertainties regarding how the nuclear environment modifies neutrino scattering.

• The Gap: While neutrino interactions have been studied, antineutrino interactions are less constrained. Antineutrino cross-sections are smaller and sensitive to different interference terms (vector-axial) and resonance channels compared to neutrinos.
• The Need: There is a critical lack of high-statistics data on antineutrino interactions across multiple nuclear targets (Carbon, Iron, Lead) in the energy regime relevant for future experiments ($\sim 6$ GeV). Existing models struggle to describe nuclear effects (such as final-state interactions and multi-nucleon correlations) consistently across different nuclei and kinematic regimes (Quasi-Elastic, Resonance, and Deep Inelastic Scattering).

2. Methodology

The MINERvA collaboration utilized data from the NuMI beam at Fermilab to measure inclusive charged-current (CC) $\bar{\nu}_\mu$ interactions.

• Beam and Exposure:
  • Data collected between 2016–2019 using the NuMI medium-energy beam with horns focused on negative mesons (producing an antineutrino-dominated flux).
  • Total exposure: $1.12 \times 10^{21}$ protons on target (POT).
  • Mean antineutrino energy: $\sim 6$ GeV.
• Detector and Targets:
  • The MINERvA detector features a passive target region with interleaved planes of Carbon (C), Iron (Fe), Lead (Pb), and water ($H_2O$), surrounded by polystyrene scintillator.
  • The active tracker downstream serves as a Hydrocarbon (CH) target.
  • The MINOS Near Detector acts as a muon range stack for momentum and charge identification.
• Event Selection:
  • Selected events with a positively charged muon ($\mu^+$) originating in the target material.
  • Kinematic cuts: $2 < E_{\mu^+} < 20$ GeV and $\theta_{\mu^+} < 17^\circ$.
  • Interaction vertex reconstruction via a deep convolutional neural network to assign events to specific target materials.
  • Backgrounds (from upstream/downstream plastic and neutrino contamination) were estimated using sideband fits and subtracted.
• Analysis Technique:
  • Unfolding: Reconstructed antimuon transverse momentum ($p_T$) distributions were unfolded using the D'Agostini iterative method (3 iterations) to correct for detector resolution and efficiency.
  • Flux Constraints: The antineutrino flux was constrained using $\nu$-$e$ scattering, inverse muon decay (IMD), and low-$\nu$ data, with specific reweighting applied above 7.5 GeV.
  • Cross-Section Ratios: Ratios of C/CH, Fe/CH, and Pb/CH were calculated to cancel common systematic uncertainties (flux, muon reconstruction) and isolate nuclear effects.

3. Key Contributions

• First Measurement: This is the first measurement of inclusive CC $\bar{\nu}_\mu$ cross-sections on C, CH, Fe, and Pb simultaneously in the $\sim 6$ GeV energy range.
• Kinematic Coverage: The analysis spans the transition from resonance production to deep-inelastic scattering (DIS), a region of high interest for DUNE and atmospheric neutrino studies.
• Model Benchmarking: The paper provides a rigorous test of state-of-the-art neutrino event generators (GENIE v3 and NEUT 5.4.1) against data from multiple nuclei, specifically focusing on the $p_T$ dependence.
• Data Release: The paper releases differential cross-sections, cross-section ratios, and full covariance/correlation matrices for future global fits and model tuning.

4. Results

• Cross-Section Measurements:
  • Differential cross-sections per nucleon were measured as a function of antimuon $p_T$.
  • Uncertainties: Total uncertainties are 5–10% for absolute cross-sections and 2–5% for ratios.
  • Interaction Modes: The data is dominated by Resonant (RES) production (~39% in Pb), followed by Soft DIS and True DIS.
• Comparison with Models:
  • Baseline Model (MINERvA Tune v4.3.0): Generally describes the peak region but underpredicts data at high $p_T$ and overpredicts at low $p_T$ for heavier nuclei (Fe, Pb).
  • Alternative Generators:
    • GENIE v3 AR23 (DUNE tune) and G18 02b yielded the lowest $\chi^2$ values across targets.
    • NEUT 5.4.1 showed significant discrepancies at low $p_T$ for Fe and Pb, attributed to differences in $A$-scaling for coherent pion production.
  • Low $p_T$ Discrepancy: All models systematically underestimate the suppression of the cross-section at low $p_T$ for heavy nuclei (Fe and Pb). This suggests missing or mis-modeled nuclear effects in the resonance regime.
  • High $p_T$ Discrepancy: Models generally underpredict the cross-section at high $p_T$, likely due to insufficient modeling of the $Q^2$ dependence of form factors in the transition to DIS.
• Ratio Analysis:
  • The ratios (Fe/CH, Pb/CH) clearly demonstrate that nuclear suppression at low $p_T$ increases with atomic mass number ($A$) more strongly than current models predict.
  • The C/CH ratio serves as a cross-check, consistent with diffractive scattering on hydrogen.

5. Significance

• Impact on Oscillation Physics: The results provide critical benchmarks for neutrino interaction models used in DUNE and Hyper-Kamiokande. The observed discrepancies in nuclear effects (particularly for heavy nuclei like Iron and Lead) indicate that current systematic uncertainties in oscillation analyses may be underestimated.
• Model Improvement: The data highlights specific deficiencies in generators, particularly regarding:
  • Nuclear effects in the resonance region (low $p_T$).
  • The treatment of multi-nucleon correlations and final-state interactions in heavy nuclei.
  • The $Q^2$ dependence of form factors in the transition region.
• Future Directions: These measurements constrain the modeling of interactions for future oscillation experiments, ensuring more accurate energy reconstruction and CP violation measurements. The paper emphasizes that high-statistics antineutrino data on multiple nuclei is essential to resolve the "nuclear effect" ambiguity.