Measurement of muon (anti-)neutrino charged-current quasielastic-like cross section using off-axis NuMI beam at ICARUS

This paper presents the first neutrino cross-section measurement from the ICARUS detector using off-axis NuMI beam data, reporting flux-averaged differential cross sections for charged-current quasielastic-like events in various kinematic variables to test neutrino event generators against complex nuclear effects.

The Gist

Imagine a giant, high-tech underwater camera sitting deep underground in Illinois. This camera, called ICARUS, is filled with 760 tons of liquid argon (frozen neon gas). Its job is to take "photos" of ghostly particles called neutrinos that are constantly raining down on Earth from space and from a particle accelerator nearby.

This paper is the report card from the first time this specific camera successfully took detailed measurements of how these neutrinos interact with the argon. Here is the breakdown of what they did and found, using simple analogies.

The Setup: A Billiard Game with Ghosts

Neutrinos are like invisible ghosts. They rarely bump into anything. When they do hit something, it's like a ghostly billiard ball hitting a real one.

• The Source: The scientists used a beam of neutrinos fired from Fermilab (a giant particle accelerator). Because the camera is slightly off to the side (not directly in the center of the beam), the neutrinos hitting it have a specific, lower-energy "speed."
• The Target: The target is the liquid argon inside the camera.
• The Goal: They wanted to study a specific type of collision called "Quasi-Elastic". Imagine a neutrino hitting a proton (a building block of the atom) and knocking it out, while the neutrino turns into a muon (a heavy cousin of an electron). The key rule here is: No pions allowed. If the collision creates a pion (another type of particle), it's a different game. They only wanted the clean "knock-out" hits.

The Challenge: The "Nuclear Fog"

The paper explains that studying these collisions is hard because the argon nucleus isn't just a single proton; it's a crowded room of protons and neutrons.

• The Analogy: Imagine trying to see a billiard ball hit another ball in a dark, crowded room. The other balls in the room might bump into the moving ball, change its direction, or absorb it before it even leaves the room.
• The Problem: Scientists have different "rulebooks" (computer models) to predict how this crowded room behaves. Some models say the balls bounce off each other a lot; others say they stick together. This uncertainty is the biggest headache for future experiments trying to measure the secrets of the universe.

What They Did: The "Photo Album"

The researchers collected data from 2.5 × 10²⁰ protons hitting a target (a massive amount of data). They then used a computer program to sort through millions of events to find the specific "clean" collisions where:

1. A muon came out.
2. A proton came out.
3. Nothing else (no pions, no extra debris) came out.

They measured four specific things about these collisions, like taking measurements of the billiard balls after the hit:

1. The Angle of the Muon: Which way did the muon fly?
2. The Angle between the Muon and Proton: How far apart did they fly from each other?
3. Two "Imbalance" Measurements: Did the momentum balance out perfectly, or was there a "kick" from the crowded room (the nucleus) that threw things off?

The Results: Do the Rulebooks Match?

Once they had their measurements, they compared them against the predictions from various computer models (the "rulebooks").

• The Verdict: The data they collected agrees with the predictions. The models aren't wrong; they are just not precise enough yet to tell which one is the best description of reality.
• The Limitation: The paper states that their "uncertainty budget" (the margin of error in their measurements) is currently too wide. It's like trying to tell the difference between two very similar shades of blue with a blurry camera. They can see the blue, but they can't yet say definitively which specific shade it is.
• The Main Culprit: The biggest source of error wasn't the neutrinos themselves, but the detector. The camera's sensitivity and how it records the "photos" of the particles introduced the most uncertainty.

The Conclusion

This paper is a milestone because it is the first time this specific camera (ICARUS) has measured these specific neutrino interactions on argon.

• Why it matters: Future experiments (like DUNE) will use similar detectors and targets. To understand the universe, they need to know exactly how neutrinos behave when they hit argon.
• The Takeaway: The scientists have provided a new set of "ground truth" data. While the current models pass the test, the data isn't precise enough yet to pick a winner among the different theories. To do that, they will need more data and a sharper understanding of how their camera works.

In short: They built a high-tech camera, took a million photos of neutrino hits, and confirmed that our current maps of how these particles behave are roughly correct, but we need better maps to navigate the future.

Technical Summary

1. Problem Statement

The primary goal of current and future long-baseline neutrino oscillation experiments (e.g., DUNE) is to precisely measure oscillation parameters, including mass ordering and CP violation. However, these measurements are currently limited by systematic uncertainties, which are dominated by the modeling of neutrino-nucleus interactions.

• The Challenge: Neutrino interactions with nuclei (specifically Argon in this context) are complex. Nuclear effects—such as the initial state momentum distribution of nucleons and Final State Interactions (FSI) where particles re-scatter or are absorbed within the nucleus—distort the final state kinematics and particle content.
• The Gap: Many event generators rely on simplified factorization schemes that treat the vertex interaction and hadron propagation separately. There is a critical need for high-precision cross-section measurements on Argon targets, specifically in kinematic variables sensitive to these nuclear effects, to validate and tune theoretical models.

2. Methodology

Experimental Setup

• Detector: The ICARUS T600 detector, a 760-ton Liquid Argon Time Projection Chamber (LArTPC), located 600 meters from the beam origin at Fermilab.
• Beam: The NuMI (Neutrinos at the Main Injector) beam operating in neutrino mode. The detector is positioned off-axis (100 mrad), resulting in a neutrino energy spectrum shifted toward lower energies (peaking around 1–2 GeV) compared to the on-axis beam.
• Dataset: Data collected during Run 1 (June–July 2022) and Run 2 (February–June 2023), corresponding to $2.5 \times 10^{20}$ protons-on-target (POT).

Signal Definition and Event Selection

• Signal Topology: Charged-Current Quasi-Elastic-like (CCQE-like) interactions defined as:
  • $\nu_\mu + \text{Ar} \to \mu^- + \text{proton(s)} + \text{neutron(s)}$
  • Strict Constraints: No pions (charged or neutral) or other mesons in the final state.
  • Kinematic Cuts:
    • Muon momentum $p_\mu > 226$ MeV/c (to ensure containment/tracking).
    • Leading proton momentum between 400 and 1000 MeV/c.
    • For Transverse Kinematic Imbalance (TKI) variables, an additional cut of $p_\mu < 0.8$ GeV/c is applied to ensure precise momentum reconstruction via the Continuous Slowing Down Approximation (CSDA).
• Background Suppression:
  • Pion Veto: Events with identified charged pions or photon-induced showers (from $\pi^0$ decay) are rejected.
  • Sideband Control: A "pion sideband" sample is defined by inverting the pion veto condition (requiring a tagged charged pion) to constrain background modeling data-driven.
  • Cosmogenic Background: Mitigated using data-driven methods and simulations (Corsika) for cosmic rays coincident with beam spills.

Simulation and Reconstruction

• Reconstruction: Uses the Pandora pattern-recognition software within the LArSoft framework to reconstruct 3D tracks and showers. Particle Identification (PID) relies on $dE/dx$ profiles and track topology.
• Simulation:
  • Flux: Modeled using Geant4 and PPFX, accounting for off-axis effects and hadron production on various target materials (C, Al, Fe).
  • Interaction: The GENIE event generator (version AR23 20i CMC) is used as the reference model. It incorporates the Valencia model for QE, SuSAv2-MEC for multi-nucleon effects, and the hA2018 model for FSI.
  • Detector: Full Geant4 simulation of particle propagation, ionization, and drift, coupled with Wire-Cell Toolkit for signal induction.

Analysis Framework

• Extraction: The GUNDAM (Global Unfolding and Data Analysis for Muon-neutrino) framework is used.
• Fitting Strategy: A simultaneous fit is performed on the signal and sideband samples to constrain backgrounds.
• Variables: Four kinematic variables are measured:
  1. $\cos \theta_\mu$: Muon angle relative to the neutrino direction.
  2. $\cos \theta_{\mu,p}$: Opening angle between the muon and the leading proton.
  3. $\delta p_T$: Transverse momentum imbalance.
  4. $\delta \alpha_T$: Transverse angle imbalance.
• Systematics: A comprehensive covariance matrix is built covering flux, detector response (gain, noise, electron lifetime, proton ID efficiency), interaction models (form factors, MEC, FSI), and particle propagation (Geant4 reweighting).

3. Key Contributions

1. First ICARUS Cross-Section Measurement: This is the first publication of a neutrino cross-section measurement from the ICARUS detector at Fermilab using NuMI data.
2. Off-Axis Argon Data: Provides a unique dataset on an Argon target with a broad energy spectrum (up to a few GeV) complementary to lower-energy (MicroBooNE) and higher-energy (ArgoNeuT) measurements.
3. Multi-Dimensional Kinematic Analysis: Reports flux-averaged differential cross-sections in four variables specifically chosen for their sensitivity to nuclear effects (initial state momentum and FSI), rather than just total cross-sections.
4. Robust Background Constrained Method: Utilizes a data-driven sideband approach for pion production to constrain background uncertainties directly from the data, reducing reliance on pure simulation for background normalization.
5. Model Comparison Framework: Systematically compares the extracted data against a wide range of theoretical predictions, including alternative GENIE configurations (LQCD form factors, MINERvA form factors, hN2018 FSI), NuWro, GiBUU, and Neut (RDWIA model).

4. Results

• Cross-Section Extraction: The paper presents the extracted flux-averaged differential cross-sections for the four kinematic variables. The signal is dominated by Quasi-Elastic (QE) interactions (~60%), followed by Multi-Nucleon (MEC, ~20%) and Resonance (RES, ~15%) contributions.
• Model Comparison:
  • The data is compared against the reference GENIE model and alternative generators.
  • Good Agreement: Overall, the data is consistent with the predictions. The p-values for the comparison between data and various models range from 0.178 to 0.988 for angular variables and 0.318 to 0.981 for TKI variables.
  • Specific Findings:
    • The Neut model (RDWIA) shows the lowest compatibility with angular variables ($p=0.178$) but agrees well with TKI variables.
    • NuWro and GiBUU show unique shapes in the $\delta p_T$ distribution (Fermi peak and high tail) but remain within one standard deviation of the data.
    • Variations in the axial form factor (LQCD vs. MINERvA fits) and FSI models (hA2018 vs. hN2018) show minor deviations but do not significantly alter the overall agreement.
• Uncertainty Budget: The total uncertainty is currently dominated by detector response (calorimetry, proton identification efficiency) rather than flux or interaction modeling. Statistical uncertainties are also significant.

5. Significance

• Validation for Future Experiments: These results provide essential input for tuning neutrino interaction models used in DUNE (Deep Underground Neutrino Experiment), which will also use a Liquid Argon TPC and a similar energy spectrum.
• Nuclear Physics Insights: By measuring variables like $\delta p_T$ and $\delta \alpha_T$, the analysis probes the complex nuclear environment (nucleon correlations and FSI) that standard QE models often fail to describe accurately.
• Limitations and Future Work: The authors note that the current statistical and systematic uncertainties are not yet sufficient to definitively favor one specific theoretical model over another (no model is rejected at the 5% significance level). Future improvements will require:
  • More data (potentially with antineutrino beam polarity).
  • Refined detector simulations to reduce the dominant systematic uncertainties related to proton identification and track reconstruction.

In summary, this paper establishes a rigorous baseline for muon-neutrino interactions on Argon, demonstrating that while current models broadly agree with data, higher precision is required to fully resolve the nuclear effects that limit the precision of next-generation neutrino oscillation measurements.