First Measurement of $\pi^+$-Ar and $p$-Ar Total Inelastic Cross Sections in the Sub-GeV Energy Regime with ProtoDUNE-SP Data

Using data from the ProtoDUNE-SP detector at CERN, this paper reports the first measurements of the total inelastic cross sections for $\pi^+$-Ar and $p$-Ar interactions in the sub-GeV energy regime, providing essential constraints for neutrino-argon interaction models critical to the upcoming DUNE experiment.

The Gist

Imagine you are trying to understand how a specific type of car (a neutrino) behaves when it crashes into a very specific, heavy wall made of liquid argon. To predict exactly how the car will crumple and what pieces will fly off, you need to know exactly how the wall reacts to different types of debris hitting it.

This paper is like a team of mechanics running a crash test to figure out exactly how argon (the wall) reacts when hit by two common types of debris: pions and protons (the debris).

Here is the breakdown of what they did and why it matters, using simple analogies:

1. The Big Goal: The "Crystal Ball" Problem

The scientists are building a giant experiment called DUNE (Deep Underground Neutrino Experiment). It's like a massive, high-tech camera buried deep underground, filled with 70,000 tons of liquid argon. Its job is to take pictures of neutrinos (ghostly particles) passing through.

However, when a neutrino hits an argon atom, it doesn't just stop; it creates a shower of other particles (like pions and protons). These new particles bounce around inside the argon nucleus before they escape. This is called a "Final State Interaction."

The Problem: The scientists didn't have a perfect "rulebook" for how these particles bounce around inside argon. They had to guess based on how they bounce off other materials (like carbon or lead). It's like trying to predict how a billiard ball will bounce off a pool table made of ice, but you've only ever studied how it bounces off wood. Your prediction might be wrong, and that mistake could ruin your measurement of the neutrino itself.

2. The Solution: The "Sandwich" Test

To fix this, they used a prototype detector called ProtoDUNE-SP. Think of this as a full-scale "mock-up" of the real camera, filled with liquid argon.

They didn't just wait for neutrinos to hit it. Instead, they fired a controlled beam of pions and protons directly into the liquid argon.

• The Beam: Imagine a machine gun shooting tiny particles at the liquid argon.
• The Trick: Usually, to measure how often a particle hits a target, you use a very thin sheet of material. But liquid argon is thick. If a particle hits the front, it might hit again before it exits.
• The "Slicing" Method: To solve this, the scientists treated the liquid argon like a loaf of bread. They virtually sliced the path of the particle into thin "slices" of energy. They tracked the particle as it entered a slice, lost a little energy (like a car slowing down on a rough road), and either bounced out or crashed inside that specific slice. This allowed them to count exactly how many "crashes" happened at every specific speed.

3. The Results: Filling the "Missing Page"

The paper reports the first-ever measurements of how often pions and protons crash into argon atoms at specific speeds (energies) that are very common in neutrino experiments.

• The Pion Test: They measured pions moving at speeds between 500 and 900 MeV (a specific unit of energy).
• The Proton Test: They measured protons moving at speeds below 450 MeV.

The Analogy: Before this, the scientists were trying to bake a cake using a recipe that said "add some flour," but they didn't know how much. They had to guess based on recipes for other cakes. This paper finally gives them the exact measurement: "You need exactly 200 grams of argon-flour for this speed of particle."

4. What They Found

When they compared their new measurements to the computer simulations (the "rulebooks" they were using before), they found:

• The simulations were actually pretty good! The new data matched the predictions from the Geant4 software (a standard physics simulation tool) very well.
• However, having the real data is crucial. It's the difference between a chef guessing the taste of a dish and actually tasting it. Now, they have the "taste test" results for argon.

5. Why This Matters for the Future

The paper states that these measurements are essential for the DUNE experiment.

• By knowing exactly how particles interact with argon, scientists can build better "rulebooks" (models).
• Better rulebooks mean less guessing when they analyze neutrino data.
• Less guessing means they can measure the properties of neutrinos (like their mass and how they change types) with much higher precision.

In Summary:
This paper is a "quality control" report. The scientists built a giant liquid argon tank, shot particles at it, and counted the collisions. They proved that their current computer models are mostly correct, but more importantly, they provided the first hard data to back those models up. This ensures that when the real DUNE experiment starts taking pictures of neutrinos, the scientists won't be misinterpreting the blurry parts of the image caused by the argon wall.

Technical Summary

Technical Summary: First Measurement of $\pi^+$–Ar and p–Ar Total Inelastic Cross Sections in the Sub-GeV Energy Regime with ProtoDUNE-SP Data

Problem Statement
The Deep Underground Neutrino Experiment (DUNE) aims to determine neutrino mass ordering and measure CP violation in the lepton sector using a massive Liquid Argon Time Projection Chamber (LArTPC) far detector. A critical challenge in reconstructing neutrino energy and identifying oscillation parameters is the accurate modeling of Final-State Interactions (FSI). When neutrinos interact with argon nuclei, the resulting hadrons (primarily nucleons and charged pions) undergo secondary scattering within the nucleus and the liquid argon medium before detection. Mismodeling these interactions introduces significant uncertainties in event reconstruction, potentially biasing neutrino energy measurements and obscuring sensitivity to the CP-violating phase.

While DUNE operates in an energy regime where hadron kinetic energies typically peak around a few hundred MeV and extend beyond 1 GeV, experimental data for hadron-argon interactions in this specific sub-GeV range has been scarce. Previous measurements relied heavily on interpolation from data obtained on solid targets like carbon and lead, or were limited to specific discrete energies (e.g., LADS experiment at 118–239 MeV) or different particle types (e.g., LArIAT for $\pi^-$). There was a distinct lack of dedicated total inelastic cross-section measurements for $\pi^+$ and protons on argon in the 10–900 MeV kinetic energy range, creating a gap in the validation of hadronic interaction models essential for the LArTPC neutrino program.

Methodology
This study utilizes data collected by the ProtoDUNE-SP detector, a 770-ton single-phase LArTPC prototype operated at the CERN Neutrino Platform. The detector was exposed to a positively charged particle beam with momentum settings of 0.3, 0.5, 1, 2, 3, 6, and 7 GeV/c. This analysis focuses on the 1 GeV/c beam data, selecting samples of $\pi^+$ and protons to measure total inelastic cross sections in the kinetic energy ranges of 500–900 MeV (for $\pi^+$) and below 450 MeV (for protons).

The analysis employs a modified "energy slicing" method, adapted from the LArIAT collaboration's "thin-slice" approach, to overcome the challenge of the LArTPC being a thick target (where the detector size exceeds the hadron mean free path).

1. Event Selection: Beam particles are identified using beamline instrumentation (Time-of-Flight and Cherenkov detectors). Events are reconstructed using the Pandora software package. Fiducial volume cuts ($z \in [30, 220]$ cm) are applied to ensure uniform identification efficiency and avoid electric field distortions near the anode plane assemblies.
2. Background Suppression: Specific vetoes are applied to remove backgrounds. For the pion sample, muons are suppressed using a Michel electron score (based on a convolutional neural network) and track length constraints. Secondary protons are rejected using a $\chi^2$ fit against the proton stopping power profile. For the proton sample, stopping protons are distinguished from inelastic events using similar stopping power criteria and the Continuous-Slowing-Down Approximation (CSDA).
3. Cross Section Calculation: The total inelastic cross section, $\sigma(E)$, is calculated using the formula:
   $$\sigma(E) = \frac{N_{int}(E)}{n N_{end}(E) \delta E \frac{dE}{dx}(E) \ln \left( \frac{N_{inc}(E)}{N_{inc}(E) - N_{end}(E)} \right)}$$
   where $N_{int}$, $N_{inc}$, and $N_{end}$ represent the number of interacting, incident, and end-vertex particles in an energy slice $\delta E$, $n$ is the argon number density, and $dE/dx$ is the stopping power.
4. Unfolding and Corrections: Detector effects, including efficiency and resolution, are corrected using a multi-dimensional unfolding procedure based on the iterative Bayesian method (D'Agostini). The response matrix is derived from Geant4 simulations (using the LArSoft toolkit and QGSP BERT physics list). Systematic uncertainties are evaluated by varying parameters related to background modeling, MC statistics, cross-section models, energy reconstruction, and space-charge corrections.

Key Contributions

• First Dedicated Measurements: This work presents the first measurement of total inelastic cross sections for $\pi^+$–Ar and p–Ar interactions in the kinetic energy ranges of 500–900 MeV and 10–450 MeV, respectively.
• Methodological Advancement: The application of a modified energy-slicing method combined with multi-dimensional unfolding to a kiloton-scale LArTPC demonstrates a viable technique for extracting cross sections from thick-target detectors without relying on thin-target approximations.
• Data-Driven Validation: The results provide a direct experimental benchmark for argon targets, moving beyond the reliance on interpolations from carbon or lead data.

Results
The measured cross sections are presented with both statistical and systematic uncertainties.

• Pion ($\pi^+$): The measured cross section in the 500–900 MeV range shows a peak structure around 165 MeV (extrapolated from the trend) corresponding to the $\Delta(1232)$ resonance. The data is consistent with the Geant4 10.6 Bertini model (QGSP BERT), yielding a $\chi^2/N_{dof}$ of 3.1/8. Other models (GENIE hA2018, hN2018, INCL) show larger deviations but cannot be strictly ruled out given current uncertainties.
• Proton (p): The proton cross section peaks around 30 MeV and decreases at higher energies due to compound nuclear processes. The data is also consistent with the Geant4 10.6 Bertini model ($\chi^2/N_{dof} = 3.9/10$).
• Scaling Laws: The results align with the empirical relation $\sigma \propto A^{2/3}$ when compared to measurements on other nuclear targets (Li, C, Al, Ca, Fe, Ni, Nb, Sn, Ho, Pb, Bi).

Significance
The paper asserts that these measurements are essential for constraining neutrino-argon interaction models. By providing the first dedicated argon data for $\pi^+$ and proton scattering in the sub-GeV regime, the results directly address the uncertainties associated with FSI and secondary interactions in DUNE. This work represents a key step toward achieving the precision required for oscillation measurements, specifically the determination of the CP-violating phase. The authors note that while uncertainties remain larger than those for other nuclear targets, these results offer a vital experimental benchmark that reduces the reliance on interpolations. The methodology established here facilitates future measurements with the ProtoDUNE-HD dataset, aiming to extend these constraints to a broader phase space and further support the physics goals of DUNE and the broader neutrino community.