Measurement of single charged pion production in charged-current $ν_μ$-Ar interactions with the MicroBooNE detector

The MicroBooNE collaboration presents the first flux-averaged charged-current $\nu_\mu$-argon cross-section measurements for final states with exactly one charged pion and no other hadrons, reporting a total cross-section of $(3.75 \pm 0.07 \pm 0.80) \times 10^{-38} \, \text{cm}^2/\text{Ar}$ at a mean energy of 0.8 GeV and demonstrating good overall agreement with neutrino interaction generators across various differential distributions.

The Gist

Imagine a giant, invisible storm of tiny particles called neutrinos raining down on Earth. These particles are ghosts; they pass through almost everything—planets, stars, even your body—without ever saying "hello." But every once in a while, one of them bumps into something.

This paper is about a team of scientists who built a massive, high-tech "net" to catch these ghostly collisions and study what happens when they do hit something. Specifically, they wanted to see what happens when a neutrino hits an argon atom (a gas used in light bulbs) and knocks out a single, charged pion (a tiny particle that acts like a messenger).

Here is the story of their adventure, broken down into simple concepts:

1. The Giant Fish Tank (The Detector)

The scientists used a detector called MicroBooNE. Think of it as a giant, 85-ton fish tank filled with liquid argon that is colder than outer space.

• How it works: When a neutrino (the ghost) finally hits an argon atom inside the tank, it creates a splash of charged particles. These particles leave a trail of electrical sparks, like a glowing trail of breadcrumbs.
• The Camera: The tank is lined with thousands of wires that act like a 3D camera. They take pictures of these sparks from three different angles, allowing the scientists to reconstruct the entire event in 3D, just like putting together a puzzle.

2. The Goal: Catching the "One-Pion" Event

The scientists were looking for a very specific type of collision:

• The Setup: A neutrino hits an argon atom.
• The Result: A muon (a heavy cousin of the electron) and exactly one charged pion fly out.
• The Challenge: The neutrino beam is messy. Sometimes it creates no pions, sometimes it creates a whole party of pions, and sometimes it creates other particles that look like pions but aren't. It's like trying to find a specific red marble in a bucket of mixed marbles, sand, and pebbles.

3. The Detective Work (Filtering the Data)

To find the right events, the team used a digital detective named Pandora and a set of smart filters called Boosted Decision Trees (BDTs).

• The Analogy: Imagine you are at a crowded party. You are looking for a specific person wearing a red hat (the pion) and holding a blue balloon (the muon).
• The Filter: The computer looks at everyone. "Is that person holding a balloon? Yes. Is that person wearing a red hat? Maybe. Wait, that's actually a red balloon, not a hat. Ignore that."
• The "Unscattered" Trick: Pions are tricky because they often bounce off other atoms inside the tank before they stop, which makes it hard to measure how fast they were going. The scientists created a special "VIP list" of pions that didn't bounce around (unscattered pions). This allowed them to measure the pion's speed accurately for the first time on argon.

4. The Big Reveal: What Did They Find?

After sifting through data from over a quintillion protons (that's 1,000,000,000,000,000,000!), they found 6,816 perfect "one-pion" events.

• The Total Count: They calculated the total "cross-section," which is basically the probability of this specific collision happening. It's like measuring how big a target the argon atom presents to the neutrino. They found it to be about 3.75 (in very tiny scientific units).
• The Comparison: The scientists compared their real-world data to predictions made by different computer simulations (called "generators"). Think of these generators as different weather forecasters trying to predict the storm.
  • The Good News: Most of the forecasters were pretty close to the truth. The data matched the models reasonably well.
  • The Bad News: When the particles flew in a very straight line (forward angles), the models got a bit confused and predicted too many collisions. It's like a weather forecaster who is great at predicting rain but keeps overestimating how much wind there will be.

5. Why Does This Matter?

You might ask, "Why do we care about neutrinos hitting argon?"

• The Future of Physics: The next big neutrino experiment, called DUNE, will use a massive detector filled with liquid argon to study why the universe is made of matter instead of antimatter.
• The Calibration: To understand the results from DUNE, scientists need to know exactly how neutrinos interact with argon. If their models are wrong, they might misinterpret the data and miss a discovery about the fundamental laws of the universe.
• The Contribution: This paper provides the "rulebook" for how neutrinos behave with argon. It's like giving the next generation of explorers a better map so they don't get lost.

Summary

In short, the MicroBooNE team built a giant, frozen camera to watch invisible ghosts bump into gas atoms. They successfully counted how often these ghosts knock out a single messenger particle (the pion) and measured how fast that messenger was going. Their results mostly match our current theories, but they found a few spots where the theories need a little tuning. This work is a crucial step toward unlocking the secrets of the universe in future experiments.

Technical Summary

1. Problem Statement

Understanding neutrino-nucleus interactions is critical for interpreting data from neutrino oscillation experiments (such as DUNE and T2K) and searching for physics beyond the Standard Model. A major source of systematic uncertainty in these experiments is the modeling of neutrino interactions on argon nuclei, particularly the production of pions.

• The Gap: While cross-sections have been measured for targets like water, carbon, and hydrocarbons, high-statistics measurements on argon are scarce. Previous argon measurements (e.g., by ArgoNeuT) had limited statistics ($\sim$273 events).
• The Challenge: Simulating these interactions is difficult due to complex nuclear effects, including multi-nucleon correlations, final state interactions (FSI), and the transition between resonance production and deep inelastic scattering. Specifically, accurately modeling the production of a single charged pion ($\pi^\pm$) in charged-current (CC) interactions is essential for background rejection in $\nu_e$ appearance searches.

2. Methodology

The analysis utilizes data from the MicroBooNE experiment, a Liquid Argon Time Projection Chamber (LArTPC) located in the Booster Neutrino Beam (BNB) at Fermilab.

• Dataset: The analysis uses data corresponding to $1.11 \times 10^{21}$ protons on target (POT) collected between 2015 and 2020.
• Signal Definition: The study targets CC1$\pi^\pm$ events:
  $$\nu_\mu (\bar{\nu}_\mu) + \text{Ar} \to \mu^\pm + \pi^\pm + X$$
  where $X$ represents any number of nucleons. The definition includes events where the pion is produced via Final State Interactions (FSI) inside the nucleus, provided exactly one charged pion exits the nucleus.
• Phase Space: Measurements are restricted to:
  • Muon momentum ($p_\mu$) > 150 MeV.
  • Pion momentum ($p_\pi$) > 100 MeV.
  • Muon-pion opening angle ($\theta_{\mu\pi}$) < 2.65 rad (to exclude back-to-back topologies difficult to distinguish from cosmic rays).
• Event Selection & Reconstruction:
  • Reconstruction: Uses the Pandora pattern recognition software to identify tracks and showers.
  • Particle Identification (PID): Employs Boosted Decision Trees (BDTs) trained on simulated data to distinguish between muons, protons, and pions. Key features include calorimetric energy loss ($dE/dx$) ratios, track topology (wiggliness), and descendant particle counts.
  • Subsets for Momentum Measurement:
    • Muon Momentum: Uses only fully contained muon tracks to estimate momentum via range (stopping distance), providing high resolution ($\sigma \approx 0.08$).
    • Pion Momentum: Uses a subset of "unscattered" pions (those that do not undergo hadronic scattering before stopping) to estimate momentum via range. This is the first such measurement on argon.
• Background Estimation: The dominant background is CC events with zero pions where a proton is misidentified as a pion. An orthogonal sideband selection (1 muon + $\ge$1 protons + 0 other particles) is used to validate background modeling.
• Unfolding: Measured event rates are unfolded to "regularized truth space" using the Wiener-SVD technique to correct for detector resolution, efficiency, and bin migration. This allows direct comparison with theoretical generators.

3. Key Contributions

• First Argon Pion Momentum Spectrum: This paper presents the first measurement of the differential cross-section with respect to pion momentum on an argon target.
• High-Statistics Dataset: With 6,816 selected signal events (after background subtraction), this analysis offers a $\sim$25x increase in statistics compared to previous argon measurements (ArgoNeuT).
• Comprehensive Kinematic Coverage: Provides flux-integrated total cross-sections and single-differential cross-sections for:
  • Muon angle ($\cos \theta_\mu$)
  • Muon momentum ($p_\mu$)
  • Pion angle ($\cos \theta_\pi$)
  • Pion momentum ($p_\pi$)
  • Muon-pion opening angle ($\theta_{\mu\pi}$)
• Generator Benchmarking: Systematically compares data against a suite of modern neutrino event generators (GENIE, NuWro, NEUT, GiBUU) using the NUISANCE framework.

4. Results

• Total Cross Section:
  The flux-integrated total cross-section at a mean neutrino energy of $\approx 0.8$ GeV is measured as:
  $$\sigma = (3.75 \pm 0.07 \text{ (stat.)} \pm 0.80 \text{ (syst.)}) \times 10^{-38} \text{ cm}^2/\text{Ar}$$
• Generator Comparisons:
  • Overall Agreement: Most generators (GENIE, NuWro, NEUT, GiBUU 2025) show good overall agreement with the total cross-section and most kinematic distributions within uncertainties.
  • Forward Muon Angles: A significant discrepancy is observed at very forward muon angles (low momentum transfer, $Q^2$). Most generators overpredict the cross-section in this region. This aligns with previous findings from MiniBooNE and MINERvA, suggesting deficiencies in resonance production modeling at low $Q^2$.
  • Pion Momentum: The measured pion momentum spectrum is generally well-described by GENIE and NuWro. However, generators with FSI disabled show significant deviations, highlighting the importance of accurate FSI modeling.
  • GiBUU Performance: GiBUU 2025 performs best for total and muon kinematics but shows the worst agreement for pion variables. GiBUU 2023 systematically underpredicts pion production.
• Uncertainties: The dominant systematic uncertainties arise from the neutrino flux (14.1%), interaction models (12.6%), and detector response (9.1%).

5. Significance

• Impact on Oscillation Experiments: These results provide crucial constraints for tuning event generators used in next-generation experiments like DUNE and Hyper-Kamiokande, which rely heavily on argon targets. Reducing uncertainties in pion production modeling directly improves the precision of $\nu_e$ appearance measurements and CP violation searches.
• FSI Understanding: By isolating "unscattered" pions, the analysis provides a unique window into the initial interaction mechanisms, separating them from the complexities of hadronic re-interactions within the nucleus.
• Model Validation: The data confirms that while current models are broadly successful, they struggle with specific kinematic regimes (low $Q^2$ forward angles), guiding future theoretical developments in neutrino-nucleus interaction physics.
• Methodological Advance: The successful application of range-based momentum reconstruction for pions in LArTPCs sets a precedent for future analyses in liquid argon detectors.