High Statistics Measurements of $\nu_{\mu}$ Charged-Current Single $\pi^{+}$ Production with Zero Pion Kinetic Energy Threshold in MINERvA

This MINERvA paper presents high-statistics measurements of $\nu_{\mu}$ charged-current single $\pi^{+}$ production cross sections down to zero pion kinetic energy, revealing significant discrepancies of up to 20% between the data and current neutrino event generator models across key kinematic regions.

The Gist

Imagine you are trying to understand how a specific type of billiard ball (a neutrino) behaves when it smashes into a table made of dense, sticky felt (an atomic nucleus). When the neutrino hits, it doesn't just bounce off; it sometimes knocks a smaller ball (a pion) out of the felt. Scientists need to know exactly how hard that small ball flies off and in what direction to understand the rules of the game.

This paper is a report from the MINERvA collaboration, a team of scientists at Fermilab, who have been watching these collisions happen. Here is the breakdown of what they did and found, using simple analogies.

The Big Problem: The "Invisible" Balls

For a long time, scientists had a blind spot. When the neutrino hit the nucleus, it would sometimes knock out a pion that was moving very slowly.

• The Old Way: Previous experiments were like security cameras that only recorded people running. If a pion was moving slowly (like a person walking), the camera didn't see it, or it couldn't measure how fast it was going. This meant scientists were missing a huge chunk of the data, specifically the "slow walkers" with almost zero energy.
• The New Trick: This paper introduces a clever new method. Instead of trying to track the slow pion directly, the scientists waited to see what happened after the pion stopped. A stopped pion eventually decays into a "Michel electron" (a tiny burst of energy). It's like waiting for a slow-moving car to park and then looking for the driver getting out. By spotting the driver (the electron), they could figure out exactly where the car (the pion) had been and how fast it was going, even if the car itself was too slow to see clearly.

The Experiment: A High-Speed Photo Shoot

The team used a massive detector called MINERvA, which is essentially a giant, high-tech sandwich made of plastic scintillator (a material that glows when hit by particles).

• The Beam: They fired a beam of neutrinos at this detector.
• The Count: They collected data from over 91,000 events where a neutrino hit a nucleus and knocked out exactly one positive pion.
• The Range: Thanks to their new "driver-spotting" trick, they could measure pions with kinetic energy ranging from 0 MeV (completely stopped) up to 350 MeV. This is the first time anyone has measured this process starting all the way down from zero.

The Results: The Models Are Missing the Mark

The scientists compared their real-world photos with the "simulations" (computer models) that physicists use to predict what should happen. Think of these models as weather forecasts for the subatomic world.

• The Good News: The models were actually pretty good at predicting the extremes. They could guess correctly how the pions behaved when they were moving very fast or when they were barely moving at all.
• The Bad News: In the middle of the road—the most common scenarios—the models were off.
  • For the muons (the other particle created in the crash), the models were off by about 15%.
  • For the pions themselves, the models were off by up to 20%.

It's like a weather forecast that correctly predicts a heatwave and a blizzard, but completely misses the mild, rainy days that happen 80% of the time.

Why This Matters (According to the Paper)

The paper states that these computer models are currently used by massive future experiments (like DUNE and Hyper-K) to figure out the secrets of the universe, such as why the universe is made of matter instead of antimatter.

If the "weather forecast" (the model) is wrong for the most common days (the main phase space), then the future experiments might get the wrong answer. The paper concludes that while some models are better than others, no single model currently exists that can accurately predict all the variables observed in this experiment.

The Takeaway

The MINERvA team has taken a giant step forward by learning how to "see" the slowest, hardest-to-detect particles using a clever indirect method. They have provided a massive new dataset that acts as a strict teacher for the computer models, showing them exactly where they are wrong so they can be fixed before the next generation of neutrino experiments begins.

Technical Summary

Technical Summary: High Statistics Measurements of $\nu_\mu$ Charged-Current Single $\pi^+$ Production with Zero Pion Kinetic Energy Threshold in MINERvA

Problem and Motivation
Accurate modeling of neutrino-nucleus interactions is a prerequisite for extracting oscillation parameters from current and future long-baseline experiments such as NOvA, T2K, HyperK, and DUNE. Pion production via resonances dominates the charged-current (CC) interaction cross-section in the energy range of $E_\nu \sim 1.5\text{--}4.5$ GeV. However, existing models struggle to account for the complex nuclear environment and final state interactions (FSI) with sufficient precision. Previous measurements by the MINERvA collaboration of $\nu_\mu$ CC single $\pi^+$ production were limited by a pion kinetic energy ($T_\pi$) threshold, leaving the low-energy region ($T_\pi \to 0$) largely unexplored. This paper addresses the need for precise, high-statistics data across the full kinematic phase space, particularly at low pion energies, to validate and tune neutrino event generators.

Methodology
The analysis utilizes $1.06 \times 10^{21}$ protons on target (POT) from the NuMI "Medium Energy" beam at Fermilab, incident on the MINERvA detector. The signal is defined as a $\nu_\mu$ CC interaction producing a single $\mu^-$, a single $\pi^+$, and any number of baryons, with no other mesons, and an experimental invariant mass $W_{\text{exp}} < 1.4$ GeV/$c^2$ to isolate the $\Delta(1232)$ resonance region.

The primary methodological advancement is the implementation of a "Michel-only" reconstruction technique for pions. While traditional tracking reconstructs pion kinematics from the pion track itself, this new method identifies pions solely via their decay chain ($\pi^+ \to \mu^+ \to e^+$), specifically looking for the Michel electron signature. This allows for the reconstruction of pion kinetic energies down to 0 MeV, a region previously inaccessible due to track length limitations.

• Event Selection: Events are categorized into "Tracked" (pion track reconstructed), "Untracked" (identified only via Michel electron), and "Overlap."
• Kinematics: For untracked pions, kinetic energy is derived from the fitted correlation between the "Pion Range" (distance from interaction vertex to Michel electron) and $T_\pi$. The pion angle is defined by the vector from the vertex to the Michel electron candidate.
• Background and Unfolding: A sideband region ($W_{\text{exp}} > 1.5$ GeV/$c^2$) is used to constrain background models. Iterative D'Agostini unfolding corrects for detector resolution and smearing.
• Simulation: The analysis employs the GENIE 2.12.6 base model modified by the MINERvA-specific tune, MnvTune v4.7.1. This tune incorporates empirical weights derived from the data itself to correct discrepancies in $T_\pi$ and $Q^2$ observed relative to the previous v4.3.1 tune.

Key Contributions

1. Zero-Energy Threshold: The paper presents the first measurement of $\nu_\mu$ CC single $\pi^+$ production with a kinetic energy threshold of $T_\pi \sim 0$, extending the measured phase space significantly compared to previous MINERvA results.
2. High Statistics: By combining tracked and untracked reconstruction methods, the analysis selected 91,843 events, substantially reducing statistical uncertainties and nearly doubling the reconstruction efficiency (from 6% to 11%) across the $T_\pi$ spectrum.
3. Differential Cross Sections: The authors provide differential cross-section measurements as a function of pion kinetic energy ($T_\pi$), pion angle ($\theta_\pi$), muon momentum ($p_\mu$), muon longitudinal momentum ($p_{||\mu}$), muon transverse momentum ($p_{T\mu}$), muon angle ($\theta_\mu$), and momentum transfer squared ($Q^2$).
4. Model Tuning: The development of MnvTune v4.7.1, which specifically addresses discrepancies in low-$T_\pi$ and $Q^2$ regions, is a direct outcome of this dataset.

Results
The measured differential cross sections were compared against several neutrino event generators, including GENIE (v2.12.6, v3 hA, v3 hN), GiBUU, NEUT, and NuWro.

• Overall Agreement: No single model accurately describes all variables across the entire phase space.
• Pion Observables: Models generally agree with data at the extremes of the kinematic regions (very low and very high $T_\pi$) but show significant discrepancies (up to 20%) in the main phase space regions.
• Muon Observables: Models tend to agree better with muon variables than pion variables, likely due to the greater availability of prior data used to inform muon modeling.
• $Q^2$ Dependence: While $Q^2$ is the variable best described by all models, all generators strongly underpredict the data at high $Q^2$.
• Specific Model Performance: GENIE v3 hN showed the best overall agreement with the data, though it still failed to capture the full range of kinematics. NEUT 5.4.1 and NuWro 19.02 performed significantly better than GENIE and GiBUU in describing the pion angle ($\theta_\pi$).

Significance
The paper claims that these results supersede previous MINERvA CC $1\pi^+$ measurements for comparisons with Carbon-Hydrogen (CH) targets, providing a more complete dataset that includes the previously unmeasured low-energy pion region. The authors emphasize that while some generators perform better than others, the persistent discrepancies highlight specific areas where model development is required. These data are intended to inform the next generation of neutrino oscillation experiments, ensuring that the systematic uncertainties associated with interaction modeling are reduced. The paper modestly concludes that the results "highlight model areas that require improvement" rather than claiming a definitive solution to the modeling challenges, noting that the new results and signal definition are now the benchmark for CH interactions.