First double-differential cross-section measurements in proton multiplicity and kinematics for mesonless $\nu_{\mu}$ charged-current interactions on argon using the MicroBooNE detector

Technical Summary: First Double-Differential Cross-Section Measurements in Proton Multiplicity and Kinematics for Mesonless $\nu_\mu$ Charged-Current Interactions on Argon

Problem Statement
Accurate modeling of neutrino-argon interactions is a critical systematic uncertainty for current and future accelerator-based neutrino experiments, specifically the Deep Underground Neutrino Experiment (DUNE) and the Short-Baseline Neutrino (SBN) program. These experiments rely on Liquid Argon Time Projection Chambers (LArTPCs) to reconstruct neutrino interaction final states. A significant challenge lies in predicting the hadronic system, particularly the number (multiplicity) and kinematics of final-state protons. The specific channel of charged-current muon neutrino scattering producing no mesons and one or more protons (denoted as CC0$\pi N_p$) is the dominant topology at neutrino energies below 1 GeV and remains relevant at higher energies. Previous measurements on argon have shown tensions between data and event generator predictions, particularly regarding correlations between kinematic distributions, but lacked the granularity to distinguish between different proton multiplicities or fully explore the role of final-state interactions (FSI) and multi-nucleon processes.

Methodology
This analysis utilizes the full dataset collected by the MicroBooNE detector at Fermi National Accelerator Laboratory (Fermilab) from the Booster Neutrino Beam (BNB), corresponding to an exposure of $1.30 \times 10^{21}$ protons on target (POT). The detector is a surface LArTPC with an active mass of 85 metric tons, situated 463 m downstream of the target.

The analysis targets CC0$\pi N_p$ events where the final state contains one or more protons and no mesons. The signal definition requires a primary muon with momentum $>0.10$ GeV/c and at least one proton with momentum in the range $[0.25, 1.00]$ GeV/c. Subleading protons are considered detectable if their momentum exceeds 0.25 GeV/c.

Key methodological components include:

• Event Selection: The analysis employs the Pandora multi-algorithm pattern-recognition toolkit for reconstruction. Unlike previous MicroBooNE CC0$\pi N_p$ analyses, this work relaxes muon containment and quality cuts to increase selection efficiency (achieving 39.3% compared to 12.3% in prior work), focusing instead on proton multiplicity and kinematics.
• Observables: The study measures double-differential cross-sections as a function of:
  • Proton multiplicity ($N_p$).
  • Momenta of the leading ($p_{p1}$) through fourth-leading ($p_{p4}$) protons.
  • Muon-proton opening angles ($\cos \theta_{\mu p_i}$) for the first four protons.
  • Total available kinetic energy of the hadronic system ($E_{avail}$).
• Unfolding and Correlations: To recover the true kinematic distributions from reconstructed data, the analysis uses an iterative Bayesian unfolding method (D'Agostini). A blockwise approach is adopted, grouping bins representing the same kinematic distribution into 11 distinct blocks. This allows for the simultaneous reporting of all distributions while preserving the full cross-block correlations via a covariance matrix.
• Uncertainty Estimation: Systematic uncertainties are evaluated using a multi-universe approach, varying simulation parameters for flux prediction, neutrino-nucleus interaction modeling (including reweighting to NuWro to span model differences), hadron reinteraction, and detector response. Statistical uncertainties account for event sharing across multiple distributions.

Key Contributions

• First Measurement of Multiplicity-Dependent Kinematics: This paper presents the first double-differential cross-section measurements of CC0$\pi N_p$ interactions on argon as a function of proton multiplicity and the kinematics of leading and subleading protons.
• Comprehensive Generator Comparison: The unfolded cross-sections are compared against predictions from several widely used event generators: GENIE (MicroBooNE tune and AR23 configurations with various FSI models), NuWro (with and without fine-tuned FSI), NEUT, and GiBUU (with and without in-medium corrections).
• Data Release: The analysis provides a comprehensive data release including measured cross-sections per bin, total uncertainties, generator predictions, and the full covariance matrices describing correlated uncertainties across the 183 bins.

Results
The comparison between data and generator predictions reveals significant discrepancies, highlighting the sensitivity of these observables to the modeling of final-state interactions:

• Global Agreement: No single generator provides a fully adequate description of the entire dataset. The best global agreement is achieved by GiBUU 2025 with in-medium corrections to the nucleon-nucleon cross sections ($\chi^2/ndof = 428.8/145$), followed by the default GiBUU and the GENIE AR23 hA configuration.
• FSI Sensitivity: The results demonstrate strong sensitivity to FSI modeling. Variations in FSI models within the GENIE AR23 configuration yield a wide range of $\chi^2$ values (from 488.1 to 1200.6), indicating that the treatment of the nuclear cascade is a leading driver of data-model discrepancies.
• Specific Discrepancies:
  • Proton Multiplicity: Significant disagreements are observed in proton multiplicity distributions, particularly for backward opening angles and subleading proton kinematics.
  • Leading Proton Opening Angle: Most generators underpredict the cross-section for single-proton events ($N_p=1$) at backward angles ($\cos \theta_{\mu p_1} < 0$).
  • Generator Specifics: NEUT systematically overpredicts multi-proton events ($N_p \ge 2$) relative to single-proton events and overestimates high-energy hadronic systems. NuWro tends to underpredict the cross-section at low momenta. The AR23 INCL configuration systematically underpredicts the overall proton yield.
  • Subleading Protons: While the leading proton distributions show strong model dependence, the angular distributions of subleading protons (2nd, 3rd, 4th) are generally well-reproduced by all generators, suggesting that the isotropy of these particles is a generic feature of intranuclear rescattering less sensitive to specific cascade models.

Significance
The paper claims that these measurements provide a unique benchmark for testing and refining the modeling of final-state interactions and multi-nucleon processes in neutrino event generators. The results directly address the modeling needs of the DUNE and SBN physics programs, which rely on accurate reconstruction of hadronic systems for neutrino energy estimation and event classification. The authors conclude that while the BUU transport framework (used in GiBUU) currently offers the most complete description, significant modeling deficiencies remain, particularly in the treatment of single-proton final states at wide opening angles and the strength of the nuclear cascade. The comprehensive data release is intended to enable the generator community to use these results for tuning and validation.