Probing Nuclear Effects with Transverse Kinematic Imbalance in Muon-neutrino Induced Charged-Current $\pi^0$ Production on Argon with the MicroBooNE Detector

Technical Summary: Probing Nuclear Effects with Transverse Kinematic Imbalance in Muon-neutrino Induced Charged-Current $\pi^0$ Production on Argon

Problem Statement
Precision neutrino oscillation measurements in upcoming experiments, such as the Deep Underground Neutrino Experiment (DUNE), Hyper-Kamiokande, and the Short-Baseline Neutrino program, rely on the accurate reconstruction of incident neutrino energy from final-state particles. This reconstruction is contingent upon reliable modeling of neutrino–nucleus interactions. A significant source of systematic uncertainty arises from nuclear effects, particularly final-state interactions (FSI), which alter the momenta and multiplicities of particles emerging from the nucleus. In the 1–4 GeV energy range, resonant pion production (dominated by the $\Delta(1232)$ resonance) is a primary interaction channel. However, existing models struggle to simultaneously describe the complex interplay of resonance excitation, decay, and hadronic propagation through the nuclear medium. Specifically, neutral pion ($\pi^0$) production is a critical background for electron-neutrino appearance searches due to its decay into photons, which can mimic electron signatures. There is a need for high-statistics measurements on argon targets to constrain these models, as previous data on carbon (e.g., from MINERvA) may not fully capture argon-specific nuclear dynamics.

Methodology
The MicroBooNE collaboration presents a measurement of muon-neutrino charged-current (CC) interactions on argon resulting in a final state of one muon, one $\pi^0$, and at least one proton ($\nu_\mu$CCNp1$\pi^0$). The analysis utilizes the full MicroBooNE Booster Neutrino Beam (BNB) dataset, corresponding to $1.10 \times 10^{21}$ protons-on-target (POT).

Key methodological components include:

• Event Selection: Events are categorized as fully contained (FC) or partially contained (PC). Selection criteria require a reconstructed muon with kinetic energy $T_\mu > 40$ MeV, at least one proton with $T_p > 60$ MeV, and exactly one reconstructed $\pi^0$ (identified via $\gamma\gamma$ showers). Events with charged pions or heavy mesons above 40 MeV are rejected to suppress deep-inelastic scattering (DIS) backgrounds.
• Reconstruction: The analysis employs an updated Multiple Coulomb Scattering (MCS) algorithm for partially contained muons and refined charge-to-energy conversion for electromagnetic showers. The signal efficiency is 12.7% with a purity of 75.6%.
• Transverse Kinematic Imbalance (TKI): The study focuses on TKI variables, which characterize the momentum imbalance in the plane transverse to the neutrino beam direction. These variables ($\delta p_T$, $\delta \alpha_T$, $\delta p^x_T$, $\delta p^y_T$) are sensitive to nuclear effects such as Fermi motion and FSI. The leading hadronic momentum is defined as $\vec{p}_h = \vec{p}_{\pi^0} + \vec{p}_p$.
• Analysis Framework: Differential cross-sections are extracted using a blockwise unfolding approach (Wiener-SVD) to preserve correlations between observables. Systematic uncertainties from flux, interaction modeling, and detector response are propagated via covariance matrices.
• Model Validation: Goodness-of-fit (GoF) tests are performed in reconstructed space using conditional constraints derived from well-measured observables to enhance sensitivity to mismodeling.
• Simulation: Predictions are compared against several neutrino interaction generators: GENIE v3.0.6 (MicroBooNE tune G18T and DUNE baseline AR23), NuWro 25.11, NEUT v5.4.0.1, and GiBUU 2025. An updated reweighting procedure is applied to the GENIE simulation to correct for an overprediction of the pion charge-exchange (CEX) cross-section.

Key Contributions

• First Measurement on Argon with TKI: This work provides the first measurement of resonance-like $\nu_\mu$ interactions on argon using transverse kinematic imbalance variables.
• Comprehensive Kinematic Characterization: The paper reports ten single-differential cross-section measurements covering the kinematics of the muon, $\pi^0$, and leading proton, as well as the four TKI observables.
• Improved Signal Definition: By requiring at least one proton in the final state, the analysis increases the fraction of baryon-resonance interactions in the selected sample compared to previous inclusive $\pi^0$ measurements.
• Enhanced Statistics and Purity: The use of the full dataset and updated selection criteria yields significantly higher statistics and improved signal purity (75.6%) compared to prior MicroBooNE results.
• Systematic Treatment of FSI: The analysis incorporates a dedicated reweighting of the GENIE intranuclear hadron transport model to address discrepancies in pion charge-exchange rates.

Results

• Cross Section: The flux-integrated total cross-section is measured to be $1.62 \times 10^{-38}$ cm$^2$/Ar.
• Model Comparison:
  • Kinematic Distributions: The kinetic energy distributions of final-state particles are generally well-reproduced by the generators, with NEUT showing the best overall agreement for individual variables. However, significant shape discrepancies are observed in angular distributions. All generators overpredict forward-going muons (potentially linked to Pauli blocking modeling) and underpredict forward-going $\pi^0$s and protons.
  • TKI Observables: The data exhibit a narrower transverse momentum imbalance ($\delta p_T$) distribution than predicted by most generators, suggesting an overestimation of transverse momentum broadening in the models. Furthermore, the transverse opening angle ($\delta \alpha_T$) distribution shows that models underestimate the data at large angles (near 180$^\circ$), a region associated with the deceleration of the hadronic system due to FSI.
  • Global Agreement: No single generator achieves uniformly good agreement across all ten observables. When considering the full covariance matrix, GENIE (G18T) yields the best overall agreement, followed closely by NEUT. The GiBUU T2 inmed model shows substantial disagreement, particularly in $\pi^0$ observables.
• Comparison with MINERvA: While both measurements on argon and carbon show that models overpredict the width of the $\delta p^x_T$ distribution, the MicroBooNE data on argon reveal a stronger preference for the imbalance vector to be oriented opposite to the muon direction (large $\delta \alpha_T$) than observed in the MINERvA carbon data.

Significance
The paper claims that this measurement provides stringent constraints on models of resonance production and hadronic transport in nuclei. The results highlight that current interaction models lack the precision to simultaneously reproduce all measured kinematic and TKI observables. Specifically, the discrepancies in the TKI variables suggest deficiencies in the modeling of the correlation between the magnitude and direction of transverse momentum imbalance, pointing to unresolved issues in the description of hadronic re-scattering and nuclear effects. These findings are essential for reducing systematic uncertainties in future long-baseline neutrino oscillation experiments, particularly DUNE, where resonance production is a dominant interaction channel. The work constitutes a necessary step toward improved interaction modeling required for precision physics.