Flux-integrated inclusive and pionless cross sections for charged-current neutrino scattering off ${}^{40}\text{Ar}$ at energies available in the MicroBooNE experiment

Technical Summary: Flux-Integrated Inclusive and Pionless Cross Sections for Charged-Current Neutrino Scattering off $^{40}$Ar

Problem Statement
Precise knowledge of neutrino-nucleus interaction cross sections at the percent level is critical for current and next-generation neutrino oscillation experiments (e.g., SBN, DUNE, Hyper-Kamiokande). While extensive data exists for carbon and oxygen, data for argon remains relatively scarce. Existing theoretical models and event generators have demonstrated an inability to describe experimental data with high accuracy, creating a need for detailed benchmarking. Specifically, there is a requirement to validate theoretical frameworks against flux-integrated inclusive and semi-inclusive (pionless) cross-section measurements for argon within the energy range of the Booster Neutrino Beam (BNB), where charged-current quasielastic (CCQE) and meson-exchange current (MEC) processes dominate.

Methodology
The authors calculate flux-integrated single- and double-differential cross sections for $\nu_\mu$ scattering off $^{40}$Ar using the Relativistic Distorted-Wave Impulse Approximation (RDWIA) combined with Two-Particle-Two-Hole (2p-2h) Meson-Exchange Currents (MEC).

• Theoretical Framework:
  • CCQE Channel: Modeled using RDWIA, which treats bound nucleon states via self-consistent solutions to the Dirac equation within an independent particle shell model (IPSM) based on a relativistic mean-field ($\sigma-\omega$) Lagrangian. Final-state interactions (FSI) are accounted for using a phenomenological relativistic optical potential (EDAD1 parametrization). Short-range nucleon-nucleon correlations are estimated to account for high-momentum components in the target.
  • MEC Channel: The 2p-2h contributions are calculated using the SuSA-MEC approach, incorporating precise parametrizations derived from exact MEC calculations. This includes one-pion exchange mechanisms (seagull, pion-in-flight, pion-pole, and delta-pole components).
  • Resonance and DIS: Contributions from resonance production (RES) and deep-inelastic scattering (DIS) are evaluated using the GENIE event generator (version 3.04.00) with the G18-10a model configuration.
  • Form Factors: The vector form factors utilize the MMD parametrization, while the axial form factor employs a dipole parameterization with an axial mass $M_A = 1.2$ GeV, a value previously determined from MiniBooNE data.
• Data Processing: Theoretical predictions are flux-integrated over the BNB spectrum and "smeared" using the unfolding matrix ($A_c$) derived from MicroBooNE data to facilitate direct comparison with experimental results.

Key Contributions

1. Validation of RDWIA+MEC for Argon: The study provides a comprehensive calculation of flux-integrated inclusive and pionless (CC0$\pi$) differential cross sections for argon, specifically tailored to the MicroBooNE experimental conditions.
2. Nuclear Effect Comparison: The paper performs a comparative analysis of differential cross sections as a function of muon kinetic energy for carbon (MiniBooNE) and argon (MicroBooNE), scaled to the number of target neutrons. This aims to isolate nuclear medium effects between the two nuclei.
3. Benchmarking: The work serves as a benchmark for refining neutrino event generators and theoretical models, addressing the discrepancy between existing models and high-precision data.

Results

• Inclusive Cross Sections: The calculated inclusive double-differential cross sections ($d^2\sigma/d\varepsilon_\mu d\cos\theta$) and single-differential cross sections ($d\sigma/d\varepsilon_\mu$ and $d\sigma/d\cos\theta$) show good agreement with MicroBooNE data within experimental uncertainties (which exceed 10%).
  • The CCQE contribution dominates, accounting for approximately 50% of the total cross section, with MEC contributing ~16%, RES ~26%, and DIS ~8%.
  • The CCQE fraction increases with muon energy, reaching ~65% above 1.2 GeV.
  • Minor discrepancies are noted: the model slightly overestimates data in the $0.8 < \cos\theta < 0.9$ range and underestimates it in the $0.9 < \cos\theta < 1.0$ range. A slight systematic underestimation is observed for muon energies $E_\mu > 0.8$ GeV.
• Pionless (CC0$\pi$) Cross Sections: For pionless scattering, the model predicts that CCQE-like interactions (CCQE + MEC) provide the dominant contribution. The calculated double-differential ($d^2\sigma/dp_\mu d\cos\theta$) and single-differential ($d\sigma/dp_\mu$ and $d\sigma/d\cos\theta$) cross sections generally agree with MicroBooNE data within the large experimental uncertainties (exceeding 15%).
• Carbon vs. Argon Comparison: When comparing pionless cross sections per neutron for carbon and argon, the theoretical difference is calculated to be approximately 6%, showing weak dependence on muon energy. However, the comparison of experimental data from MiniBooNE and MicroBooNE shows consistency within their respective uncertainties (which exceed 10%). Consequently, the current experimental precision is insufficient to quantitatively estimate the difference in nuclear effects between the two nuclei.

Significance and Claims
The paper claims that the RDWIA+MEC approach successfully describes the measured single- and double-differential cross sections for argon within experimental uncertainties. The authors emphasize that while the current data validates the model, the precision of existing measurements (uncertainties >10%) prevents a definitive quantitative extraction of nuclear effect differences between carbon and argon.

The authors conclude that for future experiments (such as those planned for the SAND detector at DUNE) to successfully study differences in nuclear effects between carbon and argon targets at energies below 2 GeV, it is crucial to measure differential cross sections with an accuracy better than 6%. This work underscores the necessity of high-precision measurements to refine multi-target cross-section models and minimize systematic uncertainties associated with nuclear medium effects in future neutrino oscillation analyses.