Improving Neutrino-Nuclei Interaction Models: Recommendations and Case Studies on Peelle's Pertinent Puzzle

TL;DR

This paper tackles Peelle’s Pertinent Puzzle (PPP) in neutrino–nuclei cross-section modeling, a barrier to high-precision oscillation measurements. It develops a covariance-matrix framework to fit model predictions to cross-section data, enabling conditional predictions and efficient, high-dimensional parameter fitting while enforcing physical boundaries. Through case studies with MicroBooNE and T2K data across GENIE and NEUT, the work identifies PPP drivers—unaccounted regularization, real vs nominal flux mismatches, and limited model coverage—and demonstrates practical mitigation via covariance simplification, nonlinear norm-shape transformations, and Quantile Mapping. The authors advocate routine model-fitting exercises in cross-section publications and provide a workflow (including QM, NUISANCE, and the conditional-constrained approach) to achieve robust, data-driven tuning of neutrino–nuclei interaction models, ultimately improving the reliability of predictions for future experiments.

Abstract

Improving the modeling of neutrino-nuclei interactions using data-driven methods is crucial for high-precision neutrino oscillation experiments. This paper investigates Peelle's Pertinent Puzzle (PPP) in the context of neutrino measurements, a longstanding challenge to fitting theoretical models to experimental data. Inconsistencies in data-model comparisons hinder efforts to enhance the accuracy and reliability of model predictions. We analyze various sources contributing to these inconsistencies and propose strategies to address them, supported by practical case studies. We advocate for incorporating model fitting exercises as a standard practice in cross section publications to enhance the robustness of results. We use a common analysis framework to explore PPP-related challenges with MicroBooNE and T2K data in an unified manner. Our findings offer valuable insights for improving the accuracy and reliability of neutrino-nuclei interaction models, particularly by systematically tuning models using data.

Figures (17)

• Figure 1: Illustration of PPP with a simple two-dimensional measurement. Data preference is represented by the color contour, model preference is represented by the black line, and the model best-fit point is represented by the magenta star. Scenarios of data-model agreement and data-model mismatch are shown on the left and right, respectively.
• Figure 2: Comparison of data correlations for the original two-bin data measurement (left) and those after the non-linear norm-shape transformation (right).
• Figure 3: Comparison of the measured MicroBooNE $d\sigma/dE_{\mu}$ cross section data (black) to the nominal GENIE model prediction with the regularization matrix applied (blue), and the fit result with the regularization matrix applied (red).
• Figure 4: Comparison of the measured MicroBooNE $d\sigma/dE_{\mu}$ cross section data (black) to the nominal GENIE model prediction without applying the regularization matrix (blue), and the fit result without applying the regularization matrix (red).
• Figure 5: Comparison of the measured MicroBooNE $d^{2}\sigma/dE_{\mu}d\cos\theta_{\mu}$ cross section data (black) to the nominal GENIE model prediction with the regularization matrix applied (blue), and the fit result with the regularization matrix applied (red). The x-axis represents the bin index.