Re-optimization of a deep neural network model for electron-carbon scattering using new experimental data

TL;DR

This work re-optimizes a data-driven DNN model for inclusive electron–carbon scattering by incorporating new Mainz 2024 and Gomez 1993 data within a bootstrap-ensemble framework, yielding a posterior cross-section model with quantified predictive uncertainties. The approach enhances agreement with new measurements and provides uncertainty maps for neutrino-relevant energies, highlighting regions where accuracies are typically 10–20% and where they exceed 100% (e.g., large-angle, high-$ heta$ domains). The methodology remains fully data-driven and transferable to other nuclei via transfer learning, while emphasizing the need for more electron-scattering data to reach few-percent precision for Hyper-Kamiokande and DUNE. The model is accessible (GitHub) and accompanied by detailed optimization settings, underscoring practical utility for neutrino cross-section studies and MC validation.

Abstract

We present an updated deep neural network model for inclusive electron-carbon scattering. Using the bootstrap model [Phys.Rev.C 110 (2024) 2, 025501] as a prior, we incorporate recent experimental data, as well as older measurements in the deep inelastic scattering region, to derive a re-optimized posterior model. We examine the impact of these new inputs on model predictions and associated uncertainties. Finally, we evaluate the resulting cross-section predictions in the kinematic range relevant to the Hyper-Kamiokande and DUNE experiments.

Figures (12)

• Figure 1: Kinematic domain covered by the previous and present analyses. The top and bottom panels show the data in the $(\omega,\theta)$ and $(\omega, Q^2)$ variables, respectively. New data used to update the cross-section model are enclosed within two ellipses. By $\theta$ and $\omega$, the scattering angle and transfer of energy are denoted, $Q^2=2E (E-\omega) (1-\cos\theta)$, where $E$ is the electron beam energy.
• Figure 2: Double-differential cross section $\frac{d^2 \sigma}{d\omega\, d\Omega}$ for inclusive electron scattering on carbon. The red line represents the posterior model predictions, with the associated $1\sigma$ uncertainty shown as a green shaded region. The blue dashed line denotes the prior model predictions Kowal:2023dcq, and the light blue area indicates their $1\sigma$ uncertainty. The red points correspond to the training dataset, while the green points indicate the test dataset. The data from Mihovilovic et al.Mihovilovic:2024ymj. In the top left corner, we specify the incoming electron energy $E$ and scattering angle $\theta$.
• Figure 3: Same as in Fig. \ref{['fig:Miho2024']} but for the data from: Gomez et al.Gomez:1993ri.
• Figure 4: Same as in Fig. \ref{['fig:Miho2024']} but for the data from: Barreau et al.Barreau:1983ht [Barr1983].
• Figure 5: Same as in Fig. \ref{['fig:Miho2024']} but for the data from: Barreau et al.Barreau:1983ht [Barr1983].