- Open Access
Efficient Monte Carlo event generation for neutrino-nucleus exclusive cross sections
Phys. Rev. D 111, 113001 – Published 6 June, 2025
DOI: https://doi.org/10.1103/v7sz-vn3b
Abstract
Modern neutrino-nucleus cross section computations need to incorporate sophisticated nuclear models to achieve greater predictive precision. However, the computational complexity of these advanced models often limits their practicality for experimental analyses. To address this challenge, we introduce a new Monte Carlo method utilizing normalizing flows to generate surrogate cross sections that closely approximate those of the original model while significantly reducing computational overhead. As a case study, we built a Monte Carlo event generator for the neutrino-nucleus cross section model developed by the Ghent group. This model employs a Hartree-Fock procedure to establish a quantum mechanical framework in which both the bound and scattering nucleon states are solutions to the mean-field nuclear potential. The surrogate cross sections generated by our method demonstrate excellent accuracy with a relative effective sample size of more than 98.4%, providing a computationally efficient alternative to traditional Monte Carlo sampling methods for differential cross sections.
Physics Subject Headings (PhySH)
Article Text
References (55)
- K. Abe et al. (T2K Collaboration), The T2K experiment, Nucl. Instrum. Methods Phys. Res., Sect. A 659, 106 (2011).
- H.-K. Proto-Collaboration, Hyper-kamiokande design report, arXiv:1805.04163.
- L. Alvarez-Ruso et al. (NuSTEC Collaboration), NuSTEC white paper: Status and challenges of neutrino–nucleus scattering, Prog. Part. Nucl. Phys. 100, 1 (2018).
- Y. Hayato, A neutrino interaction simulation program library NEUT, Acta Phys. Pol. B 40, 2477 (2009), https://inspirehep.net/literature/844435.
- C. Andreopoulos et al., The GENIE neutrino Monte Carlo generator, Nucl. Instrum. Methods Phys. Res., Sect. A 614, 87 (2010).
- T. Golan, C. Juszczak, and J. T. Sobczyk, Final state interactions effects in neutrino-nucleus interactions, Phys. Rev. C 86, 015505 (2012).
- J. Isaacson, W. I. Jay, A. Lovato, P. A. Machado, and N. Rocco, Introducing a novel event generator for electron-nucleus and neutrino-nucleus scattering, Phys. Rev. D 107, 033007 (2023).
- S. Dolan, G. Megias, and S. Bolognesi, Implementation of the susav2-meson exchange current 1p1h and 2p2h models in genie and analysis of nuclear effects in T2K measurements, Phys. Rev. D 101, 033003 (2020).
- A. Nikolakopoulos, S. Gardiner, A. Papadopoulou, S. Dolan, and R. González-Jiménez, From inclusive to semi-inclusive one-nucleon knockout in neutrino event generators, Phys. Sci. Forum. 8, 10 (2023).
- A. V. Butkevich and S. P. Mikheyev, Test of Fermi gas model and plane-wave impulse approximation against electron-nucleus scattering data, Phys. Rev. C 72, 025501 (2005).
- O. Benhar, A. Fabrocini, S. Fantoni, and I. Sick, Spectral function of finite nuclei and scattering of GeV electrons, Nucl. Phys. A579, 493 (1994).
- P. Ring, Relativistic mean field theory in finite nuclei, Prog. Part. Nucl. Phys. 37, 193 (1996).
- N. Jachowicz, K. Heyde, J. Ryckebusch, and S. Rombouts, Continuum random phase approximation approach to charged-current neutrino-nucleus scattering, Phys. Rev. C 65, 025501 (2002).
- J. McKean, R. González-Jiménez, M. Kabirnezhad, J. M. Udías, and Y. Uchida, Implementation of a relativistic distorted wave impulse approximation model into the neut event generator, arXiv:2502.10629.
- A. Nikolakopoulos, R. González-Jiménez, N. Jachowicz, K. Niewczas, F. Sánchez, and J. M. Udías, Benchmarking intranuclear cascade models for neutrino scattering with relativistic optical potentials, Phys. Rev. C 105, 054603 (2022).
- A. Nikolakopoulos, A. Ershova, R. González-Jiménez, J. Isaacson, A. M. Kelly, K. Niewczas, N. Rocco, and F. Sánchez, Final-state interactions in neutrino-induced proton knockout from argon in microboone, Phys. Rev. C 110, 054611 (2024).
- D. Douqa, S. Bordoni, L. Giannessi, F. Sánchez, C. Schloesser, and A. Nikolakopoulos, Superscaling variable and neutrino energy reconstruction from theoretical predictions to experimental limitations, Phys. Rev. D 109, 073001 (2024).
- R. González-Jiménez, M. B. Barbaro, J. A. Caballero, T. W. Donnelly, N. Jachowicz, G. D. Megias, K. Niewczas, A. Nikolakopoulos, J. W. Van Orden, and J. M. Udías, Neutrino energy reconstruction from semi-inclusive samples, Phys. Rev. C 105, 025502 (2022).
- S. Dolan, A. Nikolakopoulos, O. Page, S. Gardiner, N. Jachowicz, and V. Pandey, Implementation of the continuum random phase approximation model in the GENIE generator and an analysis of nuclear effects in low-energy transfer neutrino interactions, Phys. Rev. D 106, 073001 (2022).
- J. Schwehr, D. Cherdack, and R. Gran, GENIE implementation of IFIC valencia model for QE-like 2p2h neutrino-nucleus cross section, arXiv:1601.02038.
- H. Prasad, J. T. Sobczyk, A. M. Ankowski, J. L. Bonilla, R. D. Banerjee, K. M. Graczyk, and B. E. Kowal, New multinucleon knockout model in the NuWro Monte Carlo generator, Phys. Rev. D 111, 036032 (2025).
- T. Heimel, N. Huetsch, F. Maltoni, O. Mattelaer, T. Plehn, and R. Winterhalder, The madnis reloaded, SciPost Phys. 17, 023 (2024).
- K. M. Graczyk, B. E. Kowal, A. M. Ankowski, R. D. Banerjee, J. L. Bonilla, H. Prasad, and J. T. Sobczyk, Electron-nucleus cross sections from transfer learning, arXiv:2408.09936.
- B. et al., Machine learning and LHC event generation, SciPost Phys. 14, 079 (2023).
- J. L. Bonilla, K. M. Graczyk, A. M. Ankowski, R. D. Banerjee, B. E. Kowal, H. Prasad, and J. T. Sobczyk, Generative adversarial neural networks for simulating neutrino interactions, arXiv:2502.20244.
- D. J. Rezende and S. Mohamed, Variational inference with normalizing flows, arXiv:1505.05770.
- J. Ryckebusch, M. Vanderhaeghen, L. Machenil, and M. Waroquier, Effects of the final-state interaction in and processes, Nucl. Phys. A568, 828 (1994).
- V. Van der Sluys, J. Ryckebusch, and M. Waroquier, Two-body currents in inclusive electron scattering, Phys. Rev. C 51, 2664 (1995).
- D. Vautherin and D. M. Brink, Hartree-Fock calculations with Skyrme’s interaction. I. Spherical nuclei, Phys. Rev. C 5, 626 (1972).
- K. Heyde, The Nuclear Shell Model, Springer Series in Nuclear and Particle Physics (Springer, Berlin, Heidelberg, 2012).
- M. Waroquier, G. Wenes, and K. Heyde, An effective skyrme-type interaction for nuclear structure calculations: (II). Excited-state properties, Nucl. Phys. A404, 298 (1983).
- O. Moreno, T. W. Donnelly, J. W. Van Orden, and W. P. Ford, Semi-inclusive charged-current neutrino-nucleus reactions, Phys. Rev. D 90, 013014 (2014).
- J. E. Sobczyk, E. Hernández, S. X. Nakamura, J. Nieves, and T. Sato, Angular distributions in electroweak pion production off nucleons: Odd parity hadron terms, strong relative phases, and model dependence, Phys. Rev. D 98, 073001 (2018).
- K. Niewczas, A. Nikolakopoulos, J. T. Sobczyk, N. Jachowicz, and R. González-Jiménez, Angular distributions in Monte Carlo event generation of weak single-pion production, Phys. Rev. D 103, 053003 (2021).
- G. Peter Lepage, A new algorithm for adaptive multidimensional integration, J. Comput. Phys. 27, 192 (1978).
- C. Gao, S. Höche, J. Isaacson, C. Krause, and H. Schulz, Event generation with normalizing flows, Phys. Rev. D 101, 076002 (2020).
- C. Gao, J. Isaacson, and C. Krause, i- flow: High-dimensional integration and sampling with normalizing flows, Mach. Learn. 1, 045023 (2020).
- E. Bothmann, T. Janßen, M. Knobbe, T. Schmale, and S. Schumann, Exploring phase space with neural importance sampling, SciPost Phys. 8, 069 (2020).
- B. Stienen and R. Verheyen, Phase space sampling and inference from weighted events with autoregressive flows, SciPost Phys. 10, 038 (2021).
- T. Heimel, R. Winterhalder, A. Butter, J. Isaacson, C. Krause, F. Maltoni, O. Mattelaer, and T. Plehn, Madnis—neural multi-channel importance sampling, SciPost Phys. 15, 141 (2023).
- N. Deutschmann and N. Götz, Accelerating HEP simulations with neural importance sampling, J. High Energy Phys. 03 (2024) 083.
- A. Kofler, V. Stimper, M. Mikhasenko, M. Kagan, and L. Heinrich, Flow annealed importance sampling bootstrap meets differentiable particle physics, in Proceedings of the 38th Conference on Neural Information Processing Systems (2024), arXiv:2411.16234.
- D. P. Kingma, T. Salimans, R. Jozefowicz, X. Chen, I. Sutskever, and M. Welling, Improving variational inference with inverse autoregressive flow, arXiv:1606.04934.
- G. Papamakarios, T. Pavlakou, and I. Murray, Masked autoregressive flow for density estimation, in Advances in Neural Information Processing Systems (Curran Associates, Inc., 2017), Vol. 30, pp. 2338–2347, https://proceedings.neurips.cc/paper/2017/file/6c1da886822c67822bcf3679d04369fa-Paper.pdf.
- L. Dinh, D. Krueger, and Y. Bengio, Nice: Non-linear independent components estimation, arXiv:1410.8516.
- L. Dinh, J. Sohl-Dickstein, and S. Bengio, Density estimation using real NVP, arXiv:1605.08803.
- A. Coccaro, M. Letizia, H. Reyes-González, and R. Torre, Comparison of affine and rational quadratic spline coupling and autoregressive flows through robust statistical tests, Symmetry 16, 942 (2024).
- C. Durkan, A. Bekasov, I. Murray, and G. Papamakarios, Neural spline flows, in Advances in Neural Information Processing Systems (Curran Associates, Inc., 2019), Vol. 32, pp. 7511–7522, https://proceedings.neurips.cc/paper/2019/file/7ac71d433f282034e088473244df8c02-Paper.pdf.
- R. Delbourgo and J. A. Gregory, Piecewise rational quadratic interpolation to monotonic data, IMA J. Numer. Anal. 3, 141 (1983).
- S. Pina-Otey, F. Sánchez, T. Lux, and V. Gaitan, Exhaustive neural importance sampling applied to Monte Carlo event generation, Phys. Rev. D 102, 013003 (2020).
- M. El Baz and F. Sánchez, Fast posterior probability sampling with normalizing flows and its applicability in bayesian analysis in particle physics, Phys. Rev. D 109, 032008 (2024).
- D. J. Rezende, G. Papamakarios, S. Racanière, M. S. Albergo, G. Kanwar, P. E. Shanahan, and K. Cranmer, Normalizing flows on tori and spheres, arXiv:2002.02428.
- T. Müller, B. McWilliams, F. Rousselle, M. Gross, and J. Novák, Neural importance sampling, arXiv:1808.03856.
- K. Abe et al. (T2K Collaboration), Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with protons on target, Phys. Rev. D 91, 072010 (2015).
- A. Blondel et al., The superfgd prototype charged particle beam tests, J. Instrum. 15, P12003 (2020).