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Single pion production off free nucleons: Analysis of photon-, electron-, pion-, and neutrino-induced processes

M. Kabirnezhad*

  • *Contact author: minoo.kabirnezhad@physics.ox.ac.uk
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Phys. Rev. D 114, 053009 – Published 11 September, 2026

DOI: https://doi.org/10.1103/3rbk-gt2p

Abstract

I present a unified model for single pion production in photo-, electro-, and neutrino-nucleon interactions that is applicable across the broad kinematic range in the GeV regime relevant to accelerator-based neutrino experiments. The model incorporates vector and axial-vector transition form factors for excited nucleon states with masses up to 2 GeV, together with nonresonant background contributions, within a meson dominance framework that respects quantum chromodynamic constraints and preserves unitarity. This construction ensures the correct asymptotic behavior at large momentum transfer (Q2) while providing a consistent description of the resonance and transition regions. At very low Q2, the implementation of the conserved vector current and partially conserved axial current relations leads to reliable predictions and helps address challenges encountered in current neutrino data analyses. The unified framework enables a global analysis that combines the available electron, photon, pion, and neutrino scattering data. This comprehensive approach allows detailed studies of nucleon structure in the resonance region and provides important constraints on weak interaction form factors, where modern neutrino-nucleon data remain limited. By determining all model parameters simultaneously with their correlated uncertainties, the approach establishes a robust, data-driven foundation for precision neutrino interaction modeling in support of next-generation neutrino oscillation measurements.

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References (59)

  1. Artur M. Ankowski, Omar Benhar, and Makoto Sakuda, Improving the accuracy of neutrino energy reconstruction in charged-current quasielastic scattering off nuclear targets, Phys. Rev. D 91, 033005 (2015).
  2. G. D. Megias, J. E. Amaro, M. B. Barbaro, J. A. Caballero, and T. W. Donnelly, Inclusive electron scattering within the SuSAv2 meson-exchange current approach, Phys. Rev. D 94, 013012 (2016).
  3. R. González-Jiménez, A. Nikolakopoulos, N. Jachowicz, and J. M. Udías, Nuclear effects in electron-nucleus and neutrino-nucleus scattering within a relativistic quantum mechanical framework, Phys. Rev. C 100, 045501 (2019).
  4. R. González-Jiménez, M. B. Barbaro, J. A. Caballero, T. W. Donnelly, N. Jachowicz, G. D. Megias, K. Niewczas, A. Nikolakopoulos, and J. M. Udías, Constraints in modeling the quasielastic response in inclusive lepton-nucleus scattering, Phys. Rev. C 101, 015503 (2020).
  5. J. E. Sobczyk, B. Acharya, S. Bacca, and G. Hagen, Ab initio computation of the longitudinal response function in Ca40, Phys. Rev. Lett. 127, 072501 (2021).
  6. A. Nikolakopoulos, R. González-Jiménez, N. Jachowicz, and J. M. Udías, Assessing the theory-data tension in neutrino-induced charged pion production: The effect of final-state nucleon distortion, Phys. Rev. D 107, 053007 (2023).
  7. Alessandro Lovato, Alexis Nikolakopoulos, Noemi Rocco, and Noah Steinberg, Lepton–nucleus interactions within microscopic approaches, Universe 9, 367 (2023).
  8. Noemi Rocco, Satoshi X. Nakamura, T. S. H. Lee, and Alessandro Lovato, Electroweak pion-production on nuclei within the extended factorization scheme, Phys. Rev. C 100, 045503 (2019).
  9. 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, Phys. Rev. D 112, 032009 (2025).
  10. Stephen Dolan, Jake McKean, and Laura Munteanu, Characterising the role of final state interactions on neutrino energy estimation in the DUNE and Hyper-K era, arXiv:2605.28696.
  11. Stephen Dolan, Luke Pickering, Patrick Stowell, Callum Wilkinson, and Clarence Wret, CP-violation or nuclear excitation: Reviewing the role of neutrino interaction model uncertainties on accelerator-based neutrino oscillation measurements, arXiv:2605.28671.
  12. K. F. Muzakka et al., Compatibility of neutrino DIS data and its impact on nuclear parton distribution functions, Phys. Rev. D 106, 074004 (2022).
  13. Stephen L. Adler, Photoproduction, electroproduction and weak single pion production in the (3, 3) resonance region, Ann. Phys. (Amsterdam) 50, 189 (1968).
  14. Dieter Rein and Lalit M. Sehgal, Neutrino excitation of baryon resonances and single pion production, Ann. Phys. (Amsterdam) 133, 79 (1981).
  15. D. Rein, Angular distribution in neutrino induced single pion production processes, Z. Phys. C 35, 43 (1987).
  16. E. Hernandez, J. Nieves, and M. Valverde, Weak pion production off the nucleon, Phys. Rev. D 76, 033005 (2007).
  17. A. Mariano, C. Barbero, and G. Lopez Castro, Neutral current neutrino-nucleon scattering within a consistent isobar model and the Delta(1232) resonance-background interference, Nucl. Phys. A849, 218 (2011).
  18. S. X. Nakamura, H. Kamano, and T. Sato, Dynamical coupled-channels model for neutrino-induced meson productions in resonance region, Phys. Rev. D 92, 074024 (2015).
  19. M. Rafi Alam, M. Sajjad Athar, S. Chauhan, and S. K. Singh, Weak charged and neutral current induced one pion production off the nucleon, Int. J. Mod. Phys. E 25, 1650010 (2016).
  20. R. González-Jiménez, N. Jachowicz, K. Niewczas, J. Nys, V. Pandey, T. Van Cuyck, and N. Van Dessel, Electroweak single-pion production off the nucleon: From threshold to high invariant masses, Phys. Rev. D 95, 113007 (2017).
  21. De-Liang Yao, Luis Alvarez-Ruso, Astrid N. Hiller Blin, and M. J. Vicente Vacas, Weak pion production off the nucleon in covariant chiral perturbation theory, Phys. Rev. D 98, 076004 (2018).
  22. De-Liang Yao, Luis Alvarez-Ruso, and M. J. Vicente Vacas, Neutral-current weak pion production off the nucleon in covariant chiral perturbation theory, Phys. Lett. B 794, 109 (2019).
  23. Jan T. Sobczyk and Jakub Zmuda, Investigation of recent weak single-pion production data, Phys. Rev. C 91, 045501 (2015).
  24. Monireh Kabirnezhad, Single pion production in neutrino reactions, J. Phys. Conf. Ser. 888, 012122 (2017).
  25. Monireh Kabirnezhad, The status of neutrino interaction theory and its impact on future neutrino oscillation experiments, Proc. Sci. NOW2018 (2019) 033.
  26. Peter Lichard, Some implications of meson dominance in weak interactions, Phys. Rev. D 55, 5385 (1997).
  27. P. Stoler, Baryon form-factors at high Q**2 and the transition to perturbative QCD, Phys. Rep. 226, 103 (1993).
  28. Aaron S. Meyer, Minerba Betancourt, Richard Gran, and Richard J. Hill, Deuterium target data for precision neutrino-nucleus cross sections, Phys. Rev. D 93, 113015 (2016).
  29. Aaron S. Meyer, André Walker-Loud, and Callum Wilkinson, Status of Lattice QCD determination of nucleon form factors and their relevance for the Few-GeV neutrino program, Annu. Rev. Nucl. Part. Sci. 72, 205 (2022).
  30. Aaron S. Meyer, The nucleon axial form factor from averaging Lattice QCD results, arXiv:2601.02676.
  31. J. J. Sakurai, Theory of strong interactions, Ann. Phys. (N.Y.) 11, 1 (1960).
  32. Murray Gell-Mann and Fredrik Zachariasen, Form-factors and vector mesons, Phys. Rev. 124, 953 (1961).
  33. Cyril Adamuscin, Anna-Zuzana Dubnickova, Stanislav Dubnicka, Roman Pekarik, and Peter Weisenpacher, Asymptotic conditions for electromagnetic form factors of hadrons represented by VMD model, Eur. Phys. J. C 28, 115 (2003).
  34. M. Kabirnezhad, Single pion production in neutrino-nucleon Interactions, Phys. Rev. D 97, 013002 (2018).
  35. M. Kabirnezhad, Single pion production in electron-nucleon interactions, Phys. Rev. D 102, 053009 (2020).
  36. M. Kabirnezhad, Single-pion production in electron-proton interactions, Phys. Rev. C 107, 025502 (2023).
  37. Olga Lalakulich, Emmanuel A. Paschos, and Giorgi Piranishvili, Resonance production by neutrinos: The second resonance region, Phys. Rev. D 74, 014009 (2006).
  38. G. Vereshkov and N. Volchanskiy, Q2-evolution of nucleon-to-resonance transition form factors in QCD-inspired vector-meson-dominance model, Phys. Rev. D 76, 073007 (2007).
  39. M. Sajjad Athar, A. Fatima, and S. K. Singh, Neutrinos and their interactions with matter, Prog. Part. Nucl. Phys. 129, 104019 (2023).
  40. M. Sajjad Athar and Jorge G. Morfín, Neutrino(antineutrino)–nucleus interactions in the shallow- and deep-inelastic scattering regions, J. Phys. G 48, 034001 (2021).
  41. Pere Masjuan, Enrique Ruiz Arriola, and Wojciech Broniowski, Meson dominance of hadron form factors and large-Nc phenomenology, Phys. Rev. D 87, 014005 (2013).
  42. J. E. Amaro and E. Ruiz Arriola, Axial-vector dominance predictions in quasielastic neutrino-nucleus scattering, Phys. Rev. D 93, 053002 (2016).
  43. M. Guidal, J. M. Laget, and M. Vanderhaeghen, Pion and kaon photoproduction at high-energies: Forward and intermediate angles, Nucl. Phys. A627, 645 (1997).
  44. G. Vereshkov and O. Lalakulich, Logarithmic corrections and soft photon phenomenology in the multipole model of the nucleon form-factors, Eur. Phys. J. A 34, 223 (2007).
  45. Y. Tian et al., Exclusive π− electroproduction off the neutron in deuterium in the resonance region, Phys. Rev. C 107, 015201 (2023).
  46. Ron L. Workman, Mark W. Paris, William J. Briscoe, and Igor I. Strakovsky, Unified Chew-Mandelstam SAID analysis of pion photoproduction data, Phys. Rev. C 86, 015202 (2012).
  47. https://clasweb.jlab.org/wiki/index.php/CLAS_Single_Meson_Electroproduction_Data_Sets?utm_source=chatgpt.com.
  48. Yoshinari Hayato and Luke Pickering, The NEUT neutrino interaction simulation program library, Eur. Phys. J. Special Topics 230, 4469 (2021).
  49. D. Drechsel, S. S. Kamalov, and L. Tiator, Unitary Isobar model-MAID2007, Eur. Phys. J. A 34, 69 (2007).
  50. H. Egiyan et al., Single π+ electroproduction on the proton in the first and second resonance regions at 0.25 GeV2<Q2<0.65 GeV2 using CLAS, Phys. Rev. C 73, 025204 (2006).
  51. K. Park et al., Cross sections and beam asymmetries for e⃗p→e′nπ+ in the nucleon resonance region for 1.7≤Q2≤4.5 GeV2, Phys. Rev. C 77, 015208 (2008).
  52. M. Ungaro et al., Measurement of the N→Δ+(1232) transition at high-momentum transfer by π0 electroproduction, Phys. Rev. Lett. 97, 112003 (2006).
  53. G. M. Radecky et al., Study of single pion production by weak charged currents in low-energy neutrino d interactions, Phys. Rev. D 25, 1161 (1982); 26, 3297(E) (1982).
  54. P. Allen et al., Single π+ production in charged current neutrino—hydrogen interactions, Nucl. Phys. B176, 269 (1980).
  55. G. T. Jones et al., Experimental test of the PCAC hypothesis in the reactions νμp→μ−pπ+ and ν¯μp→μ+pπ− in the Δ(1232) region, Z. Phys. C 43, 527 (1989).
  56. M. Derrick et al., Study of the reaction νn→νpπ−, Phys. Lett. B 92, 363 (1980); 95, 461(E) (1980).
  57. W. Krenz et al., Experimental study of exclusive one pion production in all neutrino induced neutral current channels, Nucl. Phys. B135, 45 (1978).
  58. H. Faissner et al., Observation of neutrino and anti-neutrino induced coherent neutral pion production off Al27, Phys. Lett. 125B, 230 (1983).
  59. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).

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Phys. Rev. D 114, 053009– Published 11 September, 2026
  • Received 2 April 2026
  • Accepted 18 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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