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Neural-Network Extraction of Unpolarized Transverse-Momentum-Dependent Distributions

Alessandro Bacchetta1,2,*, Valerio Bertone3,†, Chiara Bissolotti4,‡, Matteo Cerutti5,6,§, Marco Radici2,∥, Simone Rodini7,¶, and Lorenzo Rossi8,9,** (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration)

  • *Contact author: alessandro.bacchetta@unipv.it
  • †Contact author: valerio.bertone@cea.fr
  • ‡Contact author: cbissolotti@anl.gov
  • §Contact author: mcerutti@jlab.org
  • ∥Contact author: marco.radici@pv.infn.it
  • Contact author: simone.rodini@desy.de
  • **Contact author: lorenzo.rossi3@unimi.it
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Phys. Rev. Lett. 135, 021904 – Published 8 July, 2025

DOI: https://doi.org/10.1103/csc2-bj91

Abstract

We present the first extraction of transverse-momentum-dependent distributions of unpolarized quarks from experimental Drell-Yan data using neural networks to parametrize their nonperturbative part. We show that neural networks outperform traditional parametrizations providing a more accurate description of data. This Letter establishes the feasibility of using neural networks to explore the multidimensional partonic structure of hadrons and paves the way for more accurate determinations based on machine-learning techniques.

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References (49)

  1. A. Bacchetta, F. Delcarro, C. Pisano, M. Radici, and A. Signori, J. High Energy Phys. 06 (2017) 081; 06 (2019) 051(E).
  2. I. Scimemi and A. Vladimirov, Eur. Phys. J. C 78, 89 (2018).
  3. V. Bertone, I. Scimemi, and A. Vladimirov, J. High Energy Phys. 06 (2019) 028.
  4. I. Scimemi and A. Vladimirov, J. High Energy Phys. 06 (2020) 137.
  5. A. Bacchetta, V. Bertone, C. Bissolotti, G. Bozzi, F. Delcarro, F. Piacenza, and M. Radici, J. High Energy Phys. 07 (2020) 117.
  6. M. Bury, F. Hautmann, S. Leal-Gomez, I. Scimemi, A. Vladimirov, and P. Zurita, J. High Energy Phys. 10 (2022) 118.
  7. A. Bacchetta, V. Bertone, C. Bissolotti, G. Bozzi, M. Cerutti, F. Piacenza, M. Radici, and A. Signori (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), J. High Energy Phys. 10 (2022) 127.
  8. V. Moos, I. Scimemi, A. Vladimirov, and P. Zurita, J. High Energy Phys. 05 (2024) 036.
  9. A. Bacchetta, V. Bertone, C. Bissolotti, G. Bozzi, M. Cerutti, F. Delcarro, M. Radici, L. Rossi, and A. Signori (MAP Collaboration), J. High Energy Phys. 08 (2024) 232.
  10. M. Čuić, K. Kumerički, and A. Schäfer, Phys. Rev. Lett. 125, 232005 (2020).
  11. R. Abdul Khalek, V. Bertone, A. Khoudli, and E. R. Nocera (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), Phys. Lett. B 834, 137456 (2022).
  12. I. P. Fernando and D. Keller, Phys. Rev. D 108, 054007 (2023).
  13. V. Bertone, A. Chiefa, and E. R. Nocera (MAP Collaboration) Phys. Lett. B 865, 139497 (2025).
  14. R. D. Ball et al. (NNPDF Collabortaion), Eur. Phys. J. C 84, 659 (2024).
  15. J. Collins, Foundations of perturbative QCD, in Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology (Cambridge University Press, Cambridge, England, 2023) Vol. 32, ISBN [Amazon][WorldCat], [Amazon][WorldCat], [Amazon][WorldCat].
  16. M. Cerutti, L. Rossi, S. Venturini, A. Bacchetta, V. Bertone, C. Bissolotti, and M. Radici (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), Phys. Rev. D 107, 014014 (2023).
  17. S. Catani, M. L. Mangano, P. Nason, and L. Trentadue, Nucl. Phys. B478, 273 (1996).
  18. A. Kulesza, G. F. Sterman, and W. Vogelsang, Phys. Rev. D 66, 014011 (2002).
  19. E. Laenen, G. F. Sterman, and W. Vogelsang, Phys. Rev. Lett. 84, 4296 (2000).
  20. A. Kulesza, G. F. Sterman, and W. Vogelsang, Phys. Rev. D 69, 014012 (2004).
  21. S. Agarwal and K. Mierle (TCS Team), ceres solver, https://github.com/ceres-solver/ceres-solver (2023).
  22. R. Abdul Khalek and V. Bertone, arXiv:2005.07039.
  23. R. D. Ball et al. (NNPDF Collaboration), Eur. Phys. J. C 77, 663 (2017).
  24. R. D. Ball et al. (NNPDF Collaboration), Eur. Phys. J. C 82, 428 (2022).
  25. L. Del Debbio, S. Forte, J. I. Latorre, A. Piccione, and J. Rojo (NNPDF Collaboration), J. High Energy Phys. 03 (2007) 039.
  26. G. Moreno et al., Phys. Rev. D 43, 2815 (1991).
  27. A. S. Ito et al., Phys. Rev. D 23, 604 (1981).
  28. P. L. McGaughey et al. (E772 Collaboration), Phys. Rev. D 50, 3038 (1994); 60, 119903(E) (1999).
  29. T. Affolder et al. (CDF Collaboration), Phys. Rev. Lett. 84, 845 (2000).
  30. T. Aaltonen et al. (CDF Collaboration), Phys. Rev. D 86, 052010 (2012).
  31. B. Abbott et al. (D0 Collaboration), Phys. Rev. D 61, 032004 (2000).
  32. V. M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 100, 102002 (2008).
  33. V. M. Abazov et al. (D0 Collaboration), Phys. Lett. B 693, 522 (2010).
  34. S. Collaboration, Phys. Lett. B 854, 138715 (2024).
  35. R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 08 (2015) 039.
  36. R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 01 (2016) 155.
  37. R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 09 (2016) 136.
  38. S. Chatrchyan et al. (CMS Collaboration), Phys. Rev. D 85, 032002 (2012).
  39. V. Khachatryan et al. (CMS Collaboration), J. High Energy Phys. 02 (2017) 096.
  40. A. M. Sirunyan et al. (CMS Collaboration), J. High Energy Phys. 12 (2019) 061.
  41. G. Aad et al. (ATLAS Collaboration), J. High Energy Phys. 09 (2014) 145.
  42. G. Aad et al. (ATLAS Collaboration), Eur. Phys. J. C 76, 291 (2016).
  43. G. Aad et al. (ATLAS Collaboration), Eur. Phys. J. C 80, 616 (2020).
  44. S. Bailey, T. Cridge, L. A. Harland-Lang, A. D. Martin, and R. S. Thorne, Eur. Phys. J. C 81, 341 (2021).
  45. A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr, and G. Watt, Eur. Phys. J. C 75, 132 (2015).
  46. C. Aidala et al. (PHENIX Collaboration), Phys. Rev. D 99, 072003 (2019).
  47. TMD fits, https://mapcollaboration.github.io.
  48. See Supplemental Material at http://link.aps.org/supplemental/10.1103/csc2-bj91 for more details about the cross-checks and further analyses regarding the reliability and the stability of the framework.
  49. R. D. Ball et al. (NNPDF Collaboration), J. High Energy Phys. 04 (2015) 040.

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Phys. Rev. Lett. 135, 021904– Published 8 July, 2025
  • Received 14 February 2025
  • Revised 16 May 2025
  • Accepted 16 June 2025
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