- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Collinear matching for leading power gluon transverse momentum distributions

Alessio Carmelo Alvaro1,2,*, Nanako Kato3,4,†, Barbara Pasquini1,2,‡, Cristian Pisano3,4,§, and Simone Rodini1,2,∥

  • *Contact author: alessiocarmelo.alvaro01@universitadipavia.it
  • †Contact author: nanako.kato@dsf.unica.it
  • ‡Contact author: barbara.pasquini@unipv.it
  • §Contact author: cristian.pisano@unica.it
  • ∥Contact author: simone.rodini@unipv.it
PDF

Phys. Rev. D 114, 054001 – Published 1 September, 2026

DOI: https://doi.org/10.1103/sw9j-sfmd

Abstract

We compute the tree-level and one-loop matching relations for leading power gluon transverse momentum dependent parton distribution functions. At tree level, working within the spinor formalism, we focus on twist-2 and twist-3 contributions, deriving the series of mass corrections for both T-even and T-odd distributions within the considered twist accuracy. At one-loop accuracy, we extend the parton-in-parton framework to include contributions beyond the leading term in the small-b expansion. Applying this methodology to the gluon sector, we obtain for the first time the Wandzura-Wilczek approximation for the gluon worm-gear T distribution. Furthermore, we develop a method to include the twist-2 contribution to the mass corrections in one-loop results and provide a closed-form expression for the mass series suitable for numerical implementations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (53)

  1. A. Bacchetta, V. Bertone, C. Bissolotti, G. Bozzi, M. Cerutti, F. Delcarro, M. Radici, L. Rossi, and A. Signori (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), J. High Energy Phys. 08 (2024) 232.
  2. A. Bacchetta, V. Bertone, C. Bissolotti, M. Cerutti, M. Radici, S. Rodini, and L. Rossi (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), Phys. Rev. Lett. 135, 021904 (2025).
  3. V. Moos, I. Scimemi, A. Vladimirov, and P. Zurita, J. High Energy Phys. 11 (2025) 134.
  4. P. C. Barry et al., arXiv:2510.13771.
  5. K. Yang, T. Liu, P. Sun, Y. Zhao, and B.-Q. Ma (Transverse Nucleon Tomography Collaboration), Phys. Rev. Lett. 134, 121902 (2025).
  6. A. Bacchetta, A. Bongallino, M. Cerutti, M. Radici, and L. Rossi (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), Phys. Rev. Lett. 134, 121901 (2025).
  7. R. Boussarie et al., arXiv:2304.03302.
  8. S. Rodini and A. Vladimirov, J. High Energy Phys. 08 (2022) 031; 12 (2022) 48.
  9. S. Rodini and A. Vladimirov, Phys. Rev. D 110, 034009 (2024).
  10. P. J. Mulders and J. Rodrigues, Phys. Rev. D 63, 094021 (2001).
  11. D. Boer, S. J. Brodsky, P. J. Mulders, and C. Pisano, Phys. Rev. Lett. 106, 132001 (2011).
  12. D. Boer and C. Pisano, Phys. Rev. D 86, 094007 (2012).
  13. J.-P. Lansberg, C. Pisano, F. Scarpa, and M. Schlegel, Phys. Lett. B 784, 217 (2018); 791, 420(E) (2019).
  14. D. Boer, W. J. den Dunnen, C. Pisano, M. Schlegel, and W. Vogelsang, Phys. Rev. Lett. 108, 032002 (2012).
  15. J.-W. Qiu, M. Schlegel, and W. Vogelsang, Phys. Rev. Lett. 107, 062001 (2011).
  16. N. Kato, L. Maxia, and C. Pisano, Phys. Rev. D 110, 034038 (2024).
  17. D. W. Sivers, Phys. Rev. D 41, 83 (1990).
  18. A. Accardi et al. (LHCspin Collaboration), arXiv:2504.16034.
  19. R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
  20. D. Boer, C. Lorcé, C. Pisano, and J. Zhou, Adv. High Energy Phys. 2015, 371396 (2015).
  21. R. Kishore, A. Mukherjee, and S. Rajesh, Phys. Rev. D 101, 054003 (2020).
  22. M. G. Echevarria, P. A. G. García, and I. Scimemi, arXiv:2603.00375.
  23. L. Zheng, E. C. Aschenauer, J. H. Lee, B.-W. Xiao, and Z.-B. Yin, Phys. Rev. D 98, 034011 (2018).
  24. M. A. Ebert, B. Mistlberger, and G. Vita, J. High Energy Phys. 09 (2020) 146.
  25. M.-x. Luo, T.-Z. Yang, H. X. Zhu, and Y. J. Zhu, J. High Energy Phys. 06 (2021) 115.
  26. Y. J. Zhu, J. High Energy Phys. 02 (2026) 115.
  27. Y. J. Zhu, J. High Energy Phys. 03 (2026) 191.
  28. Y. J. Zhu, J. High Energy Phys. 03 (2026) 093.
  29. F. Rein, S. Rodini, A. Schäfer, and A. Vladimirov, J. High Energy Phys. 01 (2023) 116.
  30. A. Vladimirov, J. High Energy Phys. 12 (2023) 008.
  31. S. Piloneta and A. Vladimirov, J. High Energy Phys. 03 (2026) 049.
  32. V. Moos and A. Vladimirov, J. High Energy Phys. 12 (2020) 145.
  33. S. Rodini, A. C. Alvaro, and B. Pasquini, Phys. Lett. B 845, 138163 (2023).
  34. C. J. Bomhof, P. J. Mulders, and F. Pijlman, Eur. Phys. J. C 47, 147 (2006).
  35. C. J. Bomhof and P. J. Mulders, Nucl. Phys. B795, 409 (2008).
  36. M. G. A. Buffing, A. Mukherjee, and P. J. Mulders, Phys. Rev. D 88, 054027 (2013).
  37. D. Kharzeev, Y. V. Kovchegov, and K. Tuchin, Phys. Rev. D 68, 094013 (2003).
  38. M. G. Echevarria, T. Kasemets, P. J. Mulders, and C. Pisano, J. High Energy Phys. 07 (2015) 158; 05 (2017) 73.
  39. R. F. del Castillo, M. G. Echevarria, Y. Makris, and I. Scimemi, J. High Energy Phys. 01 (2021) 088.
  40. D. Boer, S. Cotogno, T. van Daal, P. J. Mulders, A. Signori, and Y.-J. Zhou, J. High Energy Phys. 10 (2016) 013.
  41. C. Lorcé and B. Pasquini, J. High Energy Phys. 09 (2013) 138.
  42. I. Scimemi, A. Tarasov, and A. Vladimirov, J. High Energy Phys. 05 (2019) 125.
  43. H. K. Dreiner, H. E. Haber, and S. P. Martin, Phys. Rep. 494, 1 (2010).
  44. M. F. Sohnius, Phys. Rep. 128, 39 (1985).
  45. DLMF, NIST Digital Library of Mathematical Functions, edited by f. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, https://dlmf.nist.gov/ (Release 1.2.5 of 2025-12-15).
  46. A. Vladimirov, G. Portela, and S. Rodini, arXiv:2511.04294.
  47. J. Collins, Foundations of Perturbative QCD (Cambridge University Press, Cambridge, England, 2011), Vol. 32, ISBN [Amazon][WorldCat], [Amazon][WorldCat], [Amazon][WorldCat].
  48. V. Bertone, Eur. Phys. J. C 82, 941 (2022).
  49. V. Bertone, M. G. Echevarria, Ó. del Rio, and S. Rodini, J. High Energy Phys. 05 (2025) 183.
  50. V. Bertone, H. Dutrieux, C. Mezrag, J. M. Morgado, and H. Moutarde, Eur. Phys. J. C 82, 888 (2022).
  51. V. Bertone, R. F. del Castillo, M. G. Echevarria, Ó. del Río, and S. Rodini, Phys. Rev. D 109, 034023 (2024).
  52. D. Gutiérrez-Reyes, I. Scimemi, and A. A. Vladimirov, Phys. Lett. B 769, 84 (2017).
  53. V. A. Smirnov, Springer Tracts Mod. Phys. 211, 1 (2004).

Outline

Information

Phys. Rev. D 114, 054001– Published 1 September, 2026
  • Received 18 May 2026
  • Accepted 4 August 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation