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Rapidity-dependent spin decomposition of the nucleon

Florian Hechenberger1,*, Kiminad A. Mamo2,3,†, and Ismail Zahed1,‡

  • *Contact author: florian.hechenberger@stonybrook.edu
  • †Contact author: kamamo@wm.edu, kamamo@jlab.org
  • ‡Contact author: ismail.zahed@stonybrook.edu
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Phys. Rev. D 113, 034027 – Published 23 February, 2026

DOI: https://doi.org/10.1103/4rqm-dxz2

Abstract

We revisit the two-dimensional Fourier transform of generalized parton distributions (GPDs) at nonzero skewness. At η=0 it reduces to the standard impact-parameter density, while at η≠0 it is an off-forward amplitude that we interpret as a genuine parton–nucleon correlation. Its overall strength (the transverse-plane integral of the density) is fixed by the GPD at the kinematic point t=−cη=−4η2mN2/(1−η2) and decreases monotonically with the rapidity gap Δy=ln[(1+η)/(1−η)]=2 artanh(η). This rapidity dependence implies rapidity-modified Ji identities that connect helicity, orbital, and total angular momenta of the correlation in closed form. To quantify these effects, we construct leading-twist quark and gluon GPDs in a string-based conformal framework: conformal moments are parametrized by linear open- and closed-string Regge trajectories with slopes constrained by parton distribution functions (PDFs), hadron/glueball spectroscopy, and form-factor data, and GPDs are reconstructed over the full (x,η,t) domain by Mellin-Barnes inversion with next-to-leading order evolution. We find qualitative agreement (and fair quantitative agreement within quoted uncertainties) for several moments and selected nonsinglet x-space channels at μ=2  GeV when compared with lattice QCD, while we also identify channels with visible tension and discuss likely sources (PDF priors and t-slope systematics).

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References (38)

  1. D. Müller, D. Robaschik, B. Geyer, F. M. Dittes, and J. Hořejši, Fortschr. Phys. 42, 101 (1994).
  2. X.-D. Ji, Phys. Rev. Lett. 78, 610 (1997).
  3. A. V. Radyushkin, Phys. Lett. B 380, 417 (1996).
  4. A. V. Radyushkin, Phys. Rev. D 56, 5524 (1997).
  5. X.-D. Ji and J. Osborne, Phys. Rev. D 58, 094018 (1998).
  6. M. Diehl, Phys. Rep. 388, 41 (2003).
  7. A. V. Belitsky and A. V. Radyushkin, Phys. Rep. 418, 1 (2005).
  8. A. Accardi et al., Eur. Phys. J. A 52, 268 (2016).
  9. A. Accardi et al., Eur. Phys. J. A 60, 173 (2024).
  10. D. E. Soper, Phys. Rev. D 15, 1141 (1977).
  11. M. Burkardt, Int. J. Mod. Phys. A 18, 173 (2003).
  12. M. Diehl, Eur. Phys. J. C 25, 223 (2002); 31, 277(E) (2003).
  13. K. A. Mamo and I. Zahed, Phys. Rev. Lett. 133, 241901 (2024).
  14. K. A. Mamo and I. Zahed, Phys. Rev. D 110, 114016 (2024).
  15. F. Hechenberger, K. A. Mamo, and I. Zahed, Phys. Rev. D 112, 074018 (2025).
  16. R. C. Brower, J. Polchinski, M. J. Strassler, and C.-I. Tan, J. High Energy Phys. 12 (2007) 005.
  17. R. C. Brower, M. Djuric, and C.-I. Tan, J. High Energy Phys. 07 (2009) 063.
  18. X.-D. Ji, W. Melnitchouk, and X. Song, Phys. Rev. D 56, 5511 (1997).
  19. K. Kumericki, S. Liuti, and H. Moutarde, Eur. Phys. J. A 52, 157 (2016).
  20. D. Mueller and A. Schafer, Nucl. Phys. B739, 1 (2006).
  21. A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, Eur. Phys. J. C 63, 189 (2009).
  22. M. Hirai, S. Kumano, and N. Saito, Phys. Rev. D 74, 014015 (2006).
  23. R. Nishio and T. Watari, Phys. Rev. D 90, 125001 (2014).
  24. K. Kumericki, D. Mueller, and K. Passek-Kumericki, Nucl. Phys. B794, 244 (2008).
  25. C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, A. Scapellato, and F. Steffens, Phys. Rev. Lett. 125, 262001 (2020).
  26. J. Holligan and H.-W. Lin, Phys. Rev. D 110, 034503 (2024).
  27. C. Lorcé, Phys. Lett. B 735, 344 (2014).
  28. C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen, G. Koutsou, H. Panagopoulos, and G. Spanoudes, Phys. Rev. D 101, 094513 (2020).
  29. J. Liang, Y.-B. Yang, T. Draper, M. Gong, and K.-F. Liu, Phys. Rev. D 98, 074505 (2018).
  30. J. Green, N. Hasan, S. Meinel, M. Engelhardt, S. Krieg, J. Laeuchli, J. Negele, K. Orginos, A. Pochinsky, and S. Syritsyn, Phys. Rev. D 95, 114502 (2017).
  31. S. Bhattacharya, K. Cichy, M. Constantinou, X. Gao, A. Metz, J. Miller, S. Mukherjee, P. Petreczky, F. Steffens, and Y. Zhao, J. High Energy Phys. 01 (2025) 146.
  32. P. Hagler et al. (LHPC Collaboration), Phys. Rev. D 77, 094502 (2008).
  33. O. V. Teryaev, arXiv:hep-ph/9904376.
  34. S. J. Brodsky, D. S. Hwang, B.-Q. Ma, and I. Schmidt, Nucl. Phys. B593, 311 (2001).
  35. G. Basar, D. E. Kharzeev, H.-U. Yee, and I. Zahed, Phys. Rev. D 85, 105005 (2012).
  36. Y. Liu and I. Zahed, Phys. Rev. D 100, 046005 (2019).
  37. F. Hechenberger, GitHub, 2025, repository linked to zenodo, https://github.com/HechenMountain/stringy-gpds.
  38. F. Hechenberger, Zenodo, 2025, 10.5281/zenodo.15738460.

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Phys. Rev. D 113, 034027– Published 23 February, 2026
  • Received 31 July 2025
  • Accepted 28 January 2026
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