- Open Access
First Global Extraction of Generalized Parton Distributions from Experiment and Lattice Data with Next-to-Leading-Order Accuracy
Phys. Rev. Lett. 135, 261903 – Published 30 December, 2025
DOI: https://doi.org/10.1103/qct5-y7rp
Abstract
We report the first global extraction of generalized parton distributions, GUMP 1.0, by combining deeply virtual Compton scattering and -meson production data from Jefferson Lab and the Hadron-Electron Ring Accelerator with global fits of parton distribution functions, charge form factors, and lattice quantum chromodynamics simulations. Using a conformal moment space parametrization, we achieve a unified description across low- and high- regions at next to leading order accuracy in perturbative corrections. The results provide state-of-the-art generalized parton distributions consistent with almost all known facts, enabling three-dimensional nucleon imaging in impact parameter space and, at the same time, establishing a benchmark for future theoretical and experimental studies of the nucleon structure.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (113)
- X.-D. Ji, Phys. Rev. Lett. 74, 1071 (1995).
- X.-D. Ji, Phys. Rev. Lett. 78, 610 (1997).
- D. Müller, D. Robaschik, B. Geyer, F. M. Dittes, and J. Hořejši, Fortschr. Phys. 42, 101 (1994).
- X.-D. Ji, J. Phys. G 24, 1181 (1998).
- K. Goeke, M. V. Polyakov, and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 47, 401 (2001).
- M. Diehl, Phys. Rep. 388, 41 (2003).
- A. V. Belitsky and A. V. Radyushkin, Phys. Rep. 418, 1 (2005).
- X. Ji, Natl. Sci. Rev. 4, 213 (2017).
- R. Boussarie et al., arXiv:2304.03302.
- M. Burkardt, Phys. Rev. D 62, 071503 (2000); 66, 119903(E) (2002).
- M. Burkardt, Int. J. Mod. Phys. A 18, 173 (2003).
- X.-d. Ji, Phys. Rev. Lett. 91, 062001 (2003).
- A. V. Belitsky, X.-d. Ji, and F. Yuan, Phys. Rev. D 69, 074014 (2004).
- M. V. Polyakov, Phys. Lett. B 555, 57 (2003).
- X. Ji and C. Yang, arXiv:2508.16727.
- X.-D. Ji, Phys. Rev. D 55, 7114 (1997).
- A. V. Radyushkin, Phys. Lett. B 385, 333 (1996).
- J. C. Collins, L. Frankfurt, and M. Strikman, Phys. Rev. D 56, 2982 (1997).
- E. R. Berger, M. Diehl, and B. Pire, Eur. Phys. J. C 23, 675 (2002).
- P. Chatagnon et al. (CLAS Collaboration), Phys. Rev. Lett. 127, 262501 (2021).
- A. V. Belitsky and D. Mueller, Phys. Rev. Lett. 90, 022001 (2003).
- M. Guidal and M. Vanderhaeghen, Phys. Rev. Lett. 90, 012001 (2003).
- K. Deja, V. Martinez-Fernandez, B. Pire, P. Sznajder, and J. Wagner, Phys. Rev. D 107, 094035 (2023).
- A. Pedrak, B. Pire, L. Szymanowski, and J. Wagner, Phys. Rev. D 96, 074008 (2017); 100, 039901(E) (2019).
- G. Duplančić, S. Nabeebaccus, K. Passek-Kumerički, B. Pire, L. Szymanowski, and S. Wallon, Phys. Rev. D 107, 094023 (2023).
- J.-W. Qiu and Z. Yu, J. High Energy Phys. 08 (2022) 103.
- J.-W. Qiu and Z. Yu, Phys. Rev. D 107, 014007 (2023).
- J.-W. Qiu and Z. Yu, Phys. Rev. Lett. 131, 161902 (2023).
- O. Grocholski, B. Pire, P. Sznajder, L. Szymanowski, and J. Wagner, Phys. Rev. D 105, 094025 (2022).
- S. Nabeebaccus, J. Schoenleber, L. Szymanowski, and S. Wallon, Phys. Rev. D 111, 034040 (2025).
- J.-W. Qiu and Z. Yu, Phys. Rev. D 109, 074023 (2024).
- A. Accardi et al., Eur. Phys. J. A 60, 173 (2024).
- A. Accardi et al., Eur. Phys. J. A 52, 268 (2016).
- R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
- D. P. Anderle et al., Front. Phys. (Beijing) 16, 64701 (2021).
- V. Bertone, H. Dutrieux, C. Mezrag, H. Moutarde, and P. Sznajder, Phys. Rev. D 103, 114019 (2021).
- X. Ji, Phys. Rev. Lett. 110, 262002 (2013).
- X. Ji, Y.-S. Liu, Y. Liu, J.-H. Zhang, and Y. Zhao, Rev. Mod. Phys. 93, 035005 (2021).
- C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, A. Scapellato, and F. Steffens, Phys. Rev. Lett. 125, 262001 (2020).
- H.-W. Lin, Phys. Lett. B 824, 136821 (2022).
- J. Holligan, H.-W. Lin, R. Zhang, and Y. Zhao, J. High Energy Phys. 07 (2025) 241.
- Y. Guo, X. Ji, and K. Shiells, J. High Energy Phys. 09 (2022) 215.
- Y. Guo, X. Ji, M. G. Santiago, K. Shiells, and J. Yang, J. High Energy Phys. 05 (2023) 150.
- Y. Guo, X. Ji, M. G. Santiago, J. Yang, and H.-C. Zhang, Phys. Rev. D 112, 054036 (2025).
- K. Kumericki, D. Mueller, and K. Passek-Kumericki, Nucl. Phys. B794, 244 (2008).
- K. Kumerički and D. Mueller, Nucl. Phys. B841, 1 (2010).
- M. Čuić, G. Duplančić, K. Kumerički, and K. Passek-K., J. High Energy Phys. 12 (2023) 192.
- K. Kumerički, D. Müller, and M. Murray, Phys. Part. Nucl. 45, 723 (2014).
- B. Berthou et al., Eur. Phys. J. C 78, 478 (2018).
- R. Dupre, M. Guidal, and M. Vanderhaeghen, Phys. Rev. D 95, 011501 (2017).
- H. Moutarde, P. Sznajder, and J. Wagner, Eur. Phys. J. C 79, 614 (2019).
- K. Kumericki, S. Liuti, and H. Moutarde, Eur. Phys. J. A 52, 157 (2016).
- H. Dutrieux, H. Dutrieux, O. Grocholski, O. Grocholski, H. Moutarde, H. Moutarde, P. Sznajder, and P. Sznajder, Eur. Phys. J. C 82, 252 (2022); 82, 389(E) (2022).
- M. Almaeen, T. Alghamdi, B. Kriesten, D. Adams, Y. Li, H.-W. Lin, and S. Liuti, Eur. Phys. J. C 85, 499 (2025).
- H.-W. Lin, Phys. Rev. Lett. 127, 182001 (2021).
- M. Goharipour, H. Hashamipour, F. Irani, and K. Azizi (MMGPDs Collaboration), Phys. Rev. D 109, 074042 (2024).
- M. Hattawy et al. (CLAS Collaboration), Phys. Rev. Lett. 123, 032502 (2019).
- V. Burkert et al. (CLAS Collaboration), Eur. Phys. J. A 57, 186 (2021).
- F. Georges (Jefferson Lab Hall A Collaboration), Proc. Sci. Hadron2017 (2018) 170.
- F. Georges et al. (Jefferson Lab Hall A Collaboration), Phys. Rev. Lett. 128, 252002 (2022).
- G. Christiaens et al. (CLAS Collaboration), Phys. Rev. Lett. 130, 211902 (2023).
- F. D. Aaron et al. (H1 Collaboration), Phys. Lett. B 681, 391 (2009).
- S. Chekanov et al. (ZEUS Collaboration), PMC Phys. A 1, 6 (2007).
- F. D. Aaron et al. (H1 Collaboration), J. High Energy Phys. 05 (2010) 032.
- C. Cocuzza, W. Melnitchouk, A. Metz, and N. Sato (Jefferson Lab Angular Momentum (JAM) Collaboration), Phys. Rev. D 106, L031502 (2022).
- Z. Ye, J. Arrington, R. J. Hill, and G. Lee, Phys. Lett. B 777, 8 (2018).
- C. Alexandrou et al., Phys. Rev. D 101, 034519 (2020).
- C. Alexandrou, S. Bacchio, M. Constantinou, K. Hadjiyiannakou, K. Jansen, and G. Koutsou, Phys. Rev. D 104, 074503 (2021).
- D. C. Hackett, D. A. Pefkou, and P. E. Shanahan, Phys. Rev. Lett. 132, 251904 (2024).
- S. Bhattacharya, K. Cichy, M. Constantinou, X. Gao, A. Metz, J. Miller, S. Mukherjee, P. Petreczky, F. Steffens, and Y. Zhao, Phys. Rev. D 108, 014507 (2023).
- 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.
- M.-H. Chu, M. Colaço, S. Bhattacharya, K. Cichy, M. Constantinou, A. Metz, and F. Steffens, Phys. Rev. D 112, 094510 (2025).
- D. Mueller and A. Schafer, Nucl. Phys. B739, 1 (2006).
- D. Müller, T. Lautenschlager, K. Passek-Kumericki, and A. Schaefer, Nucl. Phys. B884, 438 (2014).
- D. Mueller, Few-Body Syst. 55, 317 (2014).
- T.-J. Hou et al., Phys. Rev. D 103, 014013 (2021).
- K. A. Mamo and I. Zahed, Phys. Rev. D 110, 114016 (2024).
- K. A. Mamo and I. Zahed, Phys. Rev. Lett. 133, 241901 (2024).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/qct5-y7rp for more details on the inputs of the analysis, GPD parametrization, and collected fit results.
- H. Dembinski et al., 10.5281/zenodo.3949207 (2020).
- F. James and M. Roos, Comput. Phys. Commun. 10, 343 (1975).
- Y. Guo, X. Ji, and K. Shiells, J. High Energy Phys. 12 (2021) 103.
- Y. Guo, X. Ji, B. Kriesten, and K. Shiells, J. High Energy Phys. 06 (2022) 096.
- A. Aktas et al. (H1 Collaboration), Eur. Phys. J. C 46, 585 (2006).
- D. Y. Ivanov, A. Schafer, L. Szymanowski, and G. Krasnikov, Eur. Phys. J. C 34, 297 (2004); 75, 75(E) (2015).
- H. Kowalski, L. Motyka, and G. Watt, Phys. Rev. D 74, 074016 (2006).
- Z.-Q. Chen and C.-F. Qiao, Phys. Lett. B 797, 134816 (2019); 809, 135759(E) (2020).
- J. Koempel, P. Kroll, A. Metz, and J. Zhou, Phys. Rev. D 85, 051502 (2012).
- J. P. Koempel, Exclusive production of quarkonia and generalized parton distributions, Ph.D. thesis, Temple University, 2015.
- C. A. Flett, J. A. Gracey, S. P. Jones, and T. Teubner, J. High Energy Phys. 08 (2021) 150.
- H. Mäntysaari and J. Penttala, Phys. Lett. B 823, 136723 (2021).
- H. Mäntysaari and J. Penttala, J. High Energy Phys. 08 (2022) 247.
- K. J. Eskola, C. A. Flett, V. Guzey, T. Löytäinen, and H. Paukkunen, Phys. Rev. C 106, 035202 (2022).
- S. V. Goloskokov, Y.-P. Xie, and X. Chen, Phys. Rev. D 110, 076029 (2024).
- C. A. Flett, J. P. Lansberg, S. Nabeebaccus, M. Nefedov, P. Sznajder, and J. Wagner, Phys. Lett. B 859, 139117 (2024).
- A. Ali et al. (GlueX Collaboration), Phys. Rev. Lett. 123, 072001 (2019).
- B. Duran et al., Nature (London) 615, 813 (2023).
- S. Adhikari et al. (GlueX Collaboration), Phys. Rev. C 108, 025201 (2023).
- Y. Guo, X. Ji, and Y. Liu, Phys. Rev. D 103, 096010 (2021).
- Y. Guo, X. Ji, Y. Liu, and J. Yang, Phys. Rev. D 108, 034003 (2023).
- Y. Guo, X. Ji, and F. Yuan, Phys. Rev. D 109, 014014 (2024).
- Y. Guo, F. Yuan, and W. Zhao, Phys. Rev. Lett. 135, 111902 (2025).
- V. D. Burkert, A. Camsonne, P. Chatagnon, K. Cichy, M. Constantinou, H. Dutrieux, I. M. Higuera-Angulo, C. Mezrag, D. Richards, and P. Sznajder, Eur. Phys. J. C 85, 838 (2025).
- S. Bhattacharya, K. Cichy, M. Constantinou, J. Dodson, X. Gao, A. Metz, S. Mukherjee, A. Scapellato, F. Steffens, and Y. Zhao, Phys. Rev. D 106, 114512 (2022).
- S. Bhattacharya et al., Phys. Rev. D 109, 034508 (2024).
- K. Shiells, Y. Guo, and X. Ji, J. High Energy Phys. 08 (2022) 048.
- X. Ji and F. Yuan, Phys. Lett. B 810, 135786 (2020).
- Y. Guo, X. Ji, and K. Shiells, Nucl. Phys. B969, 115440 (2021).
- C. Lorcé, Eur. Phys. J. C 81, 413 (2021).
- A. Freese and G. A. Miller, Phys. Rev. D 105, 014003 (2022).
- J. Y. Panteleeva, E. Epelbaum, J. Gegelia, and U. G. Meißner, Phys. Rev. D 106, 056019 (2022).
- Y. Guo et al., GUMP GPD Global Analysis, https://github.com/yuxunguo/GUMP-Global-GPDs (2025).
- K. Kumerički, gepard: Tool for studying the 3D quark and gluon distributions in the nucleon, https://gepard.phy.hr.