- Physical Review Journals
All JournalsPhysics Magazine

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

Global QCD analysis of spin PDFs in the proton with high-x and lattice constraints

C. Cocuzza1, N. T. Hunt-Smith2, W. Melnitchouk3, N. Sato3, and A. W. Thomas2 (JAM Collaboration (Spin PDF Analysis Group)

  • 1Department of Physics, William and Mary, Williamsburg, Virginia 23185, USA
  • 2CSSM and ARC Centre of Excellence for Dark Matter Particle Physics, Department of Physics, University of Adelaide, Adelaide 5005, Australia
  • 3Jefferson Lab, Newport News, Virginia 23606, USA

PDF

Phys. Rev. D 112, 114017 – Published 9 December, 2025

DOI: https://doi.org/10.1103/6fn9-1wqb

Abstract

We perform a comprehensive global QCD analysis of spin-dependent parton distribution functions (PDFs), combining all available data on inclusive and semi-inclusive deep-inelastic scattering (DIS), as well as inclusive weak boson and jet production in polarized pp collisions, simultaneously extracting spin-averaged PDFs and fragmentation functions. Including recent Jefferson Lab DIS data at high x, together with subleading power corrections to the leading-twist framework, allows us to verify the stability of the PDFs for W2≥4  GeV2 and quantify the uncertainties on the spin structure functions more reliably. We explore the use of new lattice QCD data on gluonic pseudo-Ioffe time distributions, which, together with jet production and high-x DIS data, improve the constraints on the polarized gluon PDF. The expanded kinematic reach afforded by the data into the high-x region allows us to refine the bounds on higher-twist contributions to the spin structure functions, and test the validity of the Bjorken sum rule.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (131)

  1. J. J. Ethier, N. Sato, and W. Melnitchouk, Phys. Rev. Lett. 119, 132001 (2017).
  2. N. Sato, C. Andres, J. J. Ethier, and W. Melnitchouk, Phys. Rev. D 101, 074020 (2020).
  3. E. Moffat, W. Melnitchouk, T. C. Rogers, and N. Sato, Phys. Rev. D 104, 016015 (2021).
  4. C. Cocuzza, W. Melnitchouk, A. Metz, and N. Sato, Phys. Rev. D 106, L031502 (2022).
  5. L. Adamczyk et al., Phys. Rev. Lett. 115, 092002 (2015).
  6. J. Adam et al., Phys. Rev. D 100, 052005 (2019).
  7. M. S. Abdallah et al., Phys. Rev. D 103, L091103 (2021).
  8. M. S. Abdallah et al., Phys. Rev. D 105, 092011 (2022).
  9. A. Adare et al., Phys. Rev. D 84, 012006 (2011).
  10. Y. Zhou, N. Sato, and W. Melnitchouk, Phys. Rev. D 105, 074022 (2022).
  11. J. Karpie, R. M. Whitehill, W. Melnitchouk, C. Monahan, K. Orginos, J.-W. Qiu, D. G. Richards, N. Sato, and S. Zafeiropoulos, Phys. Rev. D 109, 036031 (2024).
  12. N. T. Hunt-Smith, C. Cocuzza, W. Melnitchouk, N. Sato, A. W. Thomas, and M. J. White, Phys. Rev. Lett. 133, 161901 (2024).
  13. P. Jimenez-Delgado, A. Accardi, and W. Melnitchouk, Phys. Rev. D 89, 034025 (2014).
  14. N. Sato, W. Melnitchouk, S. E. Kuhn, J. J. Ethier, and A. Accardi, Phys. Rev. D 93, 074005 (2016).
  15. I. Borsa, M. Stratmann, W. Vogelsang, D. de Florian, and R. Sassot, Phys. Rev. Lett. 133, 151901 (2024).
  16. J. Cruz-Martinez, T. Hasenack, F. Hekhorn, G. Magni, E. R. Nocera, T. R. Rabemananjara, J. Rojo, T. Sharma, and G. van Seeventer et al., J. High Energy Phys. 07 (2025) 168.
  17. E. G. Floratos, C. Kounnas, and R. Lacaze, Nucl. Phys. B192, 417 (1981).
  18. S. Wandzura and F. Wilczek, Phys. Lett. 72B, 195 (1977).
  19. I. Schienbein et al., J. Phys. G 35, 053101 (2008).
  20. O. Nachtmann, Nucl. Phys. B63, 237 (1973).
  21. O. W. Greenberg and D. Bhaumik, Phys. Rev. D 4, 2048 (1971).
  22. S. Matsuda and T. Uematsu, Nucl. Phys. B168, 181 (1980).
  23. A. Piccione and G. Ridolfi, Nucl. Phys. B513, 301 (1998).
  24. J. Blumlein and A. Tkabladze, Nucl. Phys. B553, 427 (1999).
  25. A. Accardi and W. Melnitchouk, Phys. Lett. B 670, 114 (2008).
  26. H. Georgi and H. D. Politzer, Phys. Rev. D 14, 1829 (1976).
  27. A. De Rujula, H. Georgi, and H. D. Politzer, Ann. Phys. (N.Y.) 103, 315 (1977).
  28. A. De Rujula, H. Georgi, and H. D. Politzer, Phys. Rev. D 15, 2495 (1977).
  29. K. Bitar, P. W. Johnson, and W.-K. Tung, Phys. Lett. 83B, 114 (1979).
  30. F. M. Steffens and W. Melnitchouk, Phys. Rev. C 73, 055202 (2006).
  31. F. M. Steffens, M. D. Brown, W. Melnitchouk, and S. Sanches, Phys. Rev. C 86, 065208 (2012).
  32. J. F. Owens, A. Accardi, and W. Melnitchouk, Phys. Rev. D 87, 094012 (2013).
  33. A. Accardi, L. T. Brady, W. Melnitchouk, J. F. Owens, and N. Sato, Phys. Rev. D 93, 114017 (2016).
  34. W. Melnitchouk, R. Ent, and C. Keppel, Phys. Rep. 406, 127 (2005).
  35. R. L. Jaffe and X.-D. Ji, Phys. Rev. D 43, 724 (1991).
  36. M. Anselmino, A. Efremov, and E. Leader, Phys. Rep. 261, 1 (1995); 281, 399(E) (1997).
  37. W. Melnitchouk, G. Piller, and A. W. Thomas, Phys. Lett. B 346, 165 (1995).
  38. S. A. Kulagin, W. Melnitchouk, G. Piller, and W. Weise, Phys. Rev. C 52, 932 (1995).
  39. G. Piller, W. Melnitchouk, and A. W. Thomas, Phys. Rev. C 54, 894 (1996).
  40. S. A. Kulagin and W. Melnitchouk, Phys. Rev. C 77, 015210 (2008).
  41. S. A. Kulagin and W. Melnitchouk, Phys. Rev. C 78, 065203 (2008).
  42. J. T. Londergan, J. C. Peng, and A. W. Thomas, Rev. Mod. Phys. 82, 2009 (2010).
  43. H. Burkhardt and W. N. Cottingham, Ann. Phys. (N.Y.) 56, 453 (1970).
  44. X.-D. Ji and P. Unrau, Phys. Lett. B 333, 228 (1994).
  45. E. Stein, P. Gornicki, L. Mankiewicz, A. Schafer, and W. Greiner, Phys. Lett. B 343, 369 (1995).
  46. E. Stein, P. Gornicki, L. Mankiewicz, and A. Schafer, Phys. Lett. B 353, 107 (1995).
  47. M. Burkardt, Phys. Rev. D 88, 114502 (2013).
  48. Z. E. Meziani et al., Phys. Lett. B 613, 148 (2005).
  49. M. Osipenko, W. Melnitchouk, S. Simula, P. Bosted, V. Burkert, M. E. Christy, K. Griffioen, C. Keppel, and S. E. Kuhn, Phys. Lett. B 609, 259 (2005).
  50. A. Deur et al., Phys. Rev. Lett. 93, 212001 (2004).
  51. M. Osipenko, S. Simula, W. Melnitchouk, P. Bosted, V. Burkert, E. Christy, K. Griffioen, C. Keppel, S. Kuhn, and G. Ricco, Phys. Rev. D 71, 054007 (2005).
  52. A. Bacchetta, M. Diehl, K. Goeke, A. Metz, P. J. Mulders, and M. Schlegel, J. High Energy Phys. 02 (2007) 093.
  53. M. Stratmann and W. Vogelsang, Phys. Rev. D 64, 114007 (2001).
  54. A. Accardi, T. Hobbs, and W. Melnitchouk, J. High Energy Phys. 11 (2009) 084.
  55. J. V. Guerrero, J. J. Ethier, A. Accardi, S. W. Casper, and W. Melnitchouk, J. High Energy Phys. 09 (2015) 169.
  56. J. V. Guerrero and A. Accardi, Phys. Rev. D 97, 114012 (2018).
  57. D. Adamiak et al. (to be published).
  58. F. Ringer and W. Vogelsang, Phys. Rev. D 91, 094033 (2015).
  59. B. Jager, M. Stratmann, and W. Vogelsang, Phys. Rev. D 70, 034010 (2004).
  60. A. V. Radyushkin, Phys. Rev. D 96, 034025 (2017).
  61. I. Balitsky, W. Morris, and A. Radyushkin, J. High Energy Phys. 02 (2022) 193.
  62. S. Borsányi et al., J. High Energy Phys. 09 (2012) 010.
  63. C. Egerer et al., Phys. Rev. D 106, 094511 (2022).
  64. H.-W. Lin, W. Melnitchouk, A. Prokudin, N. Sato, and H. Shows, Phys. Rev. Lett. 120, 152502 (2018).
  65. J. Bringewatt, N. Sato, W. Melnitchouk, J.-W. Qiu, F. Steffens, and M. Constantinou, Phys. Rev. D 103, 016003 (2021).
  66. P. C. Barry et al., Phys. Rev. D 105, 114051 (2022).
  67. L. Gamberg, M. Malda, J. A. Miller, D. Pitonyak, A. Prokudin, and N. Sato, Phys. Rev. D 106, 034014 (2022).
  68. P. C. Barry, L. Gamberg, W. Melnitchouk, E. Moffat, D. Pitonyak, A. Prokudin, and N. Sato, Phys. Rev. D 108, L091504 (2023).
  69. C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl, Phys. Rev. Lett. 132, 091901 (2024).
  70. C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl, Phys. Rev. D 109, 034024 (2024).
  71. T. Anderson, W. Melnitchouk, and N. Sato, arXiv:2501.00665.
  72. R. L. Workman et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  73. N. Sato, J. J. Ethier, W. Melnitchouk, M. Hirai, S. Kumano, and A. Accardi, Phys. Rev. D 94, 114004 (2016).
  74. R. Hyndman and Y. Fan, Am. Stat. 50, 361 (1996).
  75. J. Collins, T. C. Rogers, and N. Sato, Phys. Rev. D 105, 076010 (2022).
  76. D. de Florian, S. Forte, and W. Vogelsang, Phys. Rev. D 109, 074007 (2024).
  77. J. Ashman et al., Nucl. Phys. B328, 1 (1989).
  78. B. Adeva et al., Phys. Rev. D 58, 112001 (1998).
  79. B. Adeva et al., Phys. Rev. D 60, 072004 (1999); 62, 079902(E) (2000).
  80. V. Y. Alexakhin et al., Phys. Lett. B 647, 8 (2007).
  81. M. Alekseev et al., Phys. Lett. B 690, 466 (2010).
  82. C. Adolph et al., Phys. Lett. B 753, 573 (2016).
  83. G. Baum et al., Phys. Rev. Lett. 51, 1135 (1983).
  84. P. L. Anthony et al., Phys. Rev. D 54, 6620 (1996).
  85. K. Abe et al., Phys. Rev. Lett. 79, 26 (1997).
  86. K. Abe et al., Phys. Rev. D 58, 112003 (1998).
  87. P. Anthony et al., Phys. Lett. B 463, 339 (1999).
  88. P. Anthony et al., Phys. Lett. B 493, 19 (2000).
  89. K. Ackerstaff et al., Phys. Lett. B 404, 383 (1997).
  90. A. Airapetian et al., Phys. Rev. D 75, 012007 (2007).
  91. X. Zheng et al., Phys. Rev. C 70, 065207 (2004).
  92. D. Flay et al., Phys. Rev. D 94, 052003 (2016).
  93. D. S. Parno et al., Phys. Lett. B 744, 309 (2015).
  94. Y. Prok et al., Phys. Rev. C 90, 025212 (2014).
  95. R. G. Fersch et al., Phys. Rev. C 96, 065208 (2017).
  96. N. Guler et al., Phys. Rev. C 92, 055201 (2015).
  97. P. L. Anthony et al., Phys. Lett. B 458, 529 (1999).
  98. P. L. Anthony et al., Phys. Lett. B 553, 18 (2003).
  99. A. Airapetian et al., Eur. Phys. J. C 72, 1921 (2012).
  100. A. Airapetian et al., Phys. Rev. D 71, 012003 (2005).
  101. M. Alekseev et al., Phys. Lett. B 680, 217 (2009).
  102. R. Windmolders, J. Phys. Conf. Ser. 295, 012069 (2011).
  103. B. I. Abelev et al., Phys. Rev. Lett. 97, 252001 (2006).
  104. B. I. Abelev et al., Phys. Rev. Lett. 100, 232003 (2008).
  105. L. Adamczyk et al., Phys. Rev. D 86, 032006 (2012).
  106. J. Adam et al., Phys. Rev. D 99, 051102 (2019).
  107. A. Adare et al., Phys. Rev. D 93, 051103 (2016).
  108. A. Adare et al., Phys. Rev. D 98, 032007 (2018).
  109. A. I. Signal and A. W. Thomas, Phys. Lett. B 191, 205 (1987).
  110. X. Ji and J. Tang, Phys. Lett. B 362, 182 (1995).
  111. W. Melnitchouk and M. Malheiro, Phys. Rev. C 55, 431 (1997).
  112. W. Melnitchouk and M. Malheiro, Phys. Lett. B 451, 224 (1999).
  113. X. G. Wang, C.-R. Ji, W. Melnitchouk, Y. Salamu, A. W. Thomas, and P. Wang, Phys. Rev. D 102, 116020 (2020).
  114. F. He, C.-R. Ji, W. Melnitchouk, Y. Salamu, A. W. Thomas, P. Wang, and X. G. Wang, Phys. Rev. D 105, 094007 (2022).
  115. W. Melnitchouk and A. W. Thomas, Phys. Lett. B 377, 11 (1996).
  116. W. Melnitchouk and A. W. Thomas, Acta Phys. Pol. B 27, 1407 (1996).
  117. F. E. Close and A. W. Thomas, Phys. Lett. B 212, 227 (1988).
  118. F. E. Close and W. Melnitchouk, Phys. Rev. C 68, 035210 (2003).
  119. F. E. Close, An Introduction to Quarks and Partons (Academic Press, London, 1979).
  120. I. C. Cloet, W. Bentz, and A. W. Thomas, Phys. Lett. B 621, 246 (2005).
  121. P. Jimenez-Delgado, H. Avakian, and W. Melnitchouk, Phys. Lett. B 738, 263 (2014).
  122. D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Phys. Rev. Lett. 113, 012001 (2014).
  123. E. R. Nocera, R. D. Ball, S. Forte, G. Ridolfi, and J. Rojo, Nucl. Phys. B887, 276 (2014).
  124. J. D. Bjorken, Phys. Rev. 148, 1467 (1966).
  125. B. Lampe and E. Reya, Phys. Rep. 332, 1 (2000).
  126. W. Armstrong et al., Phys. Rev. Lett. 122, 022002 (2019).
  127. https://www.lhapdf.org/.
  128. E. Moffat, T. C. Rogers, W. Melnitchouk, N. Sato, and F. Steffens, Phys. Rev. D 99, 096008 (2019).
  129. J. Collins, Foundations of Perturbative QCD, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology Vol. 32 (Cambridge University Press, Cambridge, England, 2023).
  130. B. Adeva et al., Phys. Lett. B 420, 180 (1998).
  131. M. S. Abdallah et al., Phys. Rev. D 105, 092011 (2022).

Outline

Information

Phys. Rev. D 112, 114017– Published 9 December, 2025
  • Received 23 June 2025
  • Accepted 17 October 2025
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