- Open Access
- Access by Xinjiang University
Toward precision helicity PDFs from global DIS and SIDIS fits with projected EIC measurements
Phys. Rev. D 113, 114010 – Published 5 June, 2026
DOI: https://doi.org/10.1103/wc54-mnfh
Abstract
We present HAPS-pPDF1.0, a new global determination of the helicity-dependent parton distribution functions (PDFs) of the proton, based on inclusive deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS) data within a consistent next-to-leading order (NLO) QCD framework. In addition to existing measurements, we incorporate simulated pseudodata for the future Electron-Ion Collider (EIC), considering two beam-energy configurations, and , corresponding to an extended kinematic reach down to . We focus on longitudinal double-spin asymmetries for charge-separated pion and kaon production in SIDIS off a longitudinally polarized proton target. These projected measurements significantly improve the flavor separation of sea-quark polarized PDFs (, , ) and reduce the uncertainties on both quark and gluon helicity distributions, with the largest impact at small . Polarized PDFs are extracted using a neural-network parametrization and a Monte Carlo replica methodology to propagate experimental uncertainties, while theoretical constraints such as positivity are imposed during the fit. We demonstrate that the inclusion of EIC pseudodata leads to a substantially more precise determination of polarized PDFs, with the largest impact in the small- region. The resulting polarized PDF sets are provided in the LHAPDF format.
Physics Subject Headings (PhySH)
Article Text
References (91)
- X. Ji, F. Yuan, and Y. Zhao, What we know and what we don’t know about the proton spin after 30 years, Nat. Rev. Phys. 3, 27 (2021).
- J. Ashman et al. (European Muon Collaboration), A measurement of the spin asymmetry and determination of the structure function in deep inelastic muon-proton scattering, Phys. Lett. B 206, 364 (1988).
- J. Ashman et al. (European Muon Collaboration), An investigation of the spin structure of the proton in deep inelastic scattering of polarized muons on polarized protons, Nucl. Phys. B328, 1 (1989).
- M. Anselmino, A. Efremov, and E. Leader, The theory and phenomenology of polarized deep inelastic scattering, Phys. Rep. 261, 1 (1995); 281, 399(E) (1997).
- J. J. Ethier and E. R. Nocera, Parton distributions in nucleons and nuclei, Annu. Rev. Nucl. Part. Sci. 70, 43 (2020).
- M. Gluck, E. Reya, M. Stratmann, and W. Vogelsang, Models for the polarized parton distributions of the nucleon, Phys. Rev. D 63, 094005 (2001).
- M. Hirai et al. (Asymmetry Analysis Collaboration), Determination of polarized parton distribution functions and their uncertainties, Phys. Rev. D 69, 054021 (2004).
- M. Hirai, S. Kumano, and N. Saito, Determination of polarized parton distribution functions with recent data on polarization asymmetries, Phys. Rev. D 74, 014015 (2006).
- J. Blumlein and H. Bottcher, QCD analysis of polarized deep inelastic scattering data, Nucl. Phys. B841, 205 (2010).
- E. Leader, A. V. Sidorov, and D. B. Stamenov, Determination of polarized PDFs from a QCD analysis of inclusive and semi-inclusive deep inelastic scattering data, Phys. Rev. D 82, 114018 (2010).
- D. Adamiak et al. (Jefferson Lab Angular Momentum (JAM) Collaboration), Global analysis of polarized DIS and SIDIS data with improved small-x helicity evolution, Phys. Rev. D 108, 11 (2023).
- D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Extraction of spin-dependent parton densities and their uncertainties, Phys. Rev. D 80, 034030 (2009).
- E. R. Nocera, Small- and large- nucleon spin structure from a global QCD analysis of polarized parton distribution functions, Phys. Lett. B 742, 117 (2015).
- D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Global analysis of helicity parton densities and their uncertainties, Phys. Rev. Lett. 101, 072001 (2008).
- D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Evidence for polarization of gluons in the proton, Phys. Rev. Lett. 113, 012001 (2014).
- N. Sato et al. (Jefferson Lab Angular Momentum Collaboration), Iterative Monte Carlo analysis of spin-dependent parton distributions, Phys. Rev. D 93, 074005 (2016).
- J. J. Ethier, N. Sato, and W. Melnitchouk, First simultaneous extraction of spin-dependent parton distributions and fragmentation functions from a global QCD analysis, Phys. Rev. Lett. 119, 132001 (2017).
- E. R. Nocera et al. (NNPDF Collaboration), A first unbiased global determination of polarized PDFs and their uncertainties, Nucl. Phys. B887, 276 (2014).
- I. Borsa, M. Stratmann, W. Vogelsang, D. de Florian, and R. Sassot, Next-to-next-to-leading order global analysis of polarized parton distribution functions, Phys. Rev. Lett. 133, 15 (2024).
- L. Bonino, T. Gehrmann, M. Löchner, K. Schönwald, and G. Stagnitto, Polarized neutral and charged current semi-inclusive deep-inelastic scattering at NNLO in QCD, J. High Energy Phys. 03 (2026) 109.
- S. Goyal, R. N. Lee, S. O. Moch, V. Pathak, N. Rana, and V. Ravindran, NNLO QCD corrections to unpolarized and polarized SIDIS, Phys. Rev. D 111, 9 (2025).
- L. Bonino, T. Gehrmann, M. Löchner, K. Schönwald, and G. Stagnitto, NNLO corrections to SIDIS coefficient functions, Proc. Sci., LL2024 (2024) 054 [arXiv:2408.08741].
- T. Gehrmann and M. Löchner, The unresolved behaviour of polarized scattering matrix elements at NNLO in QCD, J. High Energy Phys. 02 (2026) 097.
- F. Arbabifar, S. Atashbar Tehrani, and H. Khanpour, AAK24: Global QCD analysis on polarized parton distribution in the presence of asymmetry measurements, Eur. Phys. J. Plus 139, 834 (2024).
- H. Khanpour, S. T. Monfared, and S. Atashbar Tehrani, Study of spin-dependent structure functions of and at NNLO approximation and corresponding nuclear corrections, Phys. Rev. D 96, 074037 (2017).
- H. Khanpour, S. T. Monfared, and S. Atashbar Tehrani, Nucleon spin structure functions at NNLO in the presence of target mass corrections and higher twist effects, Phys. Rev. D 95, 074006 (2017).
- I. Borsa, G. Lucero, R. Sassot, E. C. Aschenauer, and A. S. Nunes, Revisiting helicity parton distributions at a future electron-ion collider, Phys. Rev. D 102, 094018 (2020).
- C. Cocuzza et al. (JAM Collaboration (Spin PDF Analysis Group), Global QCD analysis of spin PDFs in the proton with high-x and lattice constraints, Phys. Rev. D 112, 11 (2025).
- D. Adamiak et al. (JAM Collaboration (Small-x Analysis Group), First study of polarized proton-proton scattering with small-x helicity evolution, Phys. Rev. D 112, 094032 (2025).
- V. Bertone et al. (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), Helicity-dependent parton distribution functions at next-to-next-to-leading order accuracy from inclusive and semi-inclusive deep-inelastic scattering data, Phys. Lett. B 865, 139497 (2025).
- J. Cruz-Martinez, T. Hasenack, F. Hekhorn, G. Magni, E. R. Nocera, T. R. Rabemananjara, J. Rojo, T. Sharma, and G. van Seeventer, NNPDFpol2.0: A global determination of polarised PDFs and their uncertainties at next-to-next-to-leading order, J. High Energy Phys. 07 (2025) 168.
- R. Abdul Khalek, A. Accardi, J. Adam, D. Adamiak, W. Akers, M. Albaladejo, A. Al-bataineh, M. G. Alexeev, F. Ameli, P. Antonioli et al., Science requirements and detector concepts for the electron-ion collider: EIC yellow report, Nucl. Phys. A1026, 122447 (2022).
- R. Abdul Khalek, U. D’Alesio, M. Arratia, A. Bacchetta, M. Battaglieri, M. Begel, M. Boglione, R. Boughezal, R. Boussarie, G. Bozzi et al., Snowmass 2021 white paper: Electron ion collider for high energy physics, arXiv:2203.13199.
- M. Azizi, M. Soleymaninia, H. Hashamipour, M. Salajegheh, H. Khanpour, and U. G. Meißner, Revisiting constraints on proton PDFs from HERA DIS, Drell-Yan, W and Z boson production, and projected EIC measurements, Phys. Rev. D 111, 034023 (2025).
- N. Armesto, T. Cridge, F. Giuli, L. Harland-Lang, P. Newman, B. Schmookler, R. Thorne, and K. Wichmann, Impact of inclusive electron ion collider data on collinear parton distributions, Phys. Rev. D 109, 054019 (2024).
- J. Jiménez-López, S. Maple, P. R. Newman, and K. Wichmann, Inclusive electron-proton measurement prospects in the electron-ion collider early science stage, arXiv:2602.00860.
- M. Soleymaninia, H. Khanpour, M. Azizi, and H. Hashamipour, Improved constraints on pion fragmentation functions from simulated electron-ion collider data, Phys. Rev. D 112, 054032 (2025).
- E. C. Aschenauer, I. Borsa, R. Sassot, and C. Van Hulse, Semi-inclusive deep-inelastic scattering, parton distributions and fragmentation functions at a future electron-ion collider, Phys. Rev. D 99, 094004 (2019).
- J. K. Adkins, Y. Akiba, A. Albataineh, M. Amaryan, I. C. Arsene, C. Ayerbe Gayoso, J. Bae, X. Bai, M. D. Baker, M. Bashkanov et al., Design of the ECCE detector for the electron ion collider, Nucl. Instrum. Methods Phys. Res., Sect. A 1073, 170240 (2025).
- C. Van Hulse, J. K. Adkins, Y. Akiba, A. Albataineh, M. Amaryan, I. C. Arsene, C. Ayerbe Gayoso, J. Bae, X. Bai, M. D. Baker et al., Evaluation of longitudinal double-spin asymmetry measurements in semi-inclusive deep-inelastic scattering from the proton for the ECCE detector design, Nucl. Instrum. Methods Phys. Res., Sect. A 1056, 168563 (2023).
- F. Hekhorn and M. Stratmann, Next-to-leading order QCD corrections to inclusive heavy-flavor production in polarized deep-inelastic scattering, Phys. Rev. D 98, 014018 (2018).
- A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, and C. Schneider, The 3-loop non-singlet heavy flavor contributions to the structure function at large momentum transfer, Nucl. Phys. B897, 612 (2015).
- J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider, and K. Schönwald, The three-loop single mass polarized pure singlet operator matrix element, Nucl. Phys. B953, 114945 (2020).
- A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, K. Schönwald, and C. Schneider, The polarized transition matrix element of the variable flavor number scheme at , Nucl. Phys. B964, 115331 (2021).
- J. Blümlein, A. De Freitas, M. Saragnese, C. Schneider, and K. Schönwald, Logarithmic contributions to the polarized asymptotic massive Wilson coefficients and operator matrix elements in deeply inelastic scattering, Phys. Rev. D 104, 034030 (2021).
- I. Bierenbaum, J. Blümlein, A. De Freitas, A. Goedicke, S. Klein, and K. Schönwald, ) polarized heavy flavor corrections to deep-inelastic scattering at , Nucl. Phys. B988, 116114 (2023).
- J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider, and K. Schönwald, The first–order factorizable contributions to the three–loop massive operator matrix elements and , Nucl. Phys. B999, 116427 (2024).
- F. Hekhorn, G. Magni, E. R. Nocera, T. R. Rabemananjara, J. Rojo, A. Schaus, and R. Stegeman, Heavy quarks in polarised deep-inelastic scattering at the electron-ion collider, Eur. Phys. J. C 84, 189 (2024).
- E. B. Zijlstra and W. L. van Neerven, Order- corrections to the polarized structure function , Nucl. Phys. B417, 61 (1994); B426, 245(E) (1994); B773, 105(E) (2007); B501, 599(E) (1997).
- R. Mertig and W. L. van Neerven, The calculation of the two loop spin splitting functions , Z. Phys. C 70, 637 (1996).
- W. Vogelsang, A rederivation of the spin dependent next-to-leading order splitting functions, Phys. Rev. D 54, 2023 (1996).
- S. Moch, J. A. M. Vermaseren, and A. Vogt, The three-loop splitting functions in QCD: The helicity-dependent case, Nucl. Phys. B889, 351 (2014).
- J. Blümlein, P. Marquard, C. Schneider, and K. Schönwald, The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements, J. High Energy Phys. 01 (2022) 193; 02 (2026) 49.
- J. Blümlein, P. Marquard, C. Schneider, and K. Schönwald, The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements, Nucl. Phys. B971, 115542 (2021).
- W. Furmanski and R. Petronzio, Lepton—hadron processes beyond leading order in quantum chromodynamics, Z. Phys. C 11, 293 (1982).
- D. de Florian, M. Stratmann, and W. Vogelsang, QCD analysis of unpolarized and polarized Lambda baryon production in leading and next-to-leading order, Phys. Rev. D 57, 5811 (1998).
- R. A. Khalek et al. (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), Determination of unpolarized pion fragmentation functions using semi-inclusive deep-inelastic-scattering data, Phys. Rev. D 104, 034007 (2021).
- R. Abdul Khalek et al. (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), Pion and kaon fragmentation functions at next-to-next-to-leading order, Phys. Lett. B 834, 137456 (2022).
- R. D. Ball et al. (NNPDF Collaboration), The path to proton structure at 1% accuracy, Eur. Phys. J. C 82, 428 (2022).
- J. Blumlein and A. Tkabladze, Target mass corrections for polarized structure functions and new sum rules, Nucl. Phys. B553, 427 (1999).
- I. Schienbein, V. A. Radescu, G. P. Zeller, M. E. Christy, C. E. Keppel, K. S. McFarland, W. Melnitchouk, F. I. Olness, M. H. Reno, F. Steffens et al., A review of target mass corrections, J. Phys. G 35, 053101 (2008).
- E. Leader, A. V. Sidorov, and D. B. Stamenov, Some remarks on methods of QCD analysis of polarized DIS data, Phys. Rev. D 80, 054026 (2009).
- V. Bertone, S. Carrazza, and J. Rojo, APFEL: A PDF evolution library with QED corrections, Comput. Phys. Commun. 185, 1647 (2014).
- V. Bertone, apfel++: A new PDF evolution library in c++, Proc. Sci., DIS2017 (2018) 201 [arXiv:1708.00911].
- https://github.com/MapCollaboration/MontBlanc.
- V. Bertone, A. Chiefa, and E. R. Nocera, Mapcollaboration/denali: Sheldon chalet (2024).
- S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
- B. Adeva et al. (Spin Muon Collaboration), Spin asymmetries and structure functions of the proton and the deuteron from polarized high-energy muon scattering, Phys. Rev. D 58, 112001 (1998).
- C. Adolph et al. (COMPASS Collaboration), The spin structure function of the proton and a test of the Bjorken sum rule, Phys. Lett. B 753, 18 (2016).
- C. Adolph et al. (COMPASS Collaboration), Final COMPASS results on the deuteron spin-dependent structure function and the Bjorken sum rule, Phys. Lett. B 769, 34 (2017).
- P. L. Anthony et al. (E142 Collaboration), Deep inelastic scattering of polarized electrons by polarized He-3 and the study of the neutron spin structure, Phys. Rev. D 54, 6620 (1996).
- K. Abe et al. (E143 Collaboration), Measurements of the proton and deuteron spin structure functions and . Phys. Rev. D 58, 112003 (1998).
- K. Abe et al. (E154 Collaboration), Precision determination of the neutron spin structure function , Phys. Rev. Lett. 79, 26 (1997).
- P. L. Anthony et al. (E155 Collaboration), Measurements of the dependence of the proton and neutron spin structure functions and , Phys. Lett. B 493, 19 (2000).
- K. Ackerstaff et al. (HERMES Collaboration), Measurement of the neutron spin structure function with a polarized He-3 internal target, Phys. Lett. B 404, 383 (1997).
- A. Airapetian et al. (HERMES Collaboration), Precise determination of the spin structure function of the proton, deuteron and neutron, Phys. Rev. D 75, 012007 (2007).
- D. Flay et al. (Jefferson Lab Hall A Collaboration), Measurements of and : Probing the neutron spin structure, Phys. Rev. D 94, 052003 (2016).
- K. M. Kramer (Jefferson Lab E97-103 Collaboration), The search for higher twist effects in the spin-structure functions of the neutron, AIP Conf. Proc. 675, 615 (2003).
- X. Zheng et al. (Jefferson Lab Hall A Collaboration), Precision measurement of the neutron spin asymmetries and spin-dependent structure functions in the valence quark region, Phys. Rev. C 70, 065207 (2004).
- Y. Prok et al. (CLAS Collaboration), Precision measurements of of the proton and the deuteron with 6 GeV electrons, Phys. Rev. C 90, 025212 (2014).
- R. D. Ball et al. (NNPDF Collaboration), Unbiased determination of polarized parton distributions and their uncertainties, Nucl. Phys. B874, 36 (2013).
- N. Guler et al. (CLAS Collaboration), Precise determination of the deuteron spin structure at low to moderate with CLAS and extraction of the neutron contribution, Phys. Rev. C 92, 055201 (2015).
- R. Fersch et al. (CLAS Collaboration), Determination of the proton spin structure functions for using CLAS, Phys. Rev. C 96, 065208 (2017).
- W. Armstrong et al. (SANE Collaboration), Revealing color forces with transverse polarized electron scattering, Phys. Rev. Lett. 122, 022002 (2019).
- M. G. Alekseev et al. (COMPASS Collaboration), Quark helicity distributions from longitudinal spin asymmetries in muon-proton and muon-deuteron scattering, Phys. Lett. B 693, 227 (2010).
- A. Airapetian et al. (HERMES Collaboration), Longitudinal double-spin asymmetries in semi-inclusive deep-inelastic scattering of electrons and positrons by protons and deuterons, Phys. Rev. D 99, 112001 (2019).
- A. L. Kataev, The constraints on the nonsinglet polarized parton densities from the infrared renormalon model, JETP Lett. 77, 458 (2003).
- S. Agarwal, K. Mierle, and T. C. S. Team, Ceres Solver, 2023.
- A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr, and G. Watt, LHAPDF6: Parton density access in the LHC precision era, Eur. Phys. J. C 75, 132 (2015).
- HAPS Collaboration, Public grid of HAPS-pPDF1.0, GitHub repository available at https://github.com/HAPS-Collaboration/HAPS-pPDF1.0.
- E. Maguire, L. Heinrich, and G. Watt, HEPData: A repository for high energy physics data, J. Phys. Conf. Ser. 898, 102006 (2017); HEPData repository, available at https://www.hepdata.net/.