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Revisiting unidentified charged-hadron fragmentation functions with modern COMPASS SIDIS multiplicities
Phys. Rev. D 114, 054013 – Published 8 September, 2026
DOI: https://doi.org/10.1103/8zzz-6xkn
Abstract
We present HAPS-hFF1.0, a new global QCD analysis of unidentified charged-hadron fragmentation functions (FFs) using single-inclusive electron-positron annihilation (SIA) data together with the modern COMPASS semi-inclusive deep-inelastic scattering (SIDIS) multiplicities. The COMPASS input consists of the 2025 proton-target measurement and the revised -target multiplicities provided in the 2026 COMPASS addendum. The extraction is performed at both next-to-leading order (NLO) and next-to-next-to-leading order (NNLO), allowing us to study the perturbative stability of the QCD fit and the impact of the updated SIDIS information on the flavor structure of the FFs. The FFs are parametrized using neural networks, while experimental uncertainties are propagated through a Monte Carlo replica methodology. We find that the modern COMPASS multiplicities can be consistently described together with the SIA data and provide important charge-separated constraints on the light-quark and antiquark FFs. The comparison between the NLO and NNLO extractions indicates a stable quark-sector determination, while the gluon FF remains less directly constrained in the present analysis. Our results highlight the importance of the modern COMPASS SIDIS multiplicities for precision studies of unidentified charged-hadron fragmentation and for future global FF determinations. The resulting HAPS-hFF1.0 replicas are publicly available in standard LHAPDF format.
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References (69)
- J. Gao, X. Shen, H. Xing, Y. Zhao, and B. Zhou, Fragmentation functions of charged hadrons at next-to-next-to-leading order and constraints on the proton parton distribution functions, Phys. Rev. Lett. 135, 041902 (2025).
- J. Gao, C. Liu, X. Shen, H. Xing, and Y. Zhao, Simultaneous determination of fragmentation functions and test on momentum sum rule, Phys. Rev. Lett. 132, 261903 (2024).
- J. Gao, C. Liu, X. Shen, H. Xing, and Y. Zhao, Global analysis of fragmentation functions to charged hadrons with high-precision data from the LHC, Phys. Rev. D 110, 114019 (2024).
- R. Abdul Khalek, V. Bertone, A. Khoudli, and E. R. Nocera (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).
- I. Borsa, R. Sassot, D. de Florian, M. Stratmann, and W. Vogelsang, Towards a global QCD analysis of fragmentation functions at next-to-next-to-leading order accuracy, Phys. Rev. Lett. 129, 012002 (2022).
- R. A. Khalek, V. Bertone, and E. R. Nocera (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).
- E. Moffat, W. Melnitchouk, T. C. Rogers, and N. Sato (Jefferson Lab Angular Momentum (JAM) Collaboration), Simultaneous Monte Carlo analysis of parton densities and fragmentation functions, Phys. Rev. D 104, 016015 (2021).
- J. C. Collins, D. E. Soper, and G. F. Sterman, Factorization of hard processes in QCD, Adv. Ser. Dir. High Energy Phys. 5, 1 (1989).
- J. C. Collins and D. E. Soper, Parton distribution and decay functions, Nucl. Phys. B194, 445 (1982).
- S. Albino, B. A. Kniehl, and G. Kramer, AKK Update: Improvements from new theoretical input and experimental data, Nucl. Phys. B803, 42 (2008).
- C. Alexandrou, M. Arratia, E. C. Aschenauer, A. Avkhadiev, P. V. Balachandran, V. Bertone, I. Borsa, M. Cerutti, X. Chu, W. Cosyn et al., Precision QCD with the electron-ion collider, arXiv:2604.04765.
- 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).
- D. de Florian, R. Sassot, and M. Stratmann, Global analysis of fragmentation functions for protons and charged hadrons, Phys. Rev. D 76, 074033 (2007).
- M. Soleymaninia, M. Goharipour, and H. Khanpour, First QCD analysis of charged hadron fragmentation functions and their uncertainties at next-to-next-to-leading order, Phys. Rev. D 98, 074002 (2018).
- M. Soleymaninia, M. Goharipour, H. Khanpour, and H. Spiesberger, Simultaneous extraction of fragmentation functions of light charged hadrons with mass corrections, Phys. Rev. D 103, 054045 (2021).
- 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).
- J. Gao, C. Liu, M. Li, X. Shen, H. Xing, Y. Zhao, and Y. Zhou, Global analysis of fragmentation functions to light neutral hadrons, Phys. Rev. D 112, 054045 (2025).
- V. Bertone, N. P. Hartland, E. R. Nocera, J. Rojo, and L. Rottoli (NNPDF Collaboration), Charged hadron fragmentation functions from collider data, Eur. Phys. J. C 78, 651 (2018); 84, 155(E) (2024).
- I. Borsa, M. Stratmann, D. de Florian, and R. Sassot, Charged hadron fragmentation functions at high energy colliders, Phys. Rev. D 109, 052004 (2024).
- M. Soleymaninia, H. Hashamipour, and H. Khanpour, Neural network QCD analysis of charged hadron fragmentation functions in the presence of SIDIS data, Phys. Rev. D 105, 114018 (2022).
- G. D. Alexeev et al. (COMPASS Collaboration), Multiplicities of positive and negative pions, kaons, and unidentified hadrons from deep-inelastic scattering of muons off a liquid hydrogen target, Phys. Rev. D 112, 012002 (2025).
- G. D. Alexeev et al. (COMPASS Collaboration), Addendum to multiplicities of charged pions, kaons and unidentified charged hadrons on an isoscalar target measured by COMPASS Collaboration, Phys. Lett. B 875, 140266 (2026).
- C. Adolph et al. (COMPASS Collaboration), Multiplicities of charged pions and charged hadrons from deep-inelastic scattering of muons off an isoscalar target, Phys. Lett. B 764, 1 (2017).
- C. Adolph et al. (COMPASS Collaboration), Multiplicities of charged kaons from deep-inelastic muon scattering off an isoscalar target, Phys. Lett. B 767, 133 (2017).
- R. A. Khalek, V. Bertone, A. Khoudli, and E. R. Nocera, MapCollaboration/montblanc: A code for the determination of collinear distributions, https://github.com/MapCollaboration/MontBlanc.
- R. A. Khalek, V. Bertone, and E. R. Nocera, MapCollaboration/montblanc: Refuge du Goûter, Zenodo, version v1.1, 2022, https://zenodo.org/records/6264693.
- G. Altarelli and G. Parisi, Asymptotic freedom in parton language, Nucl. Phys. B126, 298 (1977).
- Y. L. Dokshitzer, Calculation of the structure functions for deep inelastic scattering and annihilation by perturbation theory in quantum chromodynamics, Sov. Phys. JETP 46, 641 (1977).
- V. N. Gribov and L. N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15, 438 (1972).
- L. N. Lipatov, The parton model and perturbation theory, Yad. Fiz. 20, 181 (1974).
- 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, 094007 (2025).
- L. Bonino, T. Gehrmann, and G. Stagnitto, Semi-inclusive deep-inelastic scattering at next-to-next-to-leading order in QCD, Phys. Rev. Lett. 132, 251901 (2024).
- S. Goyal, S. O. Moch, V. Pathak, N. Rana, and V. Ravindran, Next-to-next-to-leading order QCD corrections to semi-inclusive deep-inelastic scattering, Phys. Rev. Lett. 132, 251902 (2024).
- L. Bonino, T. Gehrmann, M. Löchner, K. Schönwald, and G. Stagnitto, Neutral and charged current semi-inclusive deep-inelastic scattering at NNLO QCD, J. High Energy Phys. 10 (2025) 016.
- M. Abele, D. de Florian, and W. Vogelsang, Approximate NNLO QCD corrections to semi-inclusive DIS, Phys. Rev. D 104, 094046 (2021).
- V. Bertone, S. Carrazza, N. P. Hartland, E. R. Nocera, and J. Rojo (NNPDF Collaboration), A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties, Eur. Phys. J. C 77, 516 (2017).
- G. Altarelli, R. K. Ellis, G. Martinelli, and S. Y. Pi, Processes involving fragmentation functions beyond the leading order in QCD, Nucl. Phys. B160, 301 (1979).
- D. Graudenz, One particle inclusive processes in deeply inelastic lepton—nucleon scattering, Nucl. Phys. B432, 351 (1994).
- A. Mitov, S. Moch, and A. Vogt, Next-to-next-to-leading order evolution of non-singlet fragmentation functions, Phys. Lett. B 638, 61 (2006).
- S. Moch and A. Vogt, On third-order timelike splitting functions and top-mediated Higgs decay into hadrons, Phys. Lett. B 659, 290 (2008).
- A. A. Almasy, S. Moch, and A. Vogt, On the next-to-next-to-leading order evolution of flavour-singlet fragmentation functions, Nucl. Phys. B854, 133 (2012).
- V. Bertone, S. Carrazza, and E. R. Nocera, Reference results for time-like evolution up to , J. High Energy Phys. 03 (2015) 046.
- P. J. Rijken and W. L. van Neerven, Higher order QCD corrections to the transverse and longitudinal fragmentation functions in electron—positron annihilation, Nucl. Phys. B487, 233 (1997).
- P. J. Rijken and W. L. van Neerven, contributions to the longitudinal fragmentation function in annihilation, Phys. Lett. B 386, 422 (1996).
- P. J. Rijken and W. L. van Neerven, contributions to the asymmetric fragmentation function in annihilation, Phys. Lett. B 392, 207 (1997).
- R. D. Ball et al. (NNPDF Collaboration), The path to proton structure at 1% accuracy, Eur. Phys. J. C 82, 428 (2022).
- S. Agarwal, K. Mierle et al., ceres solver, http://ceres-solver.org.
- R. Abdul Khalek and V. Bertone, On the derivatives of feed-forward neural networks, arXiv:2005.07039.
- R. Brandelik et al. (TASSO Collaboration), Charged pion, kaon, proton and anti-proton production in high-energy annihilation, Phys. Lett. 94B, 444 (1980).
- M. Althoff et al. (TASSO Collaboration), Jet production and fragmentation in annihilation at 12-GeV to 43-GeV, Z. Phys. C 22, 307 (1984).
- W. Braunschweig et al. (TASSO Collaboration), Charged multiplicity distributions and correlations in annihilation at PETRA energies, Z. Phys. C 45, 193 (1989).
- H. Aihara et al. (TPC/Two Gamma Collaboration), Charged hadron inclusive cross-sections and fractions in annihiliation , Phys. Rev. Lett. 61, 1263 (1988).
- D. Buskulic et al. (ALEPH Collaboration), Inclusive , and differential cross-sections at the Z resonance, Z. Phys. C 66, 355 (1995).
- P. Abreu et al. (DELPHI Collaboration), , and production in , , , , , Eur. Phys. J. C 5, 585 (1998).
- R. Akers et al. (OPAL Collaboration), Measurement of the production rates of charged hadrons in annihilation at the , Z. Phys. C 63, 181 (1994).
- K. Abe et al. (SLD Collaboration), Production of , , , , p and in light (), and Jets from decays, Phys. Rev. D 69, 072003 (2004).
- P. Abbon, M. Alexeev, H. Angerer, G. Baum, R. Birsa, P. Bordalo, F. Bradamante, A. Bressan, M. Chiosso, P. Ciliberti et al., Particle identification with COMPASS RICH-1, Nucl. Instrum. Methods Phys. Res., Sect. A 631, 26 (2011).
- A. A. Akhundov, D. Bardin, L. Kalinovskaya, and T. Riemann, Model independent QED corrections to the process , Fortschr. Phys. 44, 373 (1996).
- E. C. Aschenauer, A. Bazilevsky, K. Boyle, K. O. Eyser, R. Fatemi, C. Gagliardi, M. Grosse-Perdekamp, J. Lajoie, Z. Kang, Y. Kovchegov et al., The RHIC spin program: Achievements and future opportunities, arXiv:1304.0079.
- H. Spiesberger, DJANGOH, GitHub repository, https://github.com/spiesber/DJANGOH.
- E. C. Aschenauer, T. Burton, T. Martini, H. Spiesberger, and M. Stratmann, Prospects for charged current deep-inelastic scattering off polarized nucleons at a future electron-ion collider, Phys. Rev. D 88, 114025 (2013).
- A. Sandacz and P. Sznajder, HEPGEN—generator for hard exclusive leptoproduction, arXiv:1207.0333.
- A. Accardi, D. P. Anderle, and F. Ringer, Interplay of threshold resummation and hadron mass corrections in deep inelastic processes, Phys. Rev. D 91, 034008 (2015).
- J. V. Guerrero, J. J. Ethier, A. Accardi, S. W. Casper, and W. Melnitchouk, Hadron mass corrections in semi-inclusive deep-inelastic scattering, J. High Energy Phys. 09 (2015) 169.
- M. Boglione, J. Collins, L. Gamberg, J. O. Gonzalez-Hernandez, T. C. Rogers, and N. Sato, Kinematics of current region fragmentation in Semi-Inclusive deeply inelastic scattering, Phys. Lett. B 766, 245 (2017).
- M. Boglione, A. Dotson, L. Gamberg, S. Gordon, J. O. Gonzalez-Hernandez, A. Prokudin, T. C. Rogers, and N. Sato, Mapping the kinematical regimes of semi-inclusive deep inelastic scattering, J. High Energy Phys. 10 (2019) 122.
- 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).
- M. Soleymaninia, H. Khanpour, H. Spiesberger, M. Azizi, M. Klasen, and H. Hashamipour (HAPS Collaboration), HAPS-hFF1.0 Unidentified charged-hadron fragmentation-function grids, GitHub repository (2026), https://github.com/HAPS-Collaboration/HAPS-hFF1.0.
- R. Aaij et al. (LHCb Collaboration), Measurement of charged-hadron distributions in heavy-flavor jets in proton-proton collisions at , J. High Energy Phys. 04 (2026) 029.