- 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

Analysis of nuclear fragmentation functions for pions with A and ν dependence

Mengyang Li1,*, Zijian Ye2,3,†, Jun Gao1,4,‡, XiaoMin Shen3,5,§, Hongxi Xing2,4,6,∥, and Yuxiang Zhao3,4,5,7,¶

  • *Contact author: limengyang@sjtu.edu.cn
  • †Contact author: yezj@m.scnu.edu.cn
  • ‡Contact author: jung49@sjtu.edu.cn
  • §Contact author: xiaominshen@impcas.ac.cn
  • ∥Contact author: hxing@m.scnu.edu.cn
  • Contact author: yxzhao@impcas.ac.cn
PDF

Phys. Rev. D 114, 056023 – Published 23 September, 2026

DOI: https://doi.org/10.1103/wdbl-ncxk

Abstract

We present a QCD analysis of pion nuclear fragmentation functions (nFFs), which encode nuclear modifications to hadronization in high-energy nuclear collisions. Within this framework, vacuum fragmentation functions and their nuclear modifications are extracted simultaneously. The nuclear effects are parametrized as functions of the mass number A, the energy of the fragmenting parton in the target rest frame ν, and the hadron energy fraction z, allowing their dependence on these variables to be quantified. Our analysis includes semi-inclusive deep-inelastic scattering data on nuclear targets, with kinematic cuts chosen to ensure the applicability of perturbative QCD and collinear factorization. The resulting fit provides a good description of most datasets, with the nFFs well constrained in the energy fraction range z∈[0.2,0.7]. Additionally, with our new nFFs, we present next-to-leading order predictions in pp and pA collisions, which show reasonable agreement with ALICE data within the current experimental uncertainties.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (83)

  1. R. D. Field and R. P. Feynman, A parametrization of the properties of quark jets, Nucl. Phys. B136, 1 (1978).
  2. A. Metz and A. Vossen, Parton fragmentation functions, Prog. Part. Nucl. Phys. 91, 136 (2016).
  3. J. C. Collins, D. E. Soper, and G. F. Sterman, Factorization of hard processes in QCD, Nucl. Phys. B308, 833 (1989).
  4. J. C. Collins and D. E. Soper, Back-to-back jets in QCD, Nucl. Phys. B193, 381 (1981); B213, 545(E) (1983).
  5. J. C. Collins and D. E. Soper, Parton distribution and decay functions, Nucl. Phys. B194, 445 (1982).
  6. S. Forte, Parton distributions at the dawn of the LHC, Acta Phys. Pol. B 41, 2859 (2010).
  7. S. Forte and G. Watt, Progress in the determination of the partonic structure of the proton, Annu. Rev. Nucl. Part. Sci. 63, 291 (2013).
  8. J. Rojo et al., The PDF4LHC report on PDFs and LHC data: Results from Run I and preparation for Run II, J. Phys. G 42, 103103 (2015).
  9. K. Kovařík, P. M. Nadolsky, and D. E. Soper, Hadronic structure in high-energy collisions, Rev. Mod. Phys. 92, 045003 (2020).
  10. D. de Florian and R. Sassot, Nuclear parton distributions at next-to-leading order, Phys. Rev. D 69, 074028 (2004).
  11. M. Hirai, S. Kumano, and T. H. Nagai, Determination of nuclear parton distribution functions and their uncertainties in next-to-leading order, Phys. Rev. C 76, 065207 (2007).
  12. K. J. Eskola, H. Paukkunen, and C. A. Salgado, Nuclear PDFs at NLO—status report and review of the EPS09 results, Nucl. Phys. A855, 150 (2011).
  13. M. Klasen and H. Paukkunen, Nuclear parton distribution functions after the first decade of LHC data, Annu. Rev. Nucl. Part. Sci. 74, 49 (2024).
  14. P. Duwentäster, T. Ježo, M. Klasen, K. Kovařík, A. Kusina, K. F. Muzakka, F. I. Olness, R. Ruiz, I. Schienbein, and J. Y. Yu, Impact of heavy quark and quarkonium data on nuclear gluon PDFs, Phys. Rev. D 105, 114043 (2022).
  15. N. Derakhshanian, P. Risse, T. Jezo, M. Klasen, K. Kovarik, and A. Kusina, Determination of nuclear PDFs using Markov Chain Monte Carlo methods, arXiv:2603.13150.
  16. M. Klasen, nCTEQ global analysis of nuclear PDFs, Proc. Sci. DIS2025 (2025) 036 [arXiv:2510.05880].
  17. M. Klasen, Global analysis of nuclear parton distribution functions, Proc. Sci. DIS2024 (2025) 002 [arXiv:2407.10719].
  18. A. V. Kotikov and A. V. Lipatov, A simple model for nuclear modification of parton distribution functions, Chin. Phys. C 50, 034109 (2026).
  19. M. R. Adams et al. (E665 Collaboration), Scaled energy (z) distributions of charged hadrons observed in deep inelastic muon scattering at 490-GeV from xenon and deuterium targets, Phys. Rev. D 50, 1836 (1994).
  20. A. Airapetian et al. (HERMES Collaboration), Transverse momentum broadening of hadrons produced in semi-inclusive deep-inelastic scattering on nuclei, Phys. Lett. B 684, 114 (2010).
  21. S. S. Adler et al. (PHENIX Collaboration), Centrality dependence of π0 and η production at large transverse momentum in sNN=200−GeV d+Au collisions, Phys. Rev. Lett. 98, 172302 (2007).
  22. J. Adams et al. (STAR Collaboration), Pion, kaon, proton and anti-proton transverse momentum distributions from p+p and d+Au collisions at sNN=200  GeV, Phys. Lett. B 616, 8 (2005).
  23. J. Adams et al. (STAR Collaboration), Identified hadron spectra at large transverse momentum in p+p and d+Au collisions at sNN=200−GeV, Phys. Lett. B 637, 161 (2006).
  24. O. Grebenyuk, Neutral meson production in d+Au and p+p collisions at 200 GeV in STAR, Ph.D. thesis, Utrecht University, 2007.
  25. F. Arleo (Medium-Modified Collaboration), Fragmentation functions, Eur. Phys. J. C 61, 603 (2009).
  26. R. Baier, D. Schiff, and B. G. Zakharov, Energy loss in perturbative QCD, Annu. Rev. Nucl. Part. Sci. 50, 37 (2000).
  27. A. Kovner and U. A. Wiedemann, Gluon radiation and parton energy loss, arXiv:hep-ph/0304151.
  28. M. Gyulassy, I. Vitev, X.-N. Wang, and B.-W. Zhang, Jet Quenching and Radiative Energy Loss in Dense Nuclear Matter (World Scientific, Singapore, 2004), pp. 123–191.
  29. A. Majumder, A comparative study of jet-quenching schemes, J. Phys. G 34, S377 (2007).
  30. R. Sassot, M. Stratmann, and P. Zurita, Fragmentations functions in nuclear media, Phys. Rev. D 81, 054001 (2010).
  31. M. Doradau, R. T. Martinez, R. Sassot, and M. Stratmann, Pion nuclear fragmentation functions revisited, Phys. Rev. D 111, 034045 (2025).
  32. M. Alrashed, D. Anderle, Z.-B. Kang, J. Terry, and H. Xing, Three-dimensional imaging in nuclei, Phys. Rev. Lett. 129, 242001 (2022).
  33. M. Alrashed, Z.-B. Kang, J. Terry, H. Xing, and C. Zhang, Nuclear modified transverse momentum dependent parton distribution and fragmentation functions, arXiv:2312.09226.
  34. P. C. Barry, L. Gamberg, W. Melnitchouk, E. Moffat, D. Pitonyak, A. Prokudin, and N. Sato (Jefferson Lab Angular Momentum (JAM) Collaboration), Tomography of pions and protons via transverse momentum dependent distributions, Phys. Rev. D 108, L091504 (2023).
  35. A. Airapetian et al. (HERMES Collaboration), Hadronization in semi-inclusive deep-inelastic scattering on nuclei, Nucl. Phys. B780, 1 (2007).
  36. A. Airapetian et al. (HERMES Collaboration), Multidimensional study of hadronization in nuclei, Eur. Phys. J. A 47, 113 (2011).
  37. S. Moran et al. (CLAS Collaboration), Measurement of charged-pion production in deep-inelastic scattering off nuclei with the CLAS detector, Phys. Rev. C 105, 015201 (2022).
  38. F. Ceccopieri and R. Dupré, Transverse-momentum dependent model for hadronization in deep-inelastic lepton-nucleus scattering off heavy nuclei, Phys. Rev. C 110, 045202 (2024).
  39. A. Kusina et al., Impact of LHC vector boson production in heavy ion collisions on strange PDFs, Eur. Phys. J. C 80, 968 (2020).
  40. R. Abdul Khalek, R. Gauld, T. Giani, E. R. Nocera, T. R. Rabemananjara, and J. Rojo, nNNPDF3.0: Evidence for a modified partonic structure in heavy nuclei, Eur. Phys. J. C 82, 507 (2022).
  41. K. J. Eskola, P. Paakkinen, H. Paukkunen, and C. A. Salgado, EPPS21: A global QCD analysis of nuclear PDFs, Eur. Phys. J. C 82, 413 (2022).
  42. A. Airapetian et al. (HERMES Collaboration), Multiplicities of charged pions and kaons from semi-inclusive deep-inelastic scattering by the proton and the deuteron, Phys. Rev. D 87, 074029 (2013).
  43. A. Airapetian et al. (HERMES Collaboration), Multiplicity of charged and neutral pions in deep inelastic scattering of 27.5-GeV positrons on hydrogen, Eur. Phys. J. C 21, 599 (2001).
  44. K. Abe et al. (SLD Collaboration), Production of π+, π−, K+, K−, p and p¯ in light (uds), c and b jets from Z0 decays, Phys. Rev. D 69, 072003 (2004).
  45. P. Nason and B. R. Webber, Scaling violation in e+ e− fragmentation functions: QCD evolution, hadronization and heavy quark mass effects, Nucl. Phys. B421, 473 (1994); B480, 755(E) (1996).
  46. W. Furmanski and R. Petronzio, Lepton—hadron processes beyond leading order in quantum chromodynamics, Z. Phys. C 11, 293 (1982).
  47. D. Graudenz, One particle inclusive processes in deeply inelastic lepton—nucleon scattering, Nucl. Phys. B432, 351 (1994).
  48. 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).
  49. D. de Florian and Y. Rotstein Habarnau, Polarized semi-inclusive electroweak structure functions at next-to-leading-order, Eur. Phys. J. C 73, 2356 (2013).
  50. 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).
  51. 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).
  52. J. Gao, H. T. Li, H. X. Zhu, and Y. J. Zhu, Transeverse-momentum subtraction for semi-inclusive deep-inelastic scattering, arXiv:2602.06364.
  53. M. Abele, D. de Florian, and W. Vogelsang, Approximate NNLO QCD corrections to semi-inclusive DIS, Phys. Rev. D 104, 094046 (2021).
  54. M. Abele, D. de Florian, and W. Vogelsang, Threshold resummation at N3LL accuracy and approximate N3LO corrections to semi-inclusive DIS, Phys. Rev. D 106, 014015 (2022).
  55. C.-Q. He, H. Xing, T.-Z. Yang, and H. X. Zhu, Single-inclusive hadron production in electron-positron annihilation at next-to-next-to-next-to-leading order in QCD, Phys. Rev. Lett. 135, 101901 (2025).
  56. L. Dong, S. Fang, J. Gao, H. T. Li, D. Y. Shao, and Y. J. Zhu, Next-to-next-to-leading-order QCD corrections to hadron production in deep-inelastic scattering at finite transverse momentum, Phys. Rev. Lett. 137, 081902 (2026).
  57. L. Dong, S. Fang, J. Gao, H. T. Li, D. Y. Shao, H. X. Zhu, and Y. J. Zhu, Two-dimensional transverse-momentum subtraction and semi-inclusive deep-inelastic scattering at N3LO in QCD, arXiv:2603.29673.
  58. V. N. Gribov and L. N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15, 438 (1972).
  59. L. N. Lipatov, The parton model and perturbation theory, Yad. Fiz. 20, 181 (1974).
  60. G. Altarelli and G. Parisi, Asymptotic freedom in parton language, Nucl. Phys. B126, 298 (1977).
  61. Y. L. Dokshitzer, Calculation of the structure functions for deep inelastic scattering and e+e− annihilation by perturbation theory in quantum chromodynamics, Sov. Phys. JETP 46, 641 (1977).
  62. 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).
  63. S. Moch and A. Vogt, On third-order timelike splitting functions and top-mediated Higgs decay into hadrons, Phys. Lett. B 659, 290 (2008).
  64. 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).
  65. H. Chen, T.-Z. Yang, H. X. Zhu, and Y. J. Zhu, Analytic continuation and reciprocity relation for collinear splitting in QCD, Chin. Phys. C 45, 043101 (2021).
  66. M. A. Ebert, B. Mistlberger, and G. Vita, TMD fragmentation functions at N3LO, J. High Energy Phys. 07 (2021) 121.
  67. M.-x. Luo, T.-Z. Yang, H. X. Zhu, and Y. J. Zhu, Unpolarized quark and gluon TMD PDFs and FFs at N3LO, J. High Energy Phys. 06 (2021) 115.
  68. G. Curci, W. Furmanski, and R. Petronzio, Evolution of parton densities beyond leading order: The nonsinglet case, Nucl. Phys. B175, 27 (1980).
  69. W. Furmanski and R. Petronzio, Singlet parton densities beyond leading order, Phys. Lett. 97B, 437 (1980).
  70. 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).
  71. 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).
  72. 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).
  73. M. Stratmann and W. Vogelsang, Next-to-leading order evolution of polarized and unpolarized fragmentation functions, Nucl. Phys. B496, 41 (1997).
  74. G. Salam and J. Rojo, A higher order perturbative parton evolution toolkit (HOPPET), Comput. Phys. Commun. 180, 120 (2009).
  75. G. Salam and J. Rojo, The HOPPET NNLO parton evolution package, arXiv:0807.0198.
  76. C. Liu, X. Shen, B. Zhou, and J. Gao, Automated calculation of jet fragmentation at NLO in QCD, J. High Energy Phys. 09 (2023) 108.
  77. J. Pumplin, D. R. Stump, J. Huston, H.-L. Lai, P. Nadolsky, and W.-K. Tung, New generation of parton distributions with uncertainties from global QCD analysis, J. High Energy Phys. 07 (2002) 012.
  78. F. James and M. Roos, minuit—A system for function minimization and analysis of the parameter errors and correlations, Comput. Phys. Commun. 10, 343 (1975).
  79. J. Pumplin, D. R. Stump, and W. K. Tung, Multivariate fitting and the error matrix in global analysis of data, Phys. Rev. D 65, 014011 (2001).
  80. 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).
  81. A. W. Denniston et al. (nCTEQ Collaboration), Modification of quark-gluon distributions in nuclei by correlated nucleon pairs, Phys. Rev. Lett. 133, 152502 (2024).
  82. X.-N. Wang and X. Guo, Multiple parton scattering in nuclei: Parton energy loss, Nucl. Phys. A696, 788 (2001).
  83. S. Acharya et al. (ALICE Collaboration), Measurement of isolated photon-hadron correlations in sNN=5.02  TeV pp and p-Pb collisions, Phys. Rev. C 102, 044908 (2020).

Outline

Information

Phys. Rev. D 114, 056023– Published 23 September, 2026
  • Received 9 July 2026
  • Accepted 31 August 2026
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