- Physical Review Journals
All JournalsPhysics Magazine

Physical Review C

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

Pseudorapidity dependence of charged-particle production in nonsingle diffractive pp collisions in the PACIAE 4.0 model

Zhen Xie1, An-Ke Lei2,3, Hua Zheng1,*, Wen-Chao Zhang1, Dai-Mei Zhou3,†, Zhi-Lei She4, Yu-Liang Yan5, and Ben-Hao Sa3,5,‡

  • *Contact author: zhengh@snnu.edu.cn
  • †Contact author: zhoudm@mail.ccnu.edu.cn
  • ‡Contact author: sabhliuym35@qq.com
PDF

Phys. Rev. C 113, 034907 – Published 11 March, 2026

DOI: https://doi.org/10.1103/t91y-sdgy

Abstract

Studying experimental observables is a key benchmark for validating theoretical models in high energy physics. In this work, we employ the PACIAE 4.0 model to simulate nonsingle diffractive proton-proton (pp) collisions at center-of-mass energies of 0.9, 2.36, and 7 TeV, comparing the results with compact muon solenoid (CMS) experimental data on charged-particle pseudorapidity densities and transverse momentum spectra across different pseudorapidity bins, respectively. Our results show good agreement with the CMS data, particularly only using a single set of parameters for all collision energies. This demonstrates that the PACIAE 4.0 model can serve as a reliable tool for systematically studying the physics of NSD pp collisions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (61)

  1. J. Adam, et al. (ALICE Collaboration), Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions, Nat. Phys. 13, 535 (2017).
  2. V. Khachatryan, et al. (CMS Collaboration), Evidence for collectivity in pp collisions at the LHC, Phys. Lett. B 765, 193 (2017).
  3. J. Adams, et al. (STAR Collaboration), Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions, Nucl. Phys. A 757, 102 (2005).
  4. B. B. Back, et al. (PHOBOS Collaboration), The PHOBOS perspective on discoveries at RHIC, Nucl. Phys. A 757, 28 (2005).
  5. B. Alver, et al. (PHOBOS Collaboration), Phobos results on charged particle multiplicity and pseudorapidity distributions in Au+Au, Cu+Cu, d+Au, and p+p collisions at ultra-relativistic energies, Phys. Rev. C 83, 024913 (2011).
  6. 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).
  7. B. I. Abelev, et al. (STAR Collaboration), Strange particle production in p+p collisions at s = 200-GeV, Phys. Rev. C 75, 064901 (2007).
  8. E. Abbas, et al. (ALICE Collaboration), Centrality dependence of the pseudorapidity density distribution for charged particles in Pb-Pb collisions at sNN = 2.76 TeV, Phys. Lett. B 726, 610 (2013).
  9. J. Adam, et al. (ALICE Collaboration), Charged-particle multiplicities in proton–proton collisions at s=0.9 to 8 TeV, Eur. Phys. J. C 77, 33 (2017).
  10. S. Acharya, et al. (ALICE Collaboration), Production of charged pions, kaons, and (anti-)protons in Pb-Pb and inelastic pp collisions at sNN = 5.02 TeV, Phys. Rev. C 101, 044907 (2020).
  11. B. B. Abelev, et al. (ALICE Collaboration), Production of charged pions, kaons and protons at large transverse momenta in pp and Pb–Pb collisions at sNN =2.76 TeV, Phys. Lett. B 736, 196 (2014).
  12. J. Adam, et al. (ALICE Collaboration), Measurement of pion, kaon and proton production in proton–proton collisions at s=7 TeV, Eur. Phys. J. C 75, 226 (2015).
  13. J. Adam, et al. (ALICE Collaboration), Pseudorapidity and transverse-momentum distributions of charged particles in proton–proton collisions at s= 13 TeV, Phys. Lett. B 753, 319 (2016).
  14. K. Aamodt, et al. (ALICE Collaboration), Charged-particle multiplicity measurement in proton-proton collisions at s=0.9 and 2.36 TeV with ALICE at LHC, Eur. Phys. J. C 68, 89 (2010).
  15. K. Aamodt, et al. (ALICE Collaboration), Production of pions, kaons and protons in pp collisions at s=900 GeV with ALICE at the LHC, Eur. Phys. J. C 71, 1655 (2011).
  16. S. Acharya, et al. (ALICE Collaboration), Pseudorapidity densities of charged particles with transverse momentum thresholds in pp collisions at s=5.02 and 13 TeV, Phys. Rev. D 108, 072008 (2023).
  17. K. Werner, J. Jahan, I. Karpenko, T. Pierog, M. Stefaniak, and D. Vintache, Heavy ion collisions from sNN of 62.4 GeV down to 7.7 GeV in the EPOS4 framework, Phys. Rev. C 111, 014903 (2025).
  18. M. Waqas, G. X. Peng, M. Ajaz, A. M. Khubrani, E. A. Dawi, M. A. Khan, and A. Tawfik, Pseudorapidity dependence of the transverse momentum distribution of charged particles in pp collisions at 0.9, 2.36, and 7 TeV, Results Phys. 42, 105989 (2022).
  19. M. Ajaz, A. A. K. Haj Ismail, M. Waqas, M. Suleymanov, A. AbdelKader, and R. Suleymanov, Pseudorapidity dependence of the bulk properties of hadronic medium in pp collisions at 7 TeV, Sci. Rep. 12, 8142 (2022).
  20. J. Tao, H. He, H. Zheng, W. Zhang, X. Liu, L. Zhu, and A. Bonasera, Pseudo-rapidity distributions of charged particles in asymmetric collisions using Tsallis thermodynamics, Nucl. Sci. Technol. 34, 172 (2023).
  21. P.-P. Yang, M. Ajaz, M. Waqas, F.-H. Liu, and M. K. Suleymanov, Pseudorapidity dependence of the pT spectra of charged hadrons in pp collisions at s = 0.9 and 2.36 TeV, J. Phys. G 49, 055110 (2022).
  22. A.-G. Zhang, X.-Y. Peng, X. Peng, and L. Zheng, Exploring the multiplicity dependence of the flavor hierarchy for hadron production in high-energy pp collisions, Nucl. Sci. Technol. 36, 134 (2025).
  23. L. Adamczyk, et al. (STAR Collaboration), Bulk properties of the medium produced in relativistic heavy-ion collisions from the beam energy scan program, Phys. Rev. C 96, 044904 (2017).
  24. A. Toia (ALICE Collaboration), Bulk properties of Pb-Pb collisions at sNN=2.76 TeV measured by ALICE, J. Phys. G 38, 124007 (2011).
  25. A. Deppman, E. Megias, and D. P. Menezes, Fractals, nonextensive statistics, and QCD, Phys. Rev. D 101, 034019 (2020).
  26. J.-H. Shi, Z.-Y. Qin, J.-P. Zhang, J. Cao, Z.-F. Jiang, W.-C. Zhang, and H. Zheng, Nonextensive (3+1)-dimensional hydrodynamics for relativistic heavy-ion collisions, Phys. Rev. D 111, 036010 (2025).
  27. J. Tao, W. Wu, M. Wang, H. Zheng, W. Zhang, L. Zhu, and A. Bonasera, The novel scaling of Tsallis parameters from the transverse momentum spectra of charged particles in heavy-ion collisions, Particles 5, 146 (2022).
  28. L.-L. Zhu, B. Wang, M. Wang, and H. Zheng, Energy and centrality dependence of light nuclei production in relativistic heavy-ion collisions, Nucl. Sci. Technol. 33, 45 (2022).
  29. L. Zhu, H. Zheng, K. Da, H. Gong, Z. Ye, G. Liu, and R. C. Hwa, Universal energy dependence of measured temperatures for baryons produced in heavy-ion collisions, Phys. Rev. C 107, 064907 (2023).
  30. J. Q. Tao, M. Wang, H. Zheng, W. C. Zhang, L. L. Zhu, and A. Bonasera, Pseudorapidity distributions of charged particles in pp(p¯), p(d)A and AA collisions using Tsallis thermodynamics, J. Phys. G 48, 105102 (2021).
  31. L. Zhu, H. Zheng, and R. C. Hwa, Centrality and transverse-momentum dependence of hadrons in Pb+Pb collisions at energies available at the CERN Large Hadron Collider, Phys. Rev. C 104, 014902 (2021).
  32. H. Zheng and L. Zhu, Comparing the Tsallis distribution with and without thermodynamical description in p+p collisions, Adv. High Energy Phys. 2016, 9632126 (2016).
  33. M. Wang, J.-Q. Tao, H. Zheng, W.-C. Zhang, L.-L. Zhu, and A. Bonasera, Number-of-constituent-quark scaling of elliptic flow: A quantitative study, Nucl. Sci. Technol. 33, 37 (2022).
  34. L. Zhu, H. Zheng, and R. Kong, Centrality and transverse momentum dependencies of hadrons in Pb+Pb collisions at sNN=5.02 TeV and Xe+Xe collisions at sNN=5.44 TeV from a multi-phase transport model, Eur. Phys. J. A 55, 205 (2019).
  35. Y. Gao, H. Zheng, L. L. Zhu, and A. Bonasera, Description of charged particle pseudorapidity distributions in Pb+Pb collisions with Tsallis thermodynamics, Eur. Phys. J. A 53, 197 (2017).
  36. H. Zheng and L. Zhu, Can Tsallis distribution fit all the particle spectra produced at RHIC and LHC? Adv. High Energy Phys. 2015, 180491 (2015).
  37. H. Zheng, L. Zhu, and A. Bonasera, Systematic analysis of hadron spectra in p+p collisions using Tsallis distributions, Phys. Rev. D 92, 074009 (2015).
  38. C.-Y. Wong, G. Wilk, L. J. L. Cirto, and C. Tsallis, From QCD-based hard-scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high-energy pp and pp¯ collisions, Phys. Rev. D 91, 114027 (2015).
  39. R. Rath, A. Khuntia, R. Sahoo, and J. Cleymans, Event multiplicity, transverse momentum and energy dependence of charged particle production, and system thermodynamics in pp collisions at the Large Hadron Collider, J. Phys. G 47, 055111 (2020).
  40. J. Xu and C. M. Ko, Chemical freeze-out in relativistic heavy-ion collisions, Phys. Lett. B 772, 290 (2017).
  41. W. Zhao, C. M. Ko, Y.-X. Liu, G.-Y. Qin, and H. Song, Probing the partonic degrees of freedom in high-multiplicity p−Pb collisions at sNN = 5.02 TeV, Phys. Rev. Lett. 125, 072301 (2020).
  42. W. Zhao, W. Ke, W. Chen, T. Luo, and X.-N. Wang, From hydrodynamics to jet quenching, coalescence, and hadron cascade: A coupled approach to solving the RAA⊗v2 puzzle, Phys. Rev. Lett. 128, 022302 (2022).
  43. T. Sjostrand, S. Mrenna, and P. Z. Skands, PYTHIA 6.4 physics and manual, J. High Energy Phys. 05 (2006) 026.
  44. C. Bierlich, et al., A comprehensive guide to the physics and usage of PYTHIA 8.3, SciPost Phys. Codebases, 8 (2022).
  45. G. Corcella, I. G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. H. Seymour, and B. R. Webber, HERWIG 6: An event generator for hadron emission reactions with interfering gluons (including supersymmetric processes), J. High Energy Phys. 01 (2001) 010.
  46. X.-N. Wang and M. Gyulassy, HIJING: A Monte Carlo model for multiple jet production in pp, pA and AA collisions, Phys. Rev. D 44, 3501 (1991).
  47. Z.-W. Lin, C. M. Ko, B.-A. Li, B. Zhang, and S. Pal, A multi-phase transport model for relativistic heavy ion collisions, Phys. Rev. C 72, 064901 (2005).
  48. J. Weil, V. Steinberg, J. Staudenmaier, L. G. Pang, D. Oliinychenko, J. Mohs, M. Kretz, T. Kehrenberg, A. Goldschmidt, B. Bäuchle, J. Auvinen, M. Attems, and H. Petersen, Particle production and equilibrium properties within a new hadron transport approach for heavy-ion collisions, Phys. Rev. C 94, 054905 (2016).
  49. B.-H. Sa, D.-M. Zhou, Y.-L. Yan, X.-M. Li, S.-Q. Feng, B.-G. Dong, and X. Cai, PACIAE 2.0: An updated parton and hadron cascade model (program) for the relativistic nuclear collisions, Comput. Phys. Commun. 183, 333 (2012).
  50. A.-K. Lei, Y.-L. Yan, D.-M. Zhou, Z.-L. She, L. Zheng, G.-C. Yong, X.-M. Li, G. Chen, X. Cai, and B.-H. Sa, Introduction to the parton and hadron cascade model PACIAE 3.0, Phys. Rev. C 108, 064909 (2023).
  51. A.-K. Lei, Z.-L. She, Y.-L. Yan, D.-M. Zhou, L. Zheng, W.-C. Zhang, H. Zheng, L. V. Bravina, E. E. Zabrodin, and B.-H. Sa, A brief introduction to PACIAE 4.0, Comput. Phys. Commun. 310, 109520 (2025).
  52. P. Z. Skands, Tuning Monte Carlo generators: The Perugia tunes, Phys. Rev. D 82, 074018 (2010).
  53. P. Skands, S. Carrazza, and J. Rojo, Tuning PYTHIA 8.1: the Monash 2013 Tune, Eur. Phys. J. C 74, 3024 (2014).
  54. V. Khachatryan, et al. (CMS Collaboration), Event generator tunes obtained from underlying event and multiparton scattering measurements, Eur. Phys. J. C 76, 155 (2016).
  55. Z. Xie, A.-K. Lei, H. Zheng, W. Zhang, D.-M. Zhou, Z.-L. She, Y.-L. Yan, and B.-H. Sa, Pseudorapidity density distributions of charged particles and transverse-momentum spectra of identified particles in pp collisions in the PACIAE 4.0 model, Phys. Rev. C 112, 014908 (2025).
  56. V. Khachatryan, et al. (CMS Collaboration), Transverse momentum and pseudorapidity distributions of charged Hadrons in pp collisions at s=0.9 and 2.36 TeV, J. High Energy Phys. 02 (2010) 041.
  57. V. Khachatryan, et al. (CMS Collaboration), Transverse-momentum and pseudorapidity distributions of charged hadrons in pp collisions at s=7 TeV, Phys. Rev. Lett. 105, 022002 (2010).
  58. B. L. Combridge, J. Kripfganz, and J. Ranft, Hadron production at large transverse momentum and QCD, Phys. Lett. B 70, 234 (1977).
  59. R. D. Field, Applications of Perturbative QCD (Addison-Wesley Publishing Company, New York, 1989).
  60. B. Andersson, G. Gustafson, G. Ingelman, and T. Sjostrand, Parton fragmentation and string dynamics, Phys. Rep. 97, 31 (1983).
  61. M. Waqas, M. Ajaz, A. H. Ismail, A. Tawfik, M. B. Ammar, and H. I. Alrebdi, Bulk properties of charged particles as a function of pseudo-rapidity in pp collisions, Eur. Phys. J. A 60, 123 (2024).

Outline

Information

Phys. Rev. C 113, 034907– Published 11 March, 2026
  • Received 7 August 2025
  • Revised 30 October 2025
  • Accepted 20 February 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