- 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

3D initial-state dynamics across scales: A comparative study of saturation and string-based descriptions

Lucas Constantin1,*, Oscar Garcia-Montero2, Niklas Götz1, and Hannah Elfner3,1,4

  • *Contact author: constantin@itp.uni-frankfurt.de
PDF

Phys. Rev. C 114, 044906 – Published 21 October, 2026

DOI: https://doi.org/10.1103/1ptt-tdqx

Abstract

We compare the longitudinal deposition of various conserved quantities in the initial condition models of a string based (SMASH) and a saturation based (McDipper) approach. SMASH has been shown to work reasonably well at lower collision energies as an initial condition for the SMASH-vHLLE hybrid approach, while McDipper, based on the color-glass-condensate, works well in the regime of perturbative quantum chromodynamics. The two models are capable of providing longitudinally resolved initial conditions, which is essential for three-dimensional hydrodynamical simulations. The goal of this study is to interface the different regions of applicability of the two models, to investigate the initial state dynamics in the intermediate energy regime. We analyze the deposition of transverse energy, charge and baryon number across a large range of collision energies (62.4 GeV to 5.02 TeV) and find that, while they are good agreement at lower energies, their energy and baryon deposition differs substantially at higher center of mass energies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (60)

  1. J. Berges, M. P. Heller, A. Mazeliauskas, and R. Venugopalan, QCD thermalization: Ab initio approaches and interdisciplinary connections, Rev. Mod. Phys. 93, 035003 (2021).
  2. M. Arslandok, S. A. Bass, A. A. Baty, I. Bautista, C. Beattie, F. Becattini, R. Bellwied, Y. Berdnikov, A. Berdnikov, J. Bielcik, J. T. Blair, et al., Hot QCD white paper, arXiv:2303.17254.
  3. U. Heinz and R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Annu. Rev. Nucl. Part. Sci. 63, 123 (2013).
  4. H. Mäntysaari, Theoretical developments on the initial state in relativistic particle collisions, EPJ Web Conf. 296, 01019 (2024).
  5. J. D. Bjorken, Highly relativistic nucleus-nucleus collisions: The central rapidity region, Phys. Rev. D 27, 140 (1983).
  6. L.-G. Pang, H. Petersen, G.-Y. Qin, V. Roy, and X.-N. Wang, Decorrelation of anisotropic flow along the longitudinal direction, Eur. Phys. J. A 52, 97 (2016).
  7. G. Aad et al. (ATLAS Collaboration), Measurements of longitudinal flow decorrelations in pp and Xe+Xe collisions with the ATLAS detector, arXiv:2308.16745.
  8. I. G. Bearden et al. (BRAHMS Collaboration), Nuclear stopping in Au + Au collisions at sNN=200 GeV, Phys. Rev. Lett. 93, 102301 (2004).
  9. F. Becattini, F. Piccinini, and J. Rizzo, Angular momentum conservation in heavy ion collisions at very high energy, Phys. Rev. C 77, 024906 (2008).
  10. H.-Z. Wu, L.-G. Pang, X.-G. Huang, and Q. Wang, Local spin polarization in high energy heavy ion collisions, Phys. Rev. Res. 1, 033058 (2019).
  11. X.-G. Huang, J. Liao, Q. Wang, and X.-L. Xia, Vorticity and spin polarization in heavy ion collisions: Transport models, in Lecture Notes in Physics, edited by F. Becattini, J. Liao, and M. Lisa (Springer, Cham, 2021), Vol. 987.
  12. N. Sass, M. Müller, O. Garcia-Montero, and H. Elfner(SMASH Collaboration), Global angular momentum generation in heavy-ion reactions within a hadronic transport approach, Phys. Rev. C 108, 044903 (2023).
  13. M. E. Carrington and S. Mrówczyński, Angular momentum of glasma, Phys. Rev. C 113, 064910 (2026).
  14. O. Garcia-Montero, H. Elfner, and S. Schlichting, McDIPPER: A novel saturation-based 3+1D initial-state model for heavy ion collisions, Phys. Rev. C 109, 044916 (2024).
  15. L. D. McLerran and R. Venugopalan, Computing quark and gluon distribution functions for very large nuclei, Phys. Rev. D 49, 2233 (1994).
  16. 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, (SMASH Collaboration) Particle production and equilibrium properties within a new hadron transport approach for heavy-ion collisions, Phys. Rev. C 94, 054905 (2016).
  17. H. Elfner and R. Góes-Hirayama, SMASH: Results from hadronic transport for heavy-ion collisions at high densities, arXiv:2508.21477.
  18. A. Schäfer, I. Karpenko, X.-Y. Wu, J. Hammelmann, and H. Elfner(SMASH Collaboration), Particle production in a hybrid approach for a beam energy scan of Au+Au/Pb+Pb collisions between sNN = 4.3 GeV and sNN = 200.0 GeV, Eur. Phys. J. A 58, 230 (2022).
  19. B. Schenke, P. Tribedy, and R. Venugopalan, Fluctuating glasma initial conditions and flow in heavy ion collisions, Phys. Rev. Lett. 108, 252301 (2012).
  20. H. Niemi, K. J. Eskola, and R. Paatelainen, Event-by-event fluctuations in a perturbative QCD + saturation + hydrodynamics model: Determining QCD matter shear viscosity in ultrarelativistic heavy-ion collisions, Phys. Rev. C 93, 024907 (2016).
  21. M. Kuha, J. Auvinen, K. J. Eskola, H. Hirvonen, Y. Kanakubo, and H. Niemi, Monte Carlo event generator MC-EKRT with saturated minijet production for initializing (3+1)D fluid dynamics in high-energy nuclear collisions, Phys. Rev. C 111, 054914 (2025).
  22. 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).
  23. C. Shen and S. Alzhrani, Collision-geometry-based 3D initial condition for relativistic heavy-ion collisions, Phys. Rev. C 102, 014909 (2020).
  24. D. Soeder, W. Ke, J. F. Paquet, and S. A. Bass, Bayesian parameter estimation with a new three-dimensional initial-conditions model for ultrarelativistic heavy-ion collisions, arXiv:2306.08665.
  25. O. Garcia-Montero, MCDIPPER, 2023, accessed Aug. 21, 2023, https://github.com/Non-Equilibrium-QCD/McDipper.
  26. O. Garcia-Montero and S. Schlichting, Effective theories for nuclei at high energies, Eur. Phys. J. A 61, 54 (2025).
  27. A. Dumitru and L. D. McLerran, How protons shatter colored glass, Nucl. Phys. A 700, 492 (2002).
  28. T. Lappi and S. Schlichting, Linearly polarized gluons and axial charge fluctuations in the glasma, Phys. Rev. D 97, 034034 (2018).
  29. J. P. Blaizot, F. Gelis, and R. Venugopalan, High-energy pA collisions in the color glass condensate approach. II: Quark production, Nucl. Phys. A 743, 57 (2004).
  30. F. Gelis and A. Peshier, Probing colored glass via qq¯ photoproduction, Nucl. Phys. A 697, 879 (2002).
  31. F. Gelis and A. Peshier, Probing colored glass via qq¯ photoproduction. II: Diffraction, Nucl. Phys. A 707, 175 (2002).
  32. A. Dumitru and J. Jalilian-Marian, Forward quark jets from protons shattering the colored glass, Phys. Rev. Lett. 89, 022301 (2002).
  33. A. Dumitru, A. Hayashigaki, and J. Jalilian-Marian, The color glass condensate and hadron production in the forward region, Nucl. Phys. A 765, 464 (2006).
  34. H. Kowalski and D. Teaney, An impact parameter dipole saturation model, Phys. Rev. D 68, 114005 (2003).
  35. A. H. Rezaeian, M. Siddikov, M. Van de Klundert, and R. Venugopalan, Analysis of combined HERA data in the impact-parameter dependent saturation model, Phys. Rev. D 87, 034002 (2013).
  36. D. d'Enterria and C. Loizides, Progress in the Glauber model at collider energies, Annu. Rev. Nucl. Part. Sci. 71, 315 (2021).
  37. O. Garcia-Montero, S. Schlichting, and J. Zhu, Effects of subnucleonic fluctuations on the longitudinal structure of heavy-ion collisions, Phys. Rev. D 111, 076029 (2025).
  38. H. Kowalski, L. Motyka, and G. Watt, Exclusive diffractive processes at HERA within the dipole picture, Phys. Rev. D 74, 074016 (2006).
  39. C. Bierlich, S. Chakraborty, N. Desai, L. Gellersen, I. Helenius, P. Ilten, L. Lönnblad, S. Mrenna, S. Prestel, C. T. Preuss, T. Sjöstrand, P. Skands, M. Utheim, and R. Verheyen, A comprehensive guide to the physics and usage of PYTHIA 8.3, SciPost Phys. Codebases 8 (2022).
  40. P. Skands, S. Carrazza, and J. Rojo, Tuning PYTHIA 8.1: The Monash 2013 tune, Eur. Phys. J. C 74, 3024 (2014).
  41. N. Götz, I. Karpenko, and H. Elfner, Bayesian analysis of a (3+1)D hybrid approach with initial conditions from hadronic transport, Phys. Rev. C 112, 014910 (2025).
  42. G. Giacalone, G. Nijs, and W. van der Schee, Determination of the neutron skin of Pb208 from ultrarelativistic nuclear collisions, Phys. Rev. Lett. 131, 202302 (2023).
  43. G. Nijs, W. van der Schee, U. Gürsoy, and R. Snellings, Bayesian analysis of heavy ion collisions with the heavy ion computational framework Trajectum, Phys. Rev. C 103, 054909 (2021).
  44. G. Nijs, W. van der Schee, U. Gürsoy, and R. Snellings, Transverse momentum differential global analysis of heavy-ion collisions, Phys. Rev. Lett. 126, 202301 (2021).
  45. B. E. Aboona et al. (STAR Collaboration), Tracking the baryon number with nuclear collisions, Science 393, 727 (2026).
  46. J. Mohs, S. Ryu, and H. Elfner(SMASH Collaboration), Particle production via strings and baryon stopping within a hadronic transport approach, J. Phys. G 47, 065101 (2020).
  47. O. Garcia-Montero and S. Schlichting, Baryon stopping and charge deposition in heavy-ion collisions due to gluon saturation, Phys. Rev. C 111, 024912 (2025).
  48. N. Lewis, W. Lv, M. A. Ross, C. Y. Tsang, J. D. Brandenburg, Z.-W. Lin, R. Ma, Z. Tang, P. Tribedy, and Z. Xu, Search for baryon junctions in photonuclear processes and isobar collisions at RHIC, Eur. Phys. J. C 84, 590 (2024).
  49. M. Coquet, M. Winn, X. Du, J.-Y. Ollitrault, and S. Schlichting, Dilepton polarization as a signature of plasma anisotropy, Phys. Rev. Lett. 132, 232301 (2024).
  50. M. Coquet, X. Du, J.-Y. Ollitrault, S. Schlichting, and M. Winn, Intermediate mass dileptons as pre-equilibrium probes in heavy ion collisions, Phys. Lett. B 821, 136626 (2021).
  51. J. Berges, K. Reygers, N. Tanji, and R. Venugopalan, How brightly does the glasma shine? Photon production off-equilibrium, Nucl. Phys. A 967, 708 (2017).
  52. O. Garcia-Montero, N. Löher, A. Mazeliauskas, J. Berges, and K. Reygers, Probing the evolution of heavy-ion collisions using direct photon interferometry, Phys. Rev. C 102, 024915 (2020).
  53. O. Garcia-Montero, P. Plaschke, and S. Schlichting, Scaling of pre-equilibrium dilepton production in QCD kinetic theory, Phys. Rev. D 111, 034036 (2025).
  54. H. S. Scheid, Experimental overview of electromagnetic radiation in heavy-ion collisions, EPJ Web Conf. 364, 01022 (2026).
  55. X.-Y. Wu, L. Du, C. Gale, and S. Jeon, Probing the equilibration of the QCD matter created in heavy-ion collisions with dileptons, Phys. Rev. C 110, 054904 (2024).
  56. O. Garcia-Montero, Non-equilibrium photons from the bottom-up thermalization scenario, Ann. Phys. 443, 168984 (2022).
  57. L. Constantin, O. Garcia-Montero, N. Götz, and H. Elfner, 3D initial-state dynamics across scales: A comparative study of saturation and string-based descriptions, arXiv:2605.16914.
  58. J. L. Albacete, N. Armesto, J. G. Milhano, P. Quiroga Arias, and C. A. Salgado, AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks, Eur. Phys. J. C 71, 1705 (2011).
  59. S. Schlichting and B. Schenke, The shape of the proton at high energies, Phys. Lett. B 739, 313 (2014).
  60. P. Singh, G. Giacalone, B. Schenke, and S. Schlichting, Small-x structure of oxygen and neon isotopes as seen by the large hadron collider, EPJ Web Conf. 296, 10005 (2024).

Outline

Information

Phys. Rev. C 114, 044906– Published 21 October, 2026
  • Received 1 June 2026
  • Accepted 1 September 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