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Modeling Λ polarization in Au+Au collisions at sNN=200  GeV using relativistic spin hydrodynamics

Matteo Buzzegoli1,2,*, Aleksandar Gecić1,†, and Rajeev Singh1,3,‡

  • *Contact author: matteo.buzzegoli@e-uvt.ro
  • †Contact author: aleksandar.gecic10@e-uvt.ro
  • ‡Contact author: rajeev.singh@e-uvt.ro, rajeevofficial24@gmail.com
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Phys. Rev. D 114, 074017 – Published 7 October, 2026

DOI: https://doi.org/10.1103/6mm9-hrj7

Abstract

We investigate spin polarization dynamics in relativistic heavy-ion collisions using ideal relativistic spin hydrodynamics, employing nonboost-invariant longitudinal solutions as the hydrodynamic background. Operating in the small-polarization regime, where spin evolves perturbatively on top of the bulk expansion, we first analyze a (1+1)D setup with transverse homogeneity. In this framework, symmetry-constrained initial conditions for the spin potential lead to nontrivial evolution and generate both local and global Λ hyperon polarization consistent with qualitative experimental trends, though they fail to reproduce observed azimuthal structures. To address this limitation, we extend the framework by incorporating transverse flow and spatial anisotropy at freeze-out, constructing a novel (1+1+2)D model that preserves the longitudinal dynamics. We demonstrate that the inclusion of a longitudinal spin acceleration component, coupled with transverse expansion, results in the emergence of a quadrupole pattern in the longitudinal polarization. The resulting momentum-dependent and integrated observables exhibit qualitative and, after fitting the spin potential initial intensity, reasonably good quantitative agreement with experimental data for Au+Au collisions at sNN=200  GeV. Finally, we provide predictions for the in-plane transverse spin polarization, an observable that, to our knowledge, has not yet been experimentally measured.

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References (90)

  1. U. Heinz and R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Annu. Rev. Nucl. Part. Sci. 63, 123 (2013).
  2. C. Gale, S. Jeon, and B. Schenke, Hydrodynamic modeling of Heavy-Ion collisions, Int. J. Mod. Phys. A 28, 1340011 (2013).
  3. P. Braun-Munzinger, V. Koch, T. Schäfer, and J. Stachel, Properties of hot and dense matter from relativistic heavy ion collisions, Phys. Rep. 621, 76 (2016).
  4. M. Arslandok et al., Hot QCD white paper, arXiv:2303.17254.
  5. D. A. Teaney, Viscous hydrodynamics and the quark gluon plasma, in Quark-Gluon Plasma 4, edited by R. C. Hwa and X.-N. Wang (World Scientific, Singapore, 2010), pp. 207–266.
  6. T. Schäfer and D. Teaney, Nearly perfect fluidity: From cold atomic gases to hot quark gluon plasmas, Rep. Prog. Phys. 72, 126001 (2009).
  7. L. Martinoia and R. Singh, A note on the canonical approach to hydrodynamics and linear response theory, Acta Phys. Pol. B 56, 1-A4 (2025).
  8. F. Becattini, F. Piccinini, and J. Rizzo, Angular momentum conservation in heavy ion collisions at very high energy, Phys. Rev. C 77, 024906 (2008).
  9. F. Becattini, M. Buzzegoli, T. Niida, S. Pu, A.-H. Tang, and Q. Wang, Spin polarization in relativistic heavy-ion collisions, Int. J. Mod. Phys. E 33, 2430006 (2024).
  10. T. Niida and S. A. Voloshin, Polarization phenomenon in heavy-ion collisions, Int. J. Mod. Phys. E 33, 2430010 (2024).
  11. STAR Collaboration, Global Λ hyperon polarization in nuclear collisions: Evidence for the most vortical fluid, Nature (London) 548, 62 (2017).
  12. Z.-T. Liang and X.-N. Wang, Globally polarized quark-gluon plasma in non-central A+A collisions, Phys. Rev. Lett. 94, 102301 (2005); 96, 039901(E) (2006).
  13. J. Adam et al. (STAR Collaboration), Polarization of Λ (Λ¯) hyperons along the beam direction in Au+Au collisions at sNN=200  GeV, Phys. Rev. Lett. 123, 132301 (2019).
  14. S. Acharya et al. (ALICE Collaboration), Global polarization of ΛΛ¯ hyperons in Pb-Pb collisions at sNN=2.76 and 5.02 TeV, Phys. Rev. C 101, 044611 (2020); 105, 029902(E) (2022).
  15. S. Acharya et al. (ALICE Collaboration), Polarization of Λ and Λ¯ hyperons along the beam direction in Pb-Pb collisions at sNN=5.02  TeV, Phys. Rev. Lett. 128, 172005 (2022).
  16. A. Hayrapetyan et al. (CMS Collaboration), Observation of Λ hyperon local polarization in p-Pb collisions at sNN = 8.16 TeV, Phys. Rev. Lett. 135, 132301 (2025).
  17. F. Becattini, Hydrodynamics of fluids with spin, Phys. Part. Nucl. Lett. 8, 801 (2011).
  18. W. Florkowski, B. Friman, A. Jaiswal, and E. Speranza, Relativistic fluid dynamics with spin, Phys. Rev. C 97, 041901 (2018).
  19. W. Florkowski, R. Ryblewski, and A. Kumar, Relativistic hydrodynamics for spin-polarized fluids, Prog. Part. Nucl. Phys. 108, 103709 (2019).
  20. D. Montenegro, L. Tinti, and G. Torrieri, The ideal relativistic fluid limit for a medium with polarization, Phys. Rev. D 96, 056012 (2017).
  21. K. Hattori, M. Hongo, X.-G. Huang, M. Matsuo, and H. Taya, Fate of spin polarization in a relativistic fluid: An entropy-current analysis, Phys. Lett. B 795, 100 (2019).
  22. M. Hongo, X.-G. Huang, M. Kaminski, M. Stephanov, and H.-U. Yee, Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation, J. High Energy Phys. 11 (2021) 150.
  23. A. D. Gallegos, U. Gursoy, and A. Yarom, Hydrodynamics, spin currents and torsion, J. High Energy Phys. 05 (2023) 139.
  24. A. Das, W. Florkowski, A. Kumar, R. Ryblewski, and R. Singh, Semi-classical kinetic theory for massive spin-half fermions with leading-order spin effects, Acta Phys. Pol. B 54, 8-A4 (2023).
  25. R. Singh, Guiding center hydrodynamics with spin, J. Subatomic Part. Cosmol. 4, 100255 (2025).
  26. Z. Cao, K. Hattori, M. Hongo, X.-G. Huang, and H. Taya, Gyrohydrodynamics: Relativistic spinful fluid with strong vorticity, Prog. Theor. Exp. Phys. 2022, 071D01 (2022).
  27. N. Weickgenannt, D. Wagner, E. Speranza, and D. H. Rischke, Relativistic second-order dissipative spin hydrodynamics from the method of moments, Phys. Rev. D 106, 096014 (2022).
  28. N. Weickgenannt, D. Wagner, E. Speranza, and D. H. Rischke, Relativistic dissipative spin hydrodynamics from kinetic theory with a nonlocal collision term, Phys. Rev. D 106 L091901 (2022).
  29. F. Becattini, A. Daher, and X.-L. Sheng, Entropy current and entropy production in relativistic spin hydrodynamics, Phys. Lett. B 850, 138533 (2024).
  30. Z. Drogosz, W. Florkowski, and M. Hontarenko, Hybrid approach to perfect and dissipative spin hydrodynamics, Phys. Rev. D 110, 096018 (2024).
  31. A. Daher, X.-L. Sheng, D. Wagner, and F. Becattini, Dissipative currents and transport coefficients in relativistic spin hydrodynamics, Phys. Rev. D 112, 094020 (2025).
  32. N. Abboud, L. Gavassino, R. Singh, and E. Speranza, Perfect spinfluid: A divergence-type approach, Phys. Rev. D 112, 094043 (2025).
  33. S. Bhadury, Z. Drogosz, W. Florkowski, S. K. Kar, and V. Mykhaylova, Nonlinear causality and stability of perfect spin hydrodynamics and its nonperturbative character, Phys. Rev. D 113, 036017 (2026).
  34. Sapna, S. K. Singh, and D. Wagner, Spin polarization of Λ hyperons from dissipative spin hydrodynamics, Phys. Rev. C 112, 054902 (2025).
  35. H. Matsuda, K. Hattori, and K. Murase, Achieving angular-momentum conservation with physics-informed neural networks in computational relativistic spin hydrodynamics, arXiv:2512.17971.
  36. F. W. Hehl, On the energy tensor of spinning massive matter in classical field theory and general relativity, Rep. Math. Phys. 9, 55 (1976).
  37. M. Buzzegoli and A. Palermo, Emergent canonical spin tensor in the chiral-symmetric hot QCD, Phys. Rev. Lett. 133, 262301 (2024).
  38. F. Becattini and R. Singh, On the local thermodynamic relations in relativistic spin hydrodynamics, Eur. Phys. J. C 85, 1338 (2025).
  39. S. De Groot, W. Van Leeuwen, and C. Van Weert, Relativistic Kinetic Theory. Principles and Applications (North Holland, Amsterdam, 1980).
  40. W. Florkowski, A. Kumar, and R. Ryblewski, Thermodynamic versus kinetic approach to polarization-vorticity coupling, Phys. Rev. C 98, 044906 (2018).
  41. M. Buzzegoli, Pseudogauge dependence of the spin polarization and of the axial vortical effect, Phys. Rev. C 105, 044907 (2022).
  42. W. Florkowski, A. Kumar, R. Ryblewski, and R. Singh, Spin polarization evolution in a boost invariant hydrodynamical background, Phys. Rev. C 99, 044910 (2019).
  43. W. Florkowski, R. Ryblewski, R. Singh, and G. Sophys, Spin polarization dynamics in the non-boost-invariant background, Phys. Rev. D 105, 054007 (2022).
  44. S. K. Singh, R. Ryblewski, and W. Florkowski, Spin dynamics with realistic hydrodynamic background for relativistic heavy-ion collisions, Phys. Rev. C 111, 024907 (2025).
  45. R. Singh, G. Sophys, and R. Ryblewski, Spin polarization dynamics in the Gubser-expanding background, Phys. Rev. D 103, 074024 (2021).
  46. R. Singh and A. Soloviev, Spin hydrodynamics on a hyperbolic expanding background, arXiv:2603.02296.
  47. I. Karpenko and F. Becattini, Study of Λ polarization in relativistic nuclear collisions at sNN=7.7–200  GeV, Eur. Phys. J. C 77, 213 (2017).
  48. Y. Xie, D. Wang, and L. P. Csernai, Global Λ polarization in high energy collisions, Phys. Rev. C 95, 031901 (2017).
  49. 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).
  50. Y. B. Ivanov, Global Λ polarization in moderately relativistic nuclear collisions, Phys. Rev. C 103, L031903 (2021).
  51. B. Fu, K. Xu, X.-G. Huang, and H. Song, Hydrodynamic study of hyperon spin polarization in relativistic heavy ion collisions, Phys. Rev. C 103, 024903 (2021).
  52. H. Li, L.-G. Pang, Q. Wang, and X.-L. Xia, Global Λ polarization in heavy-ion collisions from a transport model, Phys. Rev. C 96, 054908 (2017).
  53. D.-X. Wei, W.-T. Deng, and X.-G. Huang, Thermal vorticity and spin polarization in heavy-ion collisions, Phys. Rev. C 99, 014905 (2019).
  54. F. Becattini, M. Buzzegoli, and A. Palermo, Spin-thermal shear coupling in a relativistic fluid, Phys. Lett. B 820, 136519 (2021).
  55. F. Becattini, M. Buzzegoli, G. Inghirami, I. Karpenko, and A. Palermo, Local polarization and isothermal local equilibrium in relativistic heavy ion collisions, Phys. Rev. Lett. 127, 272302 (2021).
  56. S. Y. F. Liu and Y. Yin, Spin polarization induced by the hydrodynamic gradients, J. High Energy Phys. 07 (2021) 188.
  57. B. Fu, S. Y. F. Liu, L. Pang, H. Song, and Y. Yin, Shear-induced spin polarization in heavy-ion collisions, Phys. Rev. Lett. 127, 142301 (2021).
  58. C. Yi, S. Pu, and D.-L. Yang, Reexamination of local spin polarization beyond global equilibrium in relativistic heavy ion collisions, Phys. Rev. C 104, 064901 (2021).
  59. A. Palermo, E. Grossi, I. Karpenko, and F. Becattini, Λ polarization in very high energy heavy ion collisions as a probe of the quark–gluon plasma formation and properties, Eur. Phys. J. C 84, 920 (2024).
  60. A. Arslan, W.-B. Dong, C. Gale, S. Jeon, Q. Wang, and X.-Y. Wu, In-plane transverse polarization in heavy-ion collisions, Phys. Rev. C 113, 034920 (2026).
  61. R. Singh, Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions, Int. J. Mod. Phys. A 38, 2330011 (2023).
  62. S. Shi, S. Jeon, and C. Gale, Family of new exact solutions for longitudinally expanding ideal fluids, Phys. Rev. C 105 L021902 (2022).
  63. S. Chen and S. Shi, Exact solution of Boltzmann equation in a longitudinal expanding system, Phys. Rev. C 109, L051901 (2024).
  64. S. Chen and S. Shi, Attractor for (1+1)D viscous hydrodynamics with general rapidity distribution, Phys. Rev. C 111, L021902 (2025).
  65. S. Chen and S. Shi, Anisotropic hydrodynamics with a boost-noninvariant expansion, Phys. Rev. D 111, 014001 (2025).
  66. H. Shao, S. Chen, and S. Shi, Onset of Bjorken flow in quantum evolution of the massive Schwinger model, arXiv:2509.10855.
  67. W. Florkowski and R. Ryblewski, Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics, Phys. Rev. C 85, 044902 (2012).
  68. P. A. Zyla et al. (Particle Data Group Collaboration), Review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
  69. F. Becattini and I. Karpenko, Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy, Phys. Rev. Lett. 120, 012302 (2018).
  70. B. B. Back et al., The significance of the fragmentation region in ultrarelativistic heavy ion collisions, Phys. Rev. Lett. 91, 052303 (2003).
  71. J. Adam et al. (STAR Collaboration), Global polarization of Λ hyperons in Au+Au collisions at sNN=200  GeV, Phys. Rev. C 98, 014910 (2018).
  72. M. S. Abdallah et al. (STAR Collaboration), Global Λ-hyperon polarization in Au+Au collisions at sNN=3  GeV, Phys. Rev. C 104, L061901 (2021).
  73. M. Abdulhamid et al. (STAR Collaboration), Hyperon polarization along the beam direction relative to the second and third harmonic event planes in isobar collisions at sNN = 200 GeV, Phys. Rev. Lett. 131, 202301 (2023).
  74. S. A. Voloshin, Vorticity and particle polarization in heavy ion collisions (experimental perspective), Eur. Phys. J. Web Conf. 171, 07002 (2018).
  75. T. Niida (STAR Collaboration), Global and local polarization of Λ hyperons in Au+Au collisions at 200 GeV from STAR, Nucl. Phys. A982, 511 (2019).
  76. G. Agakishiev et al. (HADES Collaboration), Lambda hyperon production and polarization in collisions of p(3.5 GeV)+Nb, Eur. Phys. J. A 50, 81 (2014).
  77. R. Abou Yassine et al. (HADES Collaboration), Measurement of global polarization of Λ hyperons in few-GeV heavy-ion collisions, Phys. Lett. B 835, 137506 (2022).
  78. H. Heiselberg and A.-M. Levy, Elliptic flow and HBT in noncentral nuclear collisions, Phys. Rev. C 59, 2716 (1999).
  79. J. Adams et al. (STAR Collaboration), Azimuthal anisotropy in Au+Au collisions at sNN=200  GeV, Phys. Rev. C 72, 014904 (2005).
  80. J. Adams et al. (STAR Collaboration), Transverse momentum and collision energy dependence of high p(T) hadron suppression in Au+Au collisions at ultrarelativistic energies, Phys. Rev. Lett. 91, 172302 (2003).
  81. X.-L. Xia, H. Li, Z.-B. Tang, and Q. Wang, Probing vorticity structure in heavy-ion collisions by local Λ polarization, Phys. Rev. C 98, 024905 (2018).
  82. Y. Sun, Z. Zhang, C. M. Ko, and W. Zhao, Evolution of Λ polarization in the hadronic phase of heavy-ion collisions, Phys. Rev. C 105, 034911 (2022).
  83. J. Noronha, B. Schenke, C. Shen, and W. Zhao, Progress and challenges in small systems, Int. J. Mod. Phys. E 33, 2430005 (2024).
  84. J. F. Grosse-Oetringhaus and U. A. Wiedemann, A decade of collectivity in small systems, arXiv:2407.07484.
  85. M. Buzzegoli, Kubo formulas for spin polarization in dissipative relativistic spin hydrodynamics: A first-order gradient expansion approach, J. High Energy Phys. 07 (2025) 255.
  86. C. Jauch, Local lambda polarization in light-ion with ALICE at LHC, in The 22nd International Conference on Strangeness in Quark Matter (SQM2026) (2026), https://indico.global/event/13943/contributions/143545/.
  87. G. Başar, J. Bhambure, R. Singh, and D. Teaney, Stochastic relativistic advection diffusion equation from the metropolis algorithm, Phys. Rev. C 110, 044903 (2024).
  88. J. Bhambure, A. Mazeliauskas, J.-F. Paquet, R. Singh, M. Singh, D. Teaney, and F. Zhou, Relativistic viscous hydrodynamics in the density frame: Numerical tests and comparisons, Phys. Rev. C 111, 064910 (2025).
  89. J. Bhambure, R. Singh, and D. Teaney, Stochastic relativistic viscous hydrodynamics from the metropolis algorithm, Phys. Rev. C 111, 064909 (2025),
  90. M. Buzzegoli, A. Gecić, and R. Singh, Modeling lambda polarization in Au+Au collisions at 200 GeV using relativistic spin hydrodynamics, https://github.com/rs240291/rs-HYDRO.git (2026).

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Phys. Rev. D 114, 074017– Published 7 October, 2026
  • Received 3 June 2026
  • Accepted 4 September 2026
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