- 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
  • Letter
  • Open Access

Signatures of a baryonic spin-Hall effect in dense QCD matter

Baochi Fu1,2,3,*, Long-Gang Pang4,†, Huichao Song1,2,3,‡, and Yi Yin5,§

  • *Contact author: fubaochi@pku.edu.cn
  • †Contact author: lgpang@mail.ccnu.edu.cn
  • ‡Contact author: huichaosong@pku.edu.cn
  • §Contact author: yiyin@cuhk.edu.cn
PDF

Phys. Rev. C 113, L041901 – Published 21 April, 2026

DOI: https://doi.org/10.1103/m5rj-rp7n

Abstract

Recent theoretical analyses show that spin current can be induced by the baryon chemical potential gradient ∇μB which becomes sizable in the fireballs created in heavy-ion collisions (HIC) at a beam energy of O(10) GeV. This spin transport phenomenon can be considered as the cousin effect of the spin-Hall effect (SHE) in condensed matter systems with ∇μB playing the role of the analogous electric field. In this letter, we study this important mechanism, which we call “baryonic SHE” or ∇μB-induced polarization (∇μB-IP), for differential spin polarization generation that has not been systematically explored before. We predict the signature of the baryonic SHE in HIC using a (3+1)D viscous hydrodynamic model MUSIC with a multiphase transport initial condition. We propose to use the second Fourier coefficients of the net spin polarization of Λ hyperon as sensitive probes for the baryonic SHE. Those baryonic SHE observables show a qualitative difference in sign and beam energy dependence for the situations with and without the baryonic SHE. Future experimental observation of these distinct qualitative features would provide strong evidence for the existence of this “baryonic SHE” in the hot and dense quantum chromodynamics matter.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. L. Adamczyk et al. (STAR Collaboration), Global Λ hyperon polarization in nuclear collisions, Nature (London) 548, 62 (2017).
  2. S. A. Voloshin, Vorticity and particle polarization in heavy ion collisions (experimental perspective), EPJ Web Conf. 171, 07002 (2018).
  3. 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).
  4. S. Acharya et al. (ALICE Collaboration), Global polarization of Λ and Λ¯ hyperons in Pb-Pb collisions at sNN=2.76 and 5.02 TeV, Phys. Rev. C 101, 044611 (2020).
  5. J. Adam et al. (STAR Collaboration), Polarization of Λ (Λ¯) hyperons along the beam direction in Au+Au collisions at sNN=200GeV, Phys. Rev. Lett. 123, 132301 (2019).
  6. S. Acharya et al. (ALICE Collaboration), Polarization of Λ and Λ¯ hyperons along the beam direction in Pb-Pb collisions at sNN=5.02TeV, Phys. Rev. Lett. 128, 172005 (2022).
  7. F. Becattini and M. A. Lisa, Polarization and vorticity in the quark–gluon plasma, Annu. Rev. Nucl. Part. Sci. 70, 395 (2020).
  8. F. Becattini, Spin and polarization: A new direction in relativistic heavy ion physics, Rep. Prog. Phys. 85, 122301 (2022).
  9. F. Becattini and I. Karpenko, Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy, Phys. Rev. Lett. 120, 012302 (2018).
  10. S. Y. F. Liu and Y. Yin, Spin polarization induced by the hydrodynamic gradients, J. High Energy Phys. 07 (2021) 188.
  11. 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).
  12. F. Becattini, M. Buzzegoli, and A. Palermo, Spin-thermal shear coupling in a relativistic fluid, Phys. Lett. B 820, 136519 (2021).
  13. F. Becattini, M. Buzzegoli, A. Palermo, G. Inghirami, and I. Karpenko, Local polarization and isothermal local equilibrium in relativistic heavy ion collisions, Phys. Rev. Lett. 127, 272302 (2021).
  14. I. Karpenko and F. Becattini, Study of Λ polarization in relativistic nuclear collisions at sNN=7.7–200GeV, Eur. Phys. J. C 77, 213 (2017).
  15. Y. L. Xie, M. Bleicher, H. Stöcker, D. J. Wang, and L. P. Csernai, Λ polarization in peripheral collisions at moderately relativistic energies, Phys. Rev. C 94, 054907 (2016).
  16. 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).
  17. 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).
  18. 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).
  19. Y. Guo, J. Liao, E. Wang, H. Xing, and H. Zhang, Hyperon polarization from the vortical fluid in low-energy nuclear collisions, Phys. Rev. C 104, L041902 (2021).
  20. 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).
  21. D. T. Son and N. Yamamoto, Kinetic theory with Berry curvature from quantum field theories, Phys. Rev. D 87, 085016 (2013).
  22. Y. Hidaka, S. Pu, and D.-L. Yang, Relativistic chiral kinetic theory from quantum field theories, Phys. Rev. D 95, 091901 (2017).
  23. Y. Hidaka, S. Pu, and D.-L. Yang, Nonlinear responses of chiral fluids from kinetic theory, Phys. Rev. D 97, 016004 (2018).
  24. K. Hattori, Y. Hidaka, and D.-L. Yang, Axial kinetic theory and spin transport for fermions with arbitrary mass, Phys. Rev. D 100, 096011 (2019).
  25. 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).
  26. S. Y. F. Liu and Y. Yin, Spin Hall effect in heavy-ion collisions, Phys. Rev. D 104, 054043 (2021).
  27. S. Ryu, V. Jupic, and C. Shen, Probing early-time longitudinal dynamics with the Λ hyperon's spin polarization in relativistic heavy-ion collisions, Phys. Rev. C 104, 054908 (2021).
  28. M. Dyakonov and V. Perel, Current-induced spin orientation of electrons in semiconductors, Phys. Lett. A 35, 459 (1971).
  29. J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Spin Hall effects, Rev. Mod. Phys. 87, 1213 (2015).
  30. Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Observation of the spin Hall effect in semiconductors, Science 306, 1910 (2004).
  31. J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Experimental observation of the Spin-Hall effect in a two-dimensional spin-orbit coupled semiconductor system, Phys. Rev. Lett. 94, 047204 (2005).
  32. L. Liu, T. Moriyama, D. C. Ralph, and R. A. Buhrman, Spin-torque ferromagnetic resonance induced by the spin Hall effect, Phys. Rev. Lett. 106, 036601 (2011).
  33. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Quantum spin Hall insulator state in HgTe quantum wells, Science 318, 766 (2007).
  34. F. Becattini, V. Chandra, L. Del Zanna, and E. Grossi, Relativistic distribution function for particles with spin at local thermodynamical equilibrium, Ann. Phys. 338, 32 (2013).
  35. M. Buzzegoli, Polarization in heavy ion collisions: A theoretical review, EPJ Web Conf. 276, 01011 (2023).
  36. X.-L. Sheng, F. Becattini, and D. Roselli, An improved formula for Wigner function and spin polarization in a decoupling relativistic fluid at local thermodynamic equilibrium, arXiv:2509.14301.
  37. R. Baier, P. Romatschke, D. T. Son, A. O. Starinets, and M. A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance, and holography, J. High Energy Phys. 04 (2008) 100.
  38. R.-h. Fang, L.-g. Pang, Q. Wang, and X.-n. Wang, Polarization of massive fermions in a vortical fluid, Phys. Rev. C 94, 024904 (2016).
  39. Z.-W. Lin, C. M. Ko, B.-A. Li, B. Zhang, and S. Pal, Multiphase transport model for relativistic heavy ion collisions, Phys. Rev. C 72, 064901 (2005).
  40. Y. He and Z.-W. Lin, Improved quark coalescence for a multi-phase transport model, Phys. Rev. C 96, 014910 (2017).
  41. L. Pang, Q. Wang, and X.-N. Wang, Effects of initial flow velocity fluctuation in event-by-event (3+1)D hydrodynamics, Phys. Rev. C 86, 024911 (2012).
  42. L.-G. Pang, H. Petersen, Q. Wang, and X.-N. Wang, Vortical fluid and Λ spin correlations in high-energy heavy-ion collisions, Phys. Rev. Lett. 117, 192301 (2016).
  43. Z.-T. Liang and X.-N. Wang, Globally polarized quark-gluon plasma in noncentral A+A collisions, Phys. Rev. Lett. 94, 102301 (2005); 96, 039901(E) (2006).
  44. J.-H. Gao, Z.-T. Liang, Q. Wang, and X.-N. Wang, Global polarization effect and spin-orbit coupling in strong interaction, Lect. Notes Phys. 987, 195 (2021).
  45. S. Y. F. Liu, Y. Sun, and C. M. Ko, Spin polarizations in a covariant angular-momentum-conserved chiral transport model, Phys. Rev. Lett. 125, 062301 (2020).
  46. F. Videbæk (BRAHMS Collaboration), Overview and recent results from BRAHMS, Nucl. Phys. A 830, 43c (2009).
  47. T. Anticic et al. (NA49 Collaboration), Centrality dependence of proton and antiproton spectra in Pb + Pb collisions at 40A GeV and 158A GeV measured at the CERN Super Proton Synchrotron, Phys. Rev. C 83, 014901 (2011).
  48. W. Busza, K. Rajagopal, and W. van der Schee, Heavy ion collisions: The big picture and the big questions, Annu. Rev. Nucl. Part. Sci. 68, 339 (2018).
  49. J. Mohs, S. Ryu, and H. Elfner, Particle production via strings and baryon stopping within a hadronic transport approach, J. Phys. G 47, 065101 (2020).
  50. B. Fu, L. Pang, H. Song, and Y. Yin (unpublished).
  51. X. Guo, J. Liao, and E. Wang, Spin hydrodynamic generation in the charged subatomic swirl, Sci. Rep. 10, 2196 (2020).
  52. Y. Guo, S. Shi, S. Feng, and J. Liao, Magnetic field induced polarization difference between hyperons and anti-hyperons, Phys. Lett. B 798, 134929 (2019).
  53. V. E. Ambrus and M. N. Chernodub, Hyperon–anti-hyperon polarization asymmetry in relativistic heavy-ion collisions as an interplay between chiral and helical vortical effects, Eur. Phys. J. C 82, 61 (2022).
  54. O. Vitiuk, L. V. Bravina, and E. E. Zabrodin, Is different Λ and Λ¯ polarization caused by different spatio-temporal freeze-out picture? Phys. Lett. B 803, 135298 (2020).
  55. B. Fu, L. Pang, H. Song, and Y. Yin, Signatures of the spin Hall effect in hot and dense QCD matter, arXiv:2201.12970.

Outline

Information

Phys. Rev. C 113, L041901– Published 21 April, 2026
  • Received 12 February 2022
  • Revised 28 July 2025
  • Accepted 27 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