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

Radiative corrections on vortical spin polarization in hot QCD matter

Shuo Fang1,2,*, Shi Pu3,4,†, and Di-Lun Yang5,6,‡

  • *Contact author: fangshuo@mail.ustc.edu.cn
  • †Contact author: shipu@ustc.edu.cn
  • ‡Contact author: dilunyang@gmail.com

Phys. Rev. D 112, 014038 – Published 22 July, 2025

DOI: https://doi.org/10.1103/tds1-793m

Abstract

We investigate the radiative corrections on spin polarization of relativistic fermions induced by vortical fields in thermal-equilibrium QCD matter at weak coupling. Such corrections stem from the self-energy gradients in quantum kinetic theory, which are further obtained by a more systematic and general approach through the Keldysh equation. By applying the hard-thermal-loop approximation, we obtain new corrections upon the spin-polarization spectrum and also the axial-charge current in connection to the axial/chiral vortical effect for massive quarks up to the leading order of the QCD coupling. Further influence on spin alignment of vector mesons from similar effects is also analyzed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (95)

  1. M. Gyulassy, .
  2. E. V. Shuryak, Nucl. Phys. A750, 64 (2005).
  3. M. I. Abdulhamid et al. (STAR Collaboration), Phys. Rev. X 14, 011028 (2024).
  4. X.-G. Huang, Rep. Prog. Phys. 79, 076302 (2016).
  5. J.-H. Gao, G.-L. Ma, S. Pu, and Q. Wang, Nucl. Sci. Tech. 31, 90 (2020).
  6. STAR Collaboration, Nature (London) 548, 62 (2017).
  7. F. Becattini and M. A. Lisa, Annu. Rev. Nucl. Part. Sci. 70, 395 (2020).
  8. F. Becattini, M. Buzzegoli, T. Niida, S. Pu, A.-H. Tang, and Q. Wang, Int. J. Mod. Phys. E 33, 2430006 (2024).
  9. D. E. Kharzeev, J. Liao, S. A. Voloshin, and G. Wang, Prog. Part. Nucl. Phys. 88, 1 (2016).
  10. I. Karpenko and F. Becattini, Eur. Phys. J. C 77, 213 (2017).
  11. J. Adam et al. (STAR Collaboration), Phys. Rev. Lett. 123, 132301 (2019).
  12. F. Becattini, M. Buzzegoli, G. Inghirami, I. Karpenko, and A. Palermo, Phys. Rev. Lett. 127, 272302 (2021).
  13. B. Fu, S. Y. F. Liu, L. Pang, H. Song, and Y. Yin, Phys. Rev. Lett. 127, 142301 (2021).
  14. C. Yi, S. Pu, and D.-L. Yang, Phys. Rev. C 104, 064901 (2021).
  15. X.-Y. Wu, C. Yi, G.-Y. Qin, and S. Pu, Phys. Rev. C 105, 064909 (2022).
  16. S. Acharya et al. (ALICE Collaboration), Phys. Rev. Lett. 125, 012301 (2020).
  17. M. S. Abdallah et al. (STAR Collaboration), Nature (London) 614, 244 (2023).
  18. X.-L. Sheng, L. Oliva, Z.-T. Liang, Q. Wang, and X.-N. Wang, Phys. Rev. Lett. 131, 042304 (2023).
  19. X.-L. Sheng, S. Pu, and Q. Wang, Phys. Rev. C 108, 054902 (2023).
  20. B. Müller and D.-L. Yang, Phys. Rev. D 105, L011901 (2022); 106, 039904(E) (2022).
  21. A. Kumar, B. Müller, and D.-L. Yang, Phys. Rev. D 108, 016020 (2023).
  22. D. Vasak, M. Gyulassy, and H. T. Elze, Ann. Phys. (N.Y.) 173, 462 (1987).
  23. D. T. Son and N. Yamamoto, Phys. Rev. D 87, 085016 (2013).
  24. J.-W. Chen, S. Pu, Q. Wang, and X.-N. Wang, Phys. Rev. Lett. 110, 262301 (2013).
  25. J.-H. Gao, Z.-T. Liang, S. Pu, Q. Wang, and X.-N. Wang, Phys. Rev. Lett. 109, 232301 (2012).
  26. Y. Hidaka, S. Pu, and D.-L. Yang, Phys. Rev. D 95, 091901 (2017).
  27. J.-H. Gao and Z.-T. Liang, Phys. Rev. D 100, 056021 (2019).
  28. N. Weickgenannt, X.-L. Sheng, E. Speranza, Q. Wang, and D. H. Rischke, Phys. Rev. D 100, 056018 (2019).
  29. N. Weickgenannt, E. Speranza, X.-l. Sheng, Q. Wang, and D. H. Rischke, Phys. Rev. Lett. 127, 052301 (2021).
  30. D.-L. Yang, K. Hattori, and Y. Hidaka, J. High Energy Phys. 07 (2020) 070.
  31. Y. Hidaka, S. Pu, Q. Wang, and D.-L. Yang, Prog. Part. Nucl. Phys. 127, 103989 (2022).
  32. F. Becattini, V. Chandra, L. Del Zanna, and E. Grossi, Ann. Phys. (Amsterdam) 338, 32 (2013).
  33. R.-h. Fang, L.-g. Pang, Q. Wang, and X.-n. Wang, Phys. Rev. C 94, 024904 (2016).
  34. F. Becattini, Lect. Notes Phys. 987, 15 (2021).
  35. D. Wagner, N. Weickgenannt, and E. Speranza, Phys. Rev. Res. 5, 013187 (2023).
  36. Y. Hidaka, S. Pu, and D.-L. Yang, Phys. Rev. D 97, 016004 (2018).
  37. A. Kumar, B. Müller, and D.-L. Yang, Phys. Rev. D 107, 076025 (2023).
  38. D.-L. Yang, Phys. Rev. D 111, 056005 (2025).
  39. D.-L. Yang, J. High Energy Phys. 06 (2022) 140.
  40. X.-L. Sheng, L. Oliva, and Q. Wang, Phys. Rev. D 101, 096005 (2020).
  41. D.-L. Yang, Phys. Rev. D 98, 076019 (2018).
  42. N. Weickgenannt, D. Wagner, E. Speranza, and D. H. Rischke, Phys. Rev. D 106, 096014 (2022).
  43. N. Weickgenannt, D. Wagner, E. Speranza, and D. H. Rischke, Phys. Rev. D 106, L091901 (2022).
  44. D. Wagner, Phys. Rev. D 111, 016008 (2025).
  45. S. Fang, S. Pu, and D.-L. Yang, Phys. Rev. D 106, 016002 (2022).
  46. S. Fang, S. Pu, and D.-L. Yang, Phys. Rev. D 109, 034034 (2024).
  47. S. Fang and S. Pu, Phys. Rev. D 111, 034015 (2025).
  48. S. Lin and Z. Wang, J. High Energy Phys. 12 (2022) 030.
  49. S. Lin and Z. Wang, Phys. Rev. D 111, 034032 (2025).
  50. S. Lin and J. Tian, arXiv:2410.22935.
  51. Z. Wang and S. Lin, Phys. Rev. D 111, 056023 (2025).
  52. S. Golkar and D. T. Son, J. High Energy Phys. 02 (2015) 169.
  53. D.-F. Hou, H. Liu, and H.-c. Ren, Phys. Rev. D 86, 121703 (2012).
  54. A. Vilenkin, Phys. Rev. D 20, 1807 (1979).
  55. D. T. Son and P. Surowka, Phys. Rev. Lett. 103, 191601 (2009).
  56. K. Landsteiner, E. Megias, and F. Pena-Benitez, Phys. Rev. Lett. 107, 021601 (2011).
  57. N. Yamamoto and D.-L. Yang, Phys. Rev. D 109, 056010 (2024).
  58. K. Hattori, Y. Hidaka, N. Yamamoto, and D.-L. Yang, J. High Energy Phys. 02 (2021) 001.
  59. M. Buzzegoli and D. E. Kharzeev, Phys. Rev. D 103, 116005 (2021).
  60. J.-P. Blaizot and E. Iancu, Phys. Rep. 359, 355 (2002).
  61. M. Abdulhamid et al. (STAR Collaboration), Phys. Rev. Lett. 131, 202301 (2023).
  62. L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1, Course of Theoretical Physics Vol. 5 (Butterworth-Heinemann, Oxford, 1980).
  63. J.-Y. Chen, D. T. Son, and M. A. Stephanov, Phys. Rev. Lett. 115, 021601 (2015).
  64. F. Becattini, Phys. Rev. Lett. 108, 244502 (2012).
  65. F. Becattini, L. Bucciantini, E. Grossi, and L. Tinti, Eur. Phys. J. C 75, 191 (2015).
  66. S. Weinberg, The Quantum Theory of Fields. Vol. 1: Foundations (Cambridge University Press, Cambridge, England, 2005).
  67. J. Maciejko, Lecture Notes (Springer,, 2007), vol. 9, p. 104.
  68. S. Fang and S. Pu(to be published).
  69. Y. Li and S. Y. F. Liu, arXiv:2501.17861.
  70. S. Fang, S. Pu, and D.-L. Yang (to be published).
  71. S. R. De Groot, Relativistic Kinetic Theory. Principles and Applications (North-Holland Publishing Company, Amsterdam, 1980).
  72. A. Palermo, M. Buzzegoli, and F. Becattini, J. High Energy Phys. 10 (2021) 077.
  73. F. Becattini, M. Buzzegoli, and A. Palermo, Phys. Lett. B 820, 136519 (2021).
  74. S. Y. F. Liu and Y. Yin, Phys. Rev. D 104, 054043 (2021).
  75. S. Y. F. Liu and Y. Yin, J. High Energy Phys. 07 (2021) 188.
  76. Z. Wang, X. Guo, and P. Zhuang, Eur. Phys. J. C 81, 799 (2021).
  77. M. L. Bellac, Thermal Field Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2011).
  78. N. P. Landsman and C. G. van Weert, Phys. Rep. 145, 141 (1987).
  79. K. Hattori, Y. Hidaka, and D.-L. Yang, Phys. Rev. D 100, 096011 (2019).
  80. S. Mrowczynski and U. W. Heinz, Ann. Phys. (N.Y.) 229, 1 (1994).
  81. P. B. Arnold, G. D. Moore, and L. G. Yaffe, J. High Energy Phys. 11 (2000) 001.
  82. P. B. Arnold, G. D. Moore, and L. G. Yaffe, J. High Energy Phys. 01 (2003) 030.
  83. P. B. Arnold, G. D. Moore, and L. G. Yaffe, J. High Energy Phys. 05 (2003) 051.
  84. Z.-T. Liang and X.-N. Wang, Phys. Rev. Lett. 94, 102301 (2005); 96, 039901(E) (2006).
  85. X.-L. Sheng, L. Oliva, Z.-T. Liang, Q. Wang, and X.-N. Wang, Phys. Rev. D 109, 036004 (2024).
  86. F. Li and S. Y. F. Liu, arXiv:2206.11890.
  87. W.-B. Dong, Y.-L. Yin, X.-L. Sheng, S.-Z. Yang, and Q. Wang, Phys. Rev. D 109, 056025 (2024).
  88. W. Greiner and J. Reinhardt, Field Quantization (Springer Berlin, Heidelberg, 1996).
  89. A. Kumar, D.-L. Yang, and P. Gubler, Phys. Rev. D 109, 054038 (2024).
  90. Z.-H. Zhang, X.-G. Huang, F. Becattini, and X.-L. Sheng, arXiv:2412.19416.
  91. S.-Z. Yang, X.-Q. Xie, S. Pu, J.-H. Gao, and Q. Wang, arXiv:2412.19400.
  92. A. Faessler, T. Gutsche, V. E. Lyubovitskij, and K. Pumsaard, Phys. Rev. D 73, 114021 (2006).
  93. L. Adamczyk et al. (STAR Collaboration), Phys. Rev. C 96, 044904 (2017).
  94. S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985).
  95. M. Buzzegoli, E. Grossi, and F. Becattini, J. High Energy Phys. 10 (2017) 091; 07 (2018) 119(E).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation