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Perturbative and nonperturbative properties of heavy quark transport in a thermal SU(3) gluon plasma

Jiazhen Peng1,*, Yage Zhen1,*, Jiale Lou1, Fei Sun1,2, Kejun Wu1,2, Wei Xie1,2, Zuman Zhang3,4, Shuang Li1,2,†, and Sa Wang1,2,‡

  • *These authors contributed equally to this work.
  • †Contact author: lish@ctgu.edu.cn
  • ‡Contact author: wangsa@ctgu.edu.cn
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Phys. Rev. D 114, 016005 – Published 6 July, 2026

DOI: https://doi.org/10.1103/sbqb-l664

Abstract

We investigate the perturbative and nonperturbative aspects of heavy quark transport in a thermal SU(3) gluon plasma. Based on the soft-hard factorized model, we extend the original perturbative framework to the near-critical temperature region, where nonperturbative effects become significant. The transition behavior of the semi-quark-gluon-plasma (semi-QGP) is described via a temperature-dependent background field incorporated in the background field effective theory. By implementing this approach, we quantitatively evaluate the collisional energy loss and momentum diffusion coefficients of charm and bottom quarks as functions of the incoming energy and medium temperature. Our results show a distinct suppression of both the energy loss and the diffusion coefficients relative to conventional perturbative estimates, especially near the critical temperature. This suppression originates from the emergence of a temperature-dependent color background field, which effectively reduces the color charge screening of the medium. These findings provide important theoretical insight into the phenomenology of heavy-flavor probes, offering a unified theoretical framework applicable across both high- and low-momentum regimes.

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References (65)

  1. G. D. Moore and D. Teaney, Phys. Rev. C 71, 064904 (2005).
  2. N. Haque and M. G. Mustafa, Prog. Part. Nucl. Phys. 140, 104136 (2025).
  3. S. Caron-Huot and G. D. Moore, J. High Energy Phys. 02 (2008) 081.
  4. D. Banerjee, S. Datta, R. Gavai, and P. Majumdar, Phys. Rev. D 85, 014510 (2012).
  5. H.-T. Ding, A. Francis, O. Kaczmarek, F. Karsch, H. Satz, and W. Soeldner, Phys. Rev. D 86, 014509 (2012).
  6. L. Altenkort, D. de la Cruz, O. Kaczmarek, R. Larsen, G. D. Moore, S. Mukherjee, P. Petreczky, H.-T. Shu, and S. Stendebach (HotQCD Collaboration), Phys. Rev. Lett. 132, 051902 (2024).
  7. J. Liao and E. Shuryak, Phys. Rev. C 75, 054907 (2007).
  8. J. Liao and E. Shuryak, Phys. Rev. Lett. 101, 162302 (2008).
  9. J. Liao and E. Shuryak, Phys. Rev. Lett. 102, 202302 (2009).
  10. J. Xu, J. Liao, and M. Gyulassy, J. High Energy Phys. 02 (2016) 169.
  11. H. van Hees, M. Mannarelli, V. Greco, and R. Rapp, Phys. Rev. Lett. 100, 192301 (2008).
  12. F. Riek and R. Rapp, Phys. Rev. C 82, 035201 (2010).
  13. M. He, R. J. Fries, and R. Rapp, Phys. Rev. Lett. 110, 112301 (2013).
  14. C. P. Herzog, A. Karch, P. Kovtun, C. Kozcaz, and L. G. Yaffe, J. High Energy Phys. 07 (2006) 013.
  15. S. S. Gubser, Phys. Rev. D 74, 126005 (2006).
  16. B. Chen, X. Chen, X. Li, Z.-R. Zhu, and K. Zhou, Phys. Rev. D 111, 086033 (2025).
  17. B. Chen, L. Zhu, X. Chen, D. Hou, and X. Chen, Nucl. Sci. Tech. 37, 153 (2026).
  18. J. Peng, K. Yu, S. Li, W. Xiong, F. Sun, and W. Xie, Phys. Rev. D 109, 096028 (2024).
  19. S. Li, F. Sun, W. Xie, and W. Xiong, Eur. Phys. J. C 81, 536 (2021).
  20. J. Lou, W. Wang, J. Peng, F. Sun, K. Wu, W. Xie, Z. Zhang, S. Li, and S. Wang, Phys. Rev. D 112, 116001 (2025).
  21. X. Dong, Y. Lee, and R. Rapp, Annu. Rev. Nucl. Part. Sci. 69, 417 (2019).
  22. Z. Tang, Z.-B. Tang, W. Zha, W.-M. Zha, Y. Zhang, and Y.-F. Zhang, Nucl. Sci. Tech. 31, 81 (2020).
  23. J. Chen et al., Nucl. Sci. Tech. 35, 214 (2024).
  24. S. Acharya et al. (ALICE Collaboration), J. High Energy Phys. 01 (2022) 174.
  25. S. Acharya et al. (ALICE Collaboration), Eur. Phys. J. C 84, 813 (2024).
  26. E. Braaten and T. C. Yuan, Phys. Rev. Lett. 66, 2183 (1991).
  27. J.-P. Blaizot and E. Iancu, Phys. Rep. 359, 355 (2002).
  28. E. Braaten and M. H. Thoma, Phys. Rev. D 44, 1298 (1991).
  29. E. Braaten and M. H. Thoma, Phys. Rev. D 44, R2625 (1991).
  30. P. Romatschke and M. Strickland, Phys. Rev. D 69, 065005 (2004).
  31. P. Romatschke and M. Strickland, Phys. Rev. D 71, 125008 (2005).
  32. M. Djordjevic, Phys. Rev. C 74, 064907 (2006).
  33. S. Peigne and A. Peshier, Phys. Rev. D 77, 014015 (2008).
  34. S. Peigne and A. Peshier, Phys. Rev. D 77, 114017 (2008).
  35. W. M. Alberico, A. Beraudo, A. De Pace, A. Molinari, M. Monteno, M. Nardi, and F. Prino, Eur. Phys. J. C 71, 1666 (2011).
  36. P. B. Gossiaux and J. Aichelin, Phys. Rev. C 78, 014904 (2008).
  37. R. Rapp and H. van Hees, in Quark-Gluon Plasma 4 (World Scientific, Singapore, 2010), pp. 111–206.
  38. S. Li and J. Liao, Eur. Phys. J. C 80, 671 (2020).
  39. H. A. Weldon, Phys. Rev. D 28, 2007 (1983).
  40. Y. Hidaka and R. D. Pisarski, Phys. Rev. D 80, 036004 (2009); 102, 059902(E) (2020).
  41. Q. Du, M. Du, and Y. Guo, Phys. Rev. D 110, 034011 (2024).
  42. Y. Hidaka and R. D. Pisarski, Phys. Rev. D 78, 071501 (2008).
  43. Y. Hidaka, S. Lin, R. D. Pisarski, and D. Satow, J. High Energy Phys. 10 (2015) 005.
  44. Y. Guo and Q. Du, J. High Energy Phys. 05 (2019) 042.
  45. P. N. Meisinger, T. R. Miller, and M. C. Ogilvie, Phys. Rev. D 65, 034009 (2002).
  46. Y. Hidaka and R. D. Pisarski, Phys. Rev. D 104, 074036 (2021).
  47. J. I. Kapusta and C. Gale, Finite-Temperature Field Theory: Principles and Applications, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2011).
  48. M. L. Bellac, Thermal Field Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2011).
  49. B. Singh, A. Abhishek, S. K. Das, and H. Mishra, Phys. Rev. D 100, 114019 (2019).
  50. Y. Guo and Z. Kuang, Phys. Rev. D 104, 014015 (2021).
  51. W. Liu, L. Dong, and Y. Guo, Phys. Rev. D 111, 034016 (2025).
  52. A. Bazavov, N. Brambilla, P. Petreczky, A. Vairo, and J. H. Weber (TUMQCD Collaboration), Phys. Rev. D 98, 054511 (2018).
  53. S. Caron-Huot and G. D. Moore, Phys. Rev. Lett. 100, 052301 (2008).
  54. W. M. Alberico, A. Beraudo, A. De Pace, A. Molinari, M. Monteno, M. Nardi, F. Prino, and M. Sitta, Eur. Phys. J. C 73, 2481 (2013).
  55. N. Brambilla, V. Leino, P. Petreczky, and A. Vairo, Phys. Rev. D 102, 074503 (2020).
  56. S. S. Gubser, Nucl. Phys. B790, 175 (2008).
  57. J. Casalderrey-Solana and D. Teaney, J. High Energy Phys. 04 (2007) 039.
  58. A. Francis, O. Kaczmarek, M. Laine, T. Neuhaus, and H. Ohno, Phys. Rev. D 92, 116003 (2015).
  59. S. Gupta and R. Sharma, Phys. Rev. D 97, 036025 (2018).
  60. J. Berges, M. P. Heller, A. Mazeliauskas, and R. Venugopalan, Rev. Mod. Phys. 93, 035003 (2021).
  61. S. Li, C. Wang, R. Wan, and J. Liao, Phys. Rev. C 99, 054909 (2019).
  62. M. He, H. van Hees, and R. Rapp, Prog. Part. Nucl. Phys. 130, 104020 (2023).
  63. S. Li, C. Wang, X. Yuan, and S. Feng, Phys. Rev. C 98, 014909 (2018).
  64. S. Li and C. Wang, Phys. Rev. C 98, 034914 (2018).
  65. S. Li, W. Xiong, and R. Wan, Eur. Phys. J. C 80, 1113 (2020).

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Phys. Rev. D 114, 016005– Published 6 July, 2026
  • Received 13 October 2025
  • Accepted 9 June 2026
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