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  • Open Access

Memory effect on heavy quark dynamics in hot QCD matter

Jai Prakash, Ling Hai Li, Ying Shan Zhao, and Yifeng Sun*

  • State Key Laboratory of Dark Matter Physics, Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (MOE), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

  • *Contact author: sunyfphy@sjtu.edu.cn
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Phys. Rev. D 114, 014033 – Published 16 July, 2026

DOI: https://doi.org/10.1103/pkh6-lwqg

Abstract

We study the heavy quark dynamics in the presence of memory within the framework of a generalized Langevin equation. Time correlated thermal noise with power-law decay is generated by a fractional differential equation, formulated using the Caputo fractional derivative with order parameter ν. The effect of memory is calculated through the momentum correlation, the time evolution of the average squared momentum, the average squared displacement, and the average kinetic energy. The effect of memory is further studied for the higher normalized central moments of the heavy quark transverse-momentum distribution. The results indicate that time correlated thermal noise substantially influences heavy quark dynamics in the quark gluon plasma.

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References (114)

  1. J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. 97, 162301 (2006).
  2. J. Adams et al. (STAR Collaboration), Nucl. Phys. A757, 102 (2005).
  3. K. Adcox et al. (PHENIX Collaboration), Nucl. Phys. A757, 184 (2005).
  4. K. Aamodt et al. (ALICE Collaboration), Phys. Rev. Lett. 105, 252301 (2010).
  5. I. Arsene et al. (BRAHMS Collaboration), Phys. Rev. C 72, 014908 (2005).
  6. H. van Hees and R. Rapp, Phys. Rev. C 71, 034907 (2005).
  7. R. Rapp and H. van Hees, Heavy Quarks in the Quark-Gluon Plasma (World Scientific, Singapore, 2010), pp. 111–206.
  8. S. Cao, T. Luo, G.-Y. Qin, and X.-N. Wang, Phys. Rev. C 94, 014909 (2016).
  9. S. Cao, G.-Y. Qin, and S. A. Bass, Phys. Rev. C 92, 024907 (2015).
  10. F. Scardina, S. K. Das, V. Minissale, S. Plumari, and V. Greco, Phys. Rev. C 96, 044905 (2017).
  11. M. He, H. van Hees, and R. Rapp, Prog. Part. Nucl. Phys. 130, 104020 (2023).
  12. T. Song, H. Berrehrah, D. Cabrera, J. M. Torres-Rincon, L. Tolos, W. Cassing, and E. Bratkovskaya, Phys. Rev. C 92, 014910 (2015).
  13. A. Andronic et al., Eur. Phys. J. C 76, 107 (2016).
  14. X. Dong and V. Greco, Prog. Part. Nucl. Phys. 104, 97 (2019).
  15. G. Aarts et al., Eur. Phys. J. A 53, 93 (2017).
  16. S. Plumari, V. Minissale, S. K. Das, G. Coci, and V. Greco, Eur. Phys. J. C 78, 348 (2018).
  17. P. B. Gossiaux and J. Aichelin, Phys. Rev. C 78, 014904 (2008).
  18. J. Prakash, M. Kurian, S. K. Das, and V. Chandra, Phys. Rev. D 103, 094009 (2021).
  19. J. Prakash, V. Chandra, and S. K. Das, Phys. Rev. D 108, 096016 (2023).
  20. J. Prakash and M. Y. Jamal, Eur. Phys. J. Plus 139, 778 (2024).
  21. M. Y. Jamal, J. Prakash, I. Nilima, and A. Bandyopadhyay, J. Phys. G 51, 045104 (2024).
  22. A. Zaccone, Nucl. Phys. B1000, 116483 (2024).
  23. M. Singh, M. Kurian, S. Jeon, and C. Gale, Phys. Rev. C 108, 054901 (2023).
  24. M. Kurian, M. Singh, V. Chandra, S. Jeon, and C. Gale, Phys. Rev. C 102, 044907 (2020).
  25. S. Mazumder, T. Bhattacharyya, J.-e. Alam, and S. K. Das, Phys. Rev. C 84, 044901 (2011).
  26. M. Y. Jamal, S. K. Das, and M. Ruggieri, Phys. Rev. D 103, 054030 (2021).
  27. M. Y. Jamal and B. Mohanty, Eur. Phys. J. C 81, 616 (2021).
  28. M. Y. Jamal and B. Mohanty, Eur. Phys. J. Plus 136, 130 (2021).
  29. Y. Sun, S. Plumari, and S. K. Das, Phys. Lett. B 843, 138043 (2023).
  30. S. Plumari, G. Coci, V. Minissale, S. K. Das, Y. Sun, and V. Greco, Phys. Lett. B 805, 135460 (2020).
  31. J. Prakash and M. Y. Jamal, J. Phys. G 51, 025101 (2023).
  32. X. Du and W. Qian, Phys. Rev. D 109, 076025 (2024).
  33. A. Shaikh, M. Kurian, S. K. Das, V. Chandra, S. Dash, and B. K. Nandi, Phys. Rev. D 104, 034017 (2021).
  34. A. Kumar, M. Kurian, S. K. Das, and V. Chandra, Phys. Rev. C 105, 054903 (2022).
  35. Sumit, J. Parkash, S. K. Das, and N. Haque, arXiv:2506.01922.
  36. L. Altenkort, O. Kaczmarek, R. Larsen, S. Mukherjee, P. Petreczky, H.-T. Shu, and S. Stendebach (HotQCD Collaboration), Phys. Rev. Lett. 130, 231902 (2023).
  37. S. K. Das, J. M. Torres-Rincon, and R. Rapp, Phys. Rep. 1129–1131, 1 (2025).
  38. V. Chandra and S. K. Das, Eur. Phys. J. Special Topics 233, 429 (2024).
  39. M. Debnath, R. Ghosh, M. Y. Jamal, M. Kurian, and J. Prakash, Phys. Rev. D 109, L011503 (2024).
  40. M. Y. Jamal, F.-P. Li, L.-G. Pang, and G.-Y. Qin, Phys. Rev. C 113, 034915 (2026).
  41. S. K. Das et al., Int. J. Mod. Phys. E 34, 2544003 (2025).
  42. S. K. Das et al., Int. J. Mod. Phys. E 31, 12 (2022).
  43. M. L. Sambataro, S. Plumari, S. K. Das, and V. Greco, Phys. Rev. Lett. 136, 212302 (2026).
  44. S. K. Das, O. Soloveva, T. Song, and E. Bratkovskaya, Phys. Rev. C 112, 064901 (2025).
  45. D. Dey, A. Bandyopadhyay, S. K. Das, S. Dash, V. Chandra, and B. K. Nandi, Phys. Rev. D 112, 016011 (2025).
  46. V. Minissale, S. Plumari, Y. Sun, and V. Greco, Eur. Phys. J. C 84, 228 (2024).
  47. L. Oliva, G. Parisi, V. Greco, and M. Ruggieri, Phys. Rev. D 112, 014008 (2025).
  48. S. Mazumder, T. Bhattacharyya, J.-e. Alam, and S. K. Das, Phys. Rev. C 84, 044901 (2011).
  49. T. Bhattacharyya, E. Megias, and A. Deppman, Phys. Lett. B 856, 138907 (2024).
  50. I. Grishmanovskii, T. Song, C. Greiner, and E. Bratkovskaya, Phys. Rev. D 112, 014042 (2025).
  51. N. Oei, N. Krenz, H. van Hees, C. Greiner, and J. M. Torres-Rincon, Phys. Rev. D 111, 074012 (2025).
  52. I. Grishmanovskii, O. Soloveva, T. Song, C. Greiner, and E. Bratkovskaya, Phys. Rev. C 109, 024911 (2024).
  53. M. L. Sambataro, V. Minissale, S. Plumari, and V. Greco, Phys. Lett. B 872, 140049 (2026).
  54. C. Young, B. Schenke, S. Jeon, and C. Gale, Phys. Rev. C 86, 034905 (2012).
  55. T. Lang, H. van Hees, G. Inghirami, J. Steinheimer, and M. Bleicher, Phys. Rev. C 93, 014901 (2016).
  56. S. Cao and S. A. Bass, Phys. Rev. C 84, 064902 (2011).
  57. H. van Hees, M. Mannarelli, V. Greco, and R. Rapp, Phys. Rev. Lett. 100, 192301 (2008).
  58. S. Cao et al., Phys. Rev. C 99, 054907 (2019).
  59. A. Beraudo et al., Nucl. Phys. A979, 21 (2018).
  60. F. Prino and R. Rapp, J. Phys. G 43, 093002 (2016).
  61. M. He, H. van Hees, P. B. Gossiaux, R. J. Fries, and R. Rapp, Phys. Rev. E 88, 032138 (2013).
  62. Y. Xu et al., Phys. Rev. C 99, 014902 (2019).
  63. M. He, R. J. Fries, and R. Rapp, Phys. Rev. Lett. 110, 112301 (2013).
  64. C. Zhang, L. Zheng, S. Shi, and Z.-W. Lin, Phys. Lett. B 846, 138219 (2023).
  65. C. Zhang, L. Zheng, S. Shi, and Z.-W. Lin, Phys. Lett. B 846, 138219 (2023).
  66. B. Schenke and C. Greiner, Phys. Rev. Lett. 98, 022301 (2007).
  67. J. I. Kapusta, B. Müller, and M. Stephanov, Phys. Rev. C 85, 054906 (2012).
  68. M. Ruggieri, M. Frasca, and S. K. Das, Chin. Phys. C 43, 094105 (2019).
  69. B. Schüller, A. Meistrenko, H. Van Hees, Z. Xu, and C. Greiner, Ann. Phys. (Amsterdam) 412, 168045 (2020).
  70. W. Chen, C. Greiner, and Z. Xu, Phys. Rev. E 107, 064131 (2023).
  71. C. Greiner, K. Wagner, and P.-G. Reinhard, Phys. Rev. C 49, 1693 (1994).
  72. A. E. Gegechkori, Y. A. Anischenko, P. N. Nadtochy, and G. D. Adeev, Phys. At. Nucl. 71, 2007 (2008).
  73. F. A. Ivanyuk, S. V. Radionov, C. Ishizuka, and S. Chiba, arXiv:2103.14145.
  74. J. I. Kapusta and C. Young, Phys. Rev. C 90, 044902 (2014).
  75. K. Murase and T. Hirano, arXiv:1304.3243.
  76. J. Hammelmann, J. M. Torres-Rincon, J.-B. Rose, M. Greif, and H. Elfner, Phys. Rev. D 99, 076015 (2019).
  77. M. Ruggieri, Pooja, J. Prakash, and S. K. Das, Phys. Rev. D 106, 034032 (2022).
  78. Pooja, S. K. Das, V. Greco, and M. Ruggieri, Phys. Rev. D 108, 054026 (2023).
  79. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000).
  80. R. Metzler and J. Klafter, J. Phys. A 37, R161 (2004).
  81. V. Zaburdaev, S. Denisov, and J. Klafter, Rev. Mod. Phys. 87, 483 (2015).
  82. M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature (London) 363, 31 (1993).
  83. P. Guo, C. Zeng, C. Li, and Y. Chen, Fract. Calc. Appl. Anal. 16, 123 (2013).
  84. C. Li and F. Zeng, Numer. Funct. Anal. Optim. 34, 149 (2013).
  85. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (John Wiley & Sons, Inc., New York, 1993), pp. xvi + 366.
  86. M. Caputo and F. Mainardi, Riv. Nuovo Cimento 1, 161 (1971).
  87. Fractals and Fractional Calculus in Continuum Mechanics, CISM Courses and Lectures, edited by A. Carpinteri and F. Mainardi, Vol. 378 (Springer, Vienna, 1997).
  88. M. Ciesielski and J. Leszczyński, arXiv:math-ph/0309007.
  89. T. Sandev, A. Iomin, and H. Kantz, Phys. Rev. E 91, 032108 (2015).
  90. K. Fa and E. Lenzi, Phys. Rev. E 75, 061118 (2007).
  91. S. Lim and L. Teo, J. Stat. Mech. (2009) P08015.
  92. M. Caputo, Geophys. J. Int. 13, 529 (1967).
  93. F. Mainardi, A. Mura, G. Pagnini, and R. Gorenflo, in Mathematical Methods in Engineering (Springer Netherlands, Dordrecht, 2007), pp. 23–55.
  94. S. C. Kou and X. S. Xie, Phys. Rev. Lett. 93, 180603 (2004).
  95. J. Prakash, Phys. Rev. C 110, 044902 (2024).
  96. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
  97. L. C. G. Rogers, Math. Finance 7, 95 (1997).
  98. S. C. Lim and L. P. Teo, J. Stat. Mech. (2009) P08015.
  99. T. Sandev, Živorad Tomovski, and J. L. Dubbeldam, Physica (Amsterdam) 390, 3627 (2011).
  100. T. Sandev, R. Metzler, and Živorad Tomovski, Fract. Calc. Appl. Anal. 15, 426 (2012).
  101. T. Sandev, R. Metzler, and Ž. Tomovski, J. Math. Phys. (N.Y.) 55, 023301 (2014).
  102. S. K. Das, F. Scardina, S. Plumari, and V. Greco, Phys. Rev. C 90, 044901 (2014).
  103. H. Meyer, T. Voigtmann, and T. Schilling, J. Chem. Phys. 147, 214110 (2017).
  104. H. Meyer, T. Voigtmann, and T. Schilling, J. Chem. Phys. 150, 174118 (2019).
  105. C. Widder, F. Glatzel, and T. Schilling, J. Chem. Phys. 157, 194107 (2022).
  106. M. Loève, Probability Theory, 4th ed. (Springer-Verlag, New York, 1977).
  107. A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th ed. (McGraw-Hill, Boston, 2002).
  108. G. D. Moore and D. Teaney, Phys. Rev. C 71, 064904 (2005).
  109. W. Chen, C. Greiner, and Z. Xu, Phys. Rev. E 107, 064131 (2023).
  110. T. Sandev, R. Metzler, and Z. Tomovski, J. Math. Phys. (N.Y.) 55, 023301 (2014).
  111. G. R. Kneller, J. Chem. Phys. 134, 224106 (2011).
  112. B. Svetitsky, Phys. Rev. D 37, 2484 (1988).
  113. M. Cacciari, P. Nason, and R. Vogt, Phys. Rev. Lett. 95, 122001 (2005).
  114. M. Cacciari, S. Frixione, N. Houdeau, M. L. Mangano, P. Nason, and G. Ridolfi, J. High Energy Phys. 10 (2012) 137.

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Phys. Rev. D 114, 014033– Published 16 July, 2026
  • Received 13 April 2026
  • Accepted 24 June 2026
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