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Real-time QCD static potential at high temperature

Margaret E. Carrington1,2, Cristina Manuel3,4, and Joan Soto5,4

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Phys. Rev. D 113, 016006 – Published 7 January, 2026

DOI: https://doi.org/10.1103/mzw1-bsvy

Abstract

We develop a procedure to analytically calculate higher-order contributions to the high-temperature real-time static potential in QCD. It is based on the introduction of a semihard external scale, which lies between the hard scale (the temperature) and the soft scale (the screening mass), and the method of integration by regions. We calculate the leading and next-to-leading corrections in the region where bound states transit from narrow resonances to wide ones. The calculation involves both loop diagrams calculated in the hard thermal loop (HTL) effective theory and power corrections to the HTL Lagrangian calculated in QCD. We also calculate the thermal corrections to the heavy quarkonium spectrum, and estimate the dissociation temperatures. We compare our results with recent lattice data and discuss their usefulness to guide lattice inputs in inverse problems.

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High-Temperature QCD Static Potential beyond Leading Order

Margaret E. Carrington, Cristina Manuel, and Joan Soto
Phys. Rev. Lett. 134, 011905 (2025)

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References (62)

  1. T. Matsui and H. Satz, Phys. Lett. B 178, 416 (1986).
  2. M. Laine, O. Philipsen, P. Romatschke, and M. Tassler, J. High Energy Phys. 03 (2007) 054.
  3. M. A. Escobedo and J. Soto, Phys. Rev. A 78, 032520 (2008).
  4. S. Acharya et al. (ALICE Collaboration), Phys. Lett. B 822, 136579 (2021).
  5. A. M. Sirunyan et al. (CMS Collaboration), Phys. Lett. B 790, 270 (2019).
  6. A. M. Sirunyan et al. (CMS Collaboration), Eur. Phys. J. C 78, 509 (2018).
  7. N. Brambilla, M. A. Escobedo, J. Soto, and A. Vairo, Phys. Rev. D 96, 034021 (2017).
  8. N. Brambilla, M. A. Escobedo, J. Soto, and A. Vairo, Phys. Rev. D 97, 074009 (2018).
  9. N. Brambilla, M. Á. Escobedo, M. Strickland, A. Vairo, P. Vander Griend, and J. H. Weber, J. High Energy Phys. 05 (2021) 136.
  10. N. Brambilla, M. Á. Escobedo, M. Strickland, A. Vairo, P. Vander Griend, and J. H. Weber, Phys. Rev. D 104, 094049 (2021).
  11. N. Brambilla, M. Á. Escobedo, A. Islam, M. Strickland, A. Tiwari, A. Vairo, and P. Vander Griend, J. High Energy Phys. 08 (2022) 303.
  12. M. E. Carrington, C. Manuel, and J. Soto, Phys. Rev. Lett. 134, 011905 (2025).
  13. M. Beneke and V. A. Smirnov, Nucl. Phys. B522, 321 (1998).
  14. V. A. Smirnov, Springer Tracts Mod. Phys. 250, 1 (2012).
  15. M. Jarrell and J. E. Gubernatis, Phys. Rep. 269, 133 (1996).
  16. M. Asakawa, T. Hatsuda, and Y. Nakahara, Prog. Part. Nucl. Phys. 46, 459 (2001).
  17. A. Rothkopf, J. Comput. Phys. 238, 106 (2013).
  18. Y. Burnier and A. Rothkopf, Phys. Rev. D 87, 114019 (2013).
  19. Y. Burnier and A. Rothkopf, Phys. Rev. Lett. 111, 182003 (2013).
  20. A. Rothkopf, T. Hatsuda, and S. Sasaki, Phys. Rev. Lett. 108, 162001 (2012).
  21. Y. Burnier, O. Kaczmarek, and A. Rothkopf, Phys. Rev. Lett. 114, 082001 (2015).
  22. Y. Burnier, O. Kaczmarek, and A. Rothkopf, J. High Energy Phys. 12 (2015) 101.
  23. Y. Burnier and A. Rothkopf, Phys. Rev. D 95, 054511 (2017).
  24. A. Lehmann and A. Rothkopf, J. High Energy Phys. 07 (2021) 067.
  25. K. Boguslavski, B. S. Kasmaei, and M. Strickland, J. High Energy Phys. 10 (2021) 083.
  26. D. Bala et al. (HotQCD Collaboration), Phys. Rev. D 105, 054513 (2022).
  27. L. Dong, Y. Guo, A. Islam, A. Rothkopf, and M. Strickland, J. High Energy Phys. 09 (2022) 200.
  28. 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).
  29. G. Zhou, Z. Su, B. Hao, and L. Yu, Phys. Rep. 118, 1 (1985).
  30. J. Ghiglieri, A. Kurkela, M. Strickland, and A. Vuorinen, Phys. Rep. 880, 1 (2020).
  31. A. Rothkopf, Phys. Rep. 858, 1 (2020).
  32. E. Braaten and R. D. Pisarski, Phys. Rev. D 45, R1827 (1992).
  33. W. E. Caswell and G. P. Lepage, Phys. Lett. 167B, 437 (1986).
  34. A. Pineda and J. Soto, Nucl. Phys. B, Proc. Suppl. 64, 428 (1998).
  35. N. Brambilla, J. Ghiglieri, A. Vairo, and P. Petreczky, Phys. Rev. D 78, 014017 (2008).
  36. N. Brambilla, A. Pineda, J. Soto, and A. Vairo, Rev. Mod. Phys. 77, 1423 (2005).
  37. A. Pineda, Prog. Part. Nucl. Phys. 67, 735 (2012).
  38. A. K. Rebhan, Phys. Rev. D 48, R3967 (1993).
  39. C. Y. Shi, J. Q. Zhu, Z. L. Ma, and Y. D. Li, Chin. Phys. Lett. 32, 121201 (2015).
  40. J. Q. Zhu, Z. L. Ma, C. Y. Shi, and Y. D. Li, Nucl. Phys. A942, 54 (2015).
  41. C. Manuel, J. Soto, and S. Stetina, Phys. Rev. D 94, 025017 (2016).
  42. S. Carignano, C. Manuel, and J. Soto, Phys. Lett. B 780, 308 (2018).
  43. H. Leutwyler, Phys. Lett. 98B, 447 (1981).
  44. N. Brambilla, A. Pineda, J. Soto, and A. Vairo, Phys. Lett. B 470, 215 (1999).
  45. Y. Kiyo and Y. Sumino, Phys. Lett. B 730, 76 (2014).
  46. C. Anzai, D. Moreno, and A. Pineda, Phys. Rev. D 98, 114034 (2018).
  47. R. Larsen, S. Meinel, S. Mukherjee, and P. Petreczky, Phys. Lett. B 800, 135119 (2020).
  48. M. E. Carrington, C. Manuel, and J. Soto, Proc. Sci. QNP2024 (2025) 109.
  49. A. Bazavov, N. Brambilla, X. Garcia Tormo, i, P. Petreczky, J. Soto, and A. Vairo, Phys. Rev. D 86, 114031 (2012).
  50. W. Lucha and F. F. Schoberl, Int. J. Mod. Phys. C 10, 607 (1999).
  51. G. Aarts, C. Allton, T. Harris, S. Kim, M. P. Lombardo, S. M. Ryan, and J. I. Skullerud, J. High Energy Phys. 07 (2014) 097.
  52. S. Ali et al. (HotQCD Collaboration), Phys. Rev. D 112, 054510 (2025).
  53. H. T. Ding, W. P. Huang, R. Larsen, S. Meinel, S. Mukherjee, P. Petreczky, and Z. Tang, J. High Energy Phys. 05 (2025) 149.
  54. O. Kaczmarek, F. Karsch, E. Laermann, and M. Lutgemeier, Phys. Rev. D 62, 034021 (2000).
  55. O. Kaczmarek, F. Karsch, P. Petreczky, and F. Zantow, Phys. Lett. B 543, 41 (2002).
  56. P. Petreczky and K. Petrov, Phys. Rev. D 70, 054503 (2004).
  57. O. Kaczmarek and F. Zantow, Phys. Rev. D 71, 114510 (2005).
  58. Y. Maezawa, N. Ukita, S. Aoki, S. Ejiri, T. Hatsuda, N. Ishii, and K. Kanaya (WHOT-QCD Collaboration), Phys. Rev. D 75, 074501 (2007).
  59. Y. Burnier, M. Laine, and M. Vepsalainen, J. High Energy Phys. 01 (2010) 054; 01 (2013) 180(E).
  60. A. Ekstedt, J. High Energy Phys. 06 (2023) 135.
  61. T. Gorda, R. Paatelainen, S. Säppi, and K. Seppänen, J. High Energy Phys. 08 (2023) 021.
  62. S. Titard and F. J. Yndurain, Phys. Rev. D 49, 6007 (1994).

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Phys. Rev. D 113, 016006– Published 7 January, 2026
  • Received 16 October 2025
  • Accepted 5 December 2025
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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.

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