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

Effect of the charm quark on the QCD chiral phase diagram

Fei Gao1, Yuepeng Guan2, and Shinya Matsuzaki2

Phys. Rev. D 114, 014016 – Published 6 July, 2026

DOI: https://doi.org/10.1103/8r63-rztg

Abstract

We study the influence of charm-quark dynamics on the chiral phase structure of QCD using the recently developed miniDSE scheme for the Dyson-Schwinger equations. By comparing the quark and gluon propagators in the 2+1- and 2+1+1-flavor setups within the same truncation scheme, we qualify the impact of the charm-quark loop on the QCD phase diagram. Our results show that the charm quark has only a mild effect on the crossover boundary, which remains almost unchanged within the present setup. The most visible effect is a small shift of the critical endpoint (CEP) toward lower baryon chemical potential, by approximately 3%. The present result provides a controlled estimate of the charm-loop effect within the same miniDSE truncation. It indicates that heavy-flavor contributions may become relevant when aiming at precision studies of the CEP location.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (49)

  1. M. M. Aggarwal et al. (STAR Collaboration), arXiv:1007.2613.
  2. B. Mohanty (STAR Collaboration), J. Phys. G 38, 124023 (2011).
  3. X. Luo and N. Xu, Nucl. Sci. Tech. 28, 112 (2017).
  4. T. Nonaka, J. Phys. Soc. Jpn. Conf. Proc. 26, 024007 (2019).
  5. J. Chen et al., Nucl. Sci. Tech. 35, 214 (2024).
  6. M. Buballa, Phys. Rep. 407, 205 (2005).
  7. K. Fukushima and C. Sasaki, Prog. Part. Nucl. Phys. 72, 99 (2013).
  8. M. Oertel, M. Hempel, T. Klähn, and S. Typel, Rev. Mod. Phys. 89, 015007 (2017).
  9. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  10. F. Gao and I. M. Oldengott, Phys. Rev. Lett. 128, 131301 (2022).
  11. H.-w. Zheng, F. Gao, L. Bian, S.-x. Qin, and Y.-x. Liu, Phys. Rev. D 111, L021303 (2025).
  12. F. Gao, J. Harz, C. Hati, Y. Lu, I. M. Oldengott, and G. White, J. High Energy Phys. 06 (2025) 247.
  13. G. Y. Shao, M. Di Toro, V. Greco, M. Colonna, S. Plumari, B. Liu, and Y. X. Liu, Phys. Rev. D 84, 034028 (2011).
  14. X. Y. Xin, S. X. Qin, and Y. X. Liu, Phys. Rev. D 90, 076006 (2014).
  15. S. He, S.-Y. Wu, Y. Yang, and P.-H. Yuan, J. High Energy Phys. 04 (2013) 093.
  16. K. Chelabi, Z. Fang, M. Huang, D. Li, and Y.-L. Wu, J. High Energy Phys. 04 (2016) 036.
  17. T. Kojo, D. Hou, J. Okafor, and H. Togashi, Phys. Rev. D 104, 063036 (2021).
  18. X. Chen, L. Zhang, D. Li, D. Hou, and M. Huang, J. High Energy Phys. 07 (2021) 132.
  19. M. Hippert, J. Grefa, T. A. Manning, J. Noronha, J. Noronha-Hostler, I. Portillo Vazquez, C. Ratti, R. Rougemont, and M. Trujillo, Phys. Rev. D 110, 094006 (2024).
  20. R. G. Cai, S. He, L. Li, and Y. X. Wang, Phys. Rev. D 106, L121902 (2022).
  21. X. Chen, D. Li, and M. Huang, Chin. Phys. C 43, 023105 (2019).
  22. G. Basar, Phys. Rev. C 110, 015203 (2024).
  23. A. Adam, S. Borsányi, Z. Fodor, J. N. Guenther, P. Parotto, A. Pásztor, D. Pesznyák, L. Pirelli, and C. H. Wong, Proc. Sci., LATTICE2024 (2025) 178 [arXiv:2502.03211].
  24. C. Ecker, N. Jokela, and M. Järvinen, Phys. Rev. D 113, L041302 (2026).
  25. S. Borsanyi, Z. Fodor, J. N. Guenther, R. Kara, S. D. Katz, P. Parotto, A. Pasztor, C. Ratti, and K. K. Szabo, Phys. Rev. Lett. 125, 052001 (2020).
  26. A. Bazavov et al. (HotQCD Collaboration), Phys. Lett. B 795, 15 (2019).
  27. C. Bonati, M. D’Elia, F. Negro, F. Sanfilippo, and K. Zambello, Phys. Rev. D 98, 054510 (2018).
  28. S. X. Qin, L. Chang, H. Chen, Y. X. Liu, and C. D. Roberts, Phys. Rev. Lett. 106, 172301 (2011).
  29. C. S. Fischer, J. Luecker, and C. A. Welzbacher, Phys. Rev. D 90, 034022 (2014).
  30. F. Gao and Y. X. Liu, Phys. Rev. D 94, 076009 (2016).
  31. C. S. Fischer, Prog. Part. Nucl. Phys. 105, 1 (2019).
  32. F. Gao and J. M. Pawlowski, Phys. Rev. D 102, 034027 (2020).
  33. F. Gao and J. M. Pawlowski, Phys. Lett. B 820, 136584 (2021).
  34. P. J. Gunkel and C. S. Fischer, Phys. Rev. D 104, 054022 (2021).
  35. W. J. Fu, J. M. Pawlowski, and F. Rennecke, Phys. Rev. D 101, 054032 (2020).
  36. N. Dupuis, L. Canet, A. Eichhorn, W. Metzner, J. M. Pawlowski, M. Tissier, and N. Wschebor, Phys. Rep. 910, 1 (2021).
  37. W. J. Fu, Commun. Theor. Phys. 74, 097304 (2022).
  38. B. E. Aboona et al. (STAR Collaboration), Phys. Rev. Lett. 135, 142301 (2025).
  39. H. van Hees, V. Greco, and R. Rapp, Phys. Rev. C 73, 034913 (2006).
  40. K. Goswami, K. K. Pradhan, D. Sahu, J. Dey, and R. Sahoo, Phys. Rev. D 111, 014029 (2025).
  41. C. A. Welzbacher, C. S. Fischer, and J. Luecker, J. Phys. Conf. Ser. 599, 012015 (2015).
  42. Y. Lu, F. Gao, Y.-X. Liu, and J. M. Pawlowski, Phys. Rev. D 110, 014036 (2024).
  43. C. Tang, F. Gao, and Y.-X. Liu, Phys. Rev. D 100, 056001 (2019).
  44. F. Gao, J. Papavassiliou, and J. M. Pawlowski, Phys. Rev. D 103, 094013 (2021).
  45. A. C. Aguilar, C. O. Ambrósio, F. De Soto, M. N. Ferreira, B. M. Oliveira, J. Papavassiliou, and J. Rodríguez-Quintero, Phys. Rev. D 104, 054028 (2021).
  46. Y. Lu, F. Gao, Y.-x. Liu, and J. M. Pawlowski, Phys. Rev. D 113, 054019 (2026).
  47. N. Brown and M. R. Pennington, Phys. Rev. D 38, 2266 (1988).
  48. C. S. Fischer and J. Luecker, Phys. Lett. B 718, 1036 (2013).
  49. M. D. Schwartz, Quantum Field Theory and the Standard Model (Cambridge University Press, Cambridge, England, 2014).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation