- Physical Review Journals
All JournalsPhysics Magazine

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

Jet quenching and quark energy loss from holographic QCD

Zhibin Li1,*, Danning Li2,†, and Mei Huang3,‡

  • *Contact author: lizhibin@zzu.edu.cn
  • †Contact author: lidanning@jnu.edu.cn
  • ‡Contact author: huangmei@ucas.ac.cn
PDF

Phys. Rev. D 111, 126019 – Published 26 June, 2025

DOI: https://doi.org/10.1103/52sx-qvy8

Abstract

The jet quenching parameter and energy loss of light and heavy quarks have been investigated in the framework of holographic quantum chromodynamics (QCD) models with a critical end point (CEP) at finite baryon chemical potential in Nf=2,2+1,2+1+1 systems. The properties of the jet quenching parameter and energy loss around phase boundary have been carefully studied. It is found that the dimensionless jet quenching parameter and the energy loss of light and heavy quarks exhibit evident features around the phase boundary. Specifically, all these quantities increase rapidly near the CEP phase transition temperature TCEP with fixed μCEP. Moreover, the velocity dependent behavior of heavy quark energy loss differs significantly from charged particle energy loss in quantum electrodynamics (QED) matter. For electromagnetic interaction, the energy loss of charged particle can be described by the Bethe-Bloch formula and the Lindhand-Scharff-Schiott theory at low and high velocities, respectively. However, the heavy quark energy loss at CEP is approximately proportional to velocity at low velocities and aligns with Bjorken’s results at high velocities, which indicates that the heavy quark energy loss is predominantly collisional at low velocities and gluon radiation dominant at high velocities. For light quark energy loss, the behavior of the energy loss per unit length and the total energy loss differs significantly. However, the total energy loss and stopping distance exhibit similar behavior. This implies that the stopping distance predominantly determines the total energy loss. Thus, even with increased energy loss per unit length at higher temperatures or chemical potentials, the total energy loss decreases due to the reduced stopping distance.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (78)

  1. STAR Collaboration, Precision measurement of (net-)proton number fluctuations in Au+Au collisions at RHIC, arXiv:2504.00817.
  2. Y. Shen, W. Chen, X.-y. Wu, K. Xu, and M. Huang, Net proton number cumulants from viscous hydrodynamics with an equation of state including a critical end point, Phys. Rev. C 111, 014916 (2025).
  3. R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne, and D. Schiff, Radiative energy loss and p(T) broadening of high-energy partons in nuclei, Nucl. Phys. B484, 265 (1997).
  4. Z. Shan-Liang, X. Hong-Xi, and W. En-Ke, Jet quenching effect in relativistic heavy-ion collisions, Acta Phys. Sin. 72, 200304 (2023).
  5. K. M. Burke et al. (JET Collaboration), Extracting the jet transport coefficient from jet quenching in high-energy heavy-ion collisions, Phys. Rev. C 90, 014909 (2014).
  6. D. Li, J. Liao, and M. Huang, Enhancement of jet quenching around phase transition: Result from the dynamical holographic model, Phys. Rev. D 89, 126006 (2014).
  7. J. Xu, J. Liao, and M. Gyulassy, Consistency of perfect fluidity and jet quenching in semi-quark-gluon monopole plasmas, Chin. Phys. Lett. 32, 092501 (2015).
  8. L. Du and U. Heinz, Response of a baryon-charged medium to energetic partons, Phys. Rev. C 106, 034903 (2022).
  9. M. Panero, K. Rummukainen, and A. Schäfer, Lattice study of the jet quenching parameter, Phys. Rev. Lett. 112, 162001 (2014).
  10. S. Cao et al. (JETSCAPE Collaboration), Determining the jet transport coefficient q^ from inclusive hadron suppression measurements using Bayesian parameter estimation, Phys. Rev. C 104, 024905 (2021).
  11. M. Xie, W. Ke, H. Zhang, and X.-N. Wang, Information-field-based global Bayesian inference of the jet transport coefficient, Phys. Rev. C 108, L011901 (2023).
  12. J. Wu, S. Cao, and F. Li, Critical opalescence and its impact on the jet quenching parameter, Chin. Phys. Lett. 41, 031202 (2024).
  13. H. Liu, K. Rajagopal, and U. A. Wiedemann, Calculating the jet quenching parameter from AdS/CFT, Phys. Rev. Lett. 97, 182301 (2006).
  14. H. Liu, K. Rajagopal, and U. A. Wiedemann, Wilson loops in heavy ion collisions and their calculation in AdS/CFT, J. High Energy Phys. 03 (2007) 066.
  15. D. Li, S. He, and M. Huang, Temperature dependent transport coefficients in a dynamical holographic QCD model, J. High Energy Phys. 06 (2015) 046.
  16. X. Zhu and Z.-q. Zhang, Jet quenching parameter from a soft wall AdS/QCD model, Chin. Phys. C 44, 105105 (2020).
  17. X. Cao and H. Liu, Impact of the phase transition on quark-gluon plasma with an extremely strong magnetic field in holographic QCD, Phys. Rev. D 111, 026008 (2025).
  18. Y. Chen, D. Li, and M. Huang, The dynamical holographic QCD method for hadron physics and QCD matter, Commun. Theor. Phys. 74, 097201 (2022).
  19. R. Rougemont, Jet quenching parameters in strongly coupled anisotropic plasmas in the presence of magnetic fields, Phys. Rev. D 102, 034009 (2020).
  20. J.-X. Chen and D.-F. Hou, Heavy quark potential and jet quenching parameter in a rotating D-instanton background, Eur. Phys. J. C 84, 447 (2024).
  21. A. Ficnar, Holographic jet quenching, Ph.D. thesis, Columbia University, 2014.
  22. P. Jacobs and X.-N. Wang, Matter in extremis: Ultrarelativistic nuclear collisions at RHIC, Prog. Part. Nucl. Phys. 54, 443 (2005).
  23. M. Yousuf Jamal and V. Chandra, Energy loss of heavy quarks in the isotropic collisional hot QCD medium, Eur. Phys. J. C 79, 761 (2019).
  24. S. S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74, 126005 (2006).
  25. C. P. Herzog, A. Karch, P. Kovtun, C. Kozcaz, and L. G. Yaffe, Energy loss of a heavy quark moving through N=4 supersymmetric Yang-Mills plasma, J. High Energy Phys. 07 (2006) 013.
  26. U. Gursoy, E. Kiritsis, G. Michalogiorgakis, and F. Nitti, Thermal transport and drag force in improved holographic QCD, J. High Energy Phys. 12 (2009) 056.
  27. R. Rougemont, A. Ficnar, S. Finazzo, and J. Noronha, Energy loss, equilibration, and thermodynamics of a baryon rich strongly coupled quark-gluon plasma, J. High Energy Phys. 04 (2016) 102.
  28. Z.-R. Zhu, J.-X. Chen, X.-M. Liu, and D. Hou, Thermodynamics and energy loss in D dimensions from holographic QCD model, Eur. Phys. J. C 82, 560 (2022).
  29. J. Grefa, M. Hippert, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, Transport coefficients of the quark-gluon plasma at the critical point and across the first-order line, Phys. Rev. D 106, 034024 (2022).
  30. Z.-R. Zhu and D. Hou, Inverse magnetic catalysis and energy loss in a holographic QCD model, Phys. Rev. D 110, 066010 (2024).
  31. B. Chen, X. Chen, X. Li, Z.-R. Zhu, and K. Zhou, Exploring transport properties of quark-gluon plasma in flavor-dependent systems with a holographic model, Phys. Rev. D 111, 086033 (2025).
  32. T. Domurcukgul and R. Morad, Holographic drag force in non-conformal plasma, Eur. Phys. J. C 82, 304 (2022).
  33. S. I. Finazzo, R. Critelli, R. Rougemont, and J. Noronha, Momentum transport in strongly coupled anisotropic plasmas in the presence of strong magnetic fields, Phys. Rev. D 94, 054020 (2016); 96, 019903(E) (2017).
  34. S. S. Gubser, D. R. Gulotta, S. S. Pufu, and F. D. Rocha, Gluon energy loss in the gauge-string duality, J. High Energy Phys. 10 (2008) 052.
  35. P. M. Chesler, K. Jensen, and A. Karch, Jets in strongly-coupled N=4 super Yang-Mills theory, Phys. Rev. D 79, 025021 (2009).
  36. A. Ficnar, J. Noronha, and M. Gyulassy, Falling strings and light quark jet quenching at LHC, Nucl. Phys. A910–911, 252 (2013).
  37. A. Ficnar, S. S. Gubser, and M. Gyulassy, Shooting string holography of jet quenching at RHIC and LHC, Phys. Lett. B 738, 464 (2014).
  38. A. Ficnar and S. S. Gubser, Finite momentum at string endpoints, Phys. Rev. D 89, 026002 (2014).
  39. Z.-R. Zhu, S.-Q. Feng, Y.-F. Shi, and Y. Zhong, Energy loss of heavy and light quarks in holographic magnetized background, Phys. Rev. D 99, 126001 (2019).
  40. X. Chen and M. Huang, Machine learning holographic black hole from lattice QCD equation of state, Phys. Rev. D 109, L051902 (2024).
  41. X. Chen and M. Huang, Flavor dependent critical endpoint from holographic QCD through machine learning, J. High Energy Phys. 02 (2025) 123.
  42. R.-G. Cai, S. He, L. Li, and H.-A. Zeng, Neural ordinary differential equations for mapping the magnetic QCD phase diagram via holography, arXiv:2406.12772.
  43. Q. Fu, S. He, L. Li, and Z. Li, Revisiting holographic model for thermal and dense QCD with a critical point, arXiv:2404.12109.
  44. A. Karch, E. Katz, D. T. Son, and M. A. Stephanov, Linear confinement and AdS/QCD, Phys. Rev. D 74, 015005 (2006).
  45. D. Li, S. He, M. Huang, and Q.-S. Yan, Thermodynamics of deformed AdS5 model with a positive/negative quadratic correction in graviton-dilaton system, J. High Energy Phys. 09 (2011) 041.
  46. D. Li, M. Huang, and Q.-S. Yan, A dynamical soft-wall holographic QCD model for chiral symmetry breaking and linear confinement, Eur. Phys. J. C 73, 2615 (2013).
  47. K. Chelabi, Z. Fang, M. Huang, D. Li, and Y.-L. Wu, Chiral phase transition in the soft-wall model of AdS/QCD, J. High Energy Phys. 04 (2016) 036.
  48. K. Chelabi, Z. Fang, M. Huang, D. Li, and Y.-L. Wu, Realization of chiral symmetry breaking and restoration in holographic QCD, Phys. Rev. D 93, 101901 (2016).
  49. Z. Fang, S. He, and D. Li, Chiral and deconfining phase transitions from holographic QCD study, Nucl. Phys. B907, 187 (2016).
  50. Z. Fang and Y.-L. Wu, Equation of state and chiral transition in soft-wall AdS/QCD with more realistic gravitational background, arXiv:1909.06917.
  51. O. DeWolfe, S. S. Gubser, and C. Rosen, A holographic critical point, Phys. Rev. D 83, 086005 (2011).
  52. O. DeWolfe, S. S. Gubser, and C. Rosen, Dynamic critical phenomena at a holographic critical point, Phys. Rev. D 84, 126014 (2011).
  53. R.-G. Cai, S. He, and D. Li, A hQCD model and its phase diagram in Einstein-Maxwell-dilaton system, J. High Energy Phys. 03 (2012) 033.
  54. R.-G. Cai, S. Chakrabortty, S. He, and L. Li, Some aspects of QGP phase in a hQCD model, J. High Energy Phys. 02 (2013) 068.
  55. S. I. Finazzo and J. Noronha, Holographic calculation of the electric conductivity of the strongly coupled quark-gluon plasma near the deconfinement transition, Phys. Rev. D 89, 106008 (2014).
  56. Y. Yang and P.-H. Yuan, A refined holographic QCD model and QCD phase structure, J. High Energy Phys. 11 (2014) 149.
  57. R. Critelli, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, Critical point in the phase diagram of primordial quark-gluon matter from black hole physics, Phys. Rev. D 96, 096026 (2017).
  58. Z. Li, Y. Chen, D. Li, and M. Huang, Locating the QCD critical end point through the peaked baryon number susceptibilities along the freeze-out line, Chin. Phys. C 42, 013103 (2018).
  59. Y. Chen, M. Huang, and Q.-S. Yan, Gravitation waves from QCD and electroweak phase transitions, J. High Energy Phys. 05 (2018) 178.
  60. J. Knaute, R. Yaresko, and B. Kämpfer, Holographic QCD phase diagram with critical point from Einstein–Maxwell-dilaton dynamics, Phys. Lett. B 778, 419 (2018).
  61. Z. Fang, Y.-L. Wu, and L. Zhang, Chiral phase transition and QCD phase diagram from AdS/QCD, Phys. Rev. D 99, 034028 (2019).
  62. A. Ballon-Bayona, H. Boschi-Filho, E. F. Capossoli, and D. M. Rodrigues, Criticality from Einstein-Maxwell-dilaton holography at finite temperature and density, Phys. Rev. D 102, 126003 (2020).
  63. M.-W. Li, Y. Yang, and P.-H. Yuan, Analytic study on chiral phase transition in holographic QCD, J. High Energy Phys. 02 (2021) 055.
  64. J. Grefa, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, Hot and dense quark-gluon plasma thermodynamics from holographic black holes, Phys. Rev. D 104, 034002 (2021).
  65. S. He, L. Li, Z. Li, and S.-J. Wang, Gravitational waves and primordial black hole productions from gluodynamics by holography, Sci. China Phys. Mech. Astron. 67, 240411 (2024).
  66. J. Grefa, M. Hippert, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, QCD equilibrium and dynamical properties from holographic black holes, Suppl. Rev. Mex. Fis. Suppl. 3, 040910 (2022).
  67. J. Grefa, M. Hippert, R. Kunnawalkam Elayavalli, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, Holographic transport coefficients and jet energy loss for the hot and dense quark-gluon plasma, EPJ Web Conf. 296, 14014 (2024).
  68. S. He, S.-Y. Wu, Y. Yang, and P.-H. Yuan, Phase structure in a dynamical soft-wall holographic QCD model, J. High Energy Phys. 04 (2013) 093.
  69. M.-W. Li, Y. Yang, and P.-H. Yuan, Approaching confinement structure for light quarks in a holographic soft wall QCD model, Phys. Rev. D 96, 066013 (2017).
  70. J. D. Bjorken, Energy loss of energetic partons in quark—gluon plasma: Possible extinction of high p(t) jets in hadron—hadron collisions, Report No. FERMILAB-PUB-82-059-THY, No. FERMILAB-PUB-82-059-T, 1982.
  71. K.-H. Schmidt, E. Hanelt, H. Geissel, G. Münzenberg, and J. Dufour, The momentum-loss achromat—A new method for the isotopical separation of relativistic heavy ions, Nucl. Instrum. Methods Phys. Res., Sect. A 260, 287 (1987).
  72. J. Lindhard and M. Scharff, Energy dissipation by ions in the keV region, Phys. Rev. 124, 128 (1961).
  73. N. Bohr, Velocity-range relation for fission fragments, Phys. Rev. 59, 270 (1941).
  74. H. Stoecker et al., Collective effects and nuclear stopping, Nucl. Phys. A566, 15C (1994).
  75. H. Appelshauser et al. (NA49 Collaboration), Baryon stopping and charged particle distributions in central Pb+Pb collisions at 158-GeV per nucleon, Phys. Rev. Lett. 82, 2471 (1999).
  76. A. Peshier, The QCD collisional energy loss revised, Phys. Rev. Lett. 97, 212301 (2006).
  77. N. Armesto et al., Comparison of jet quenching formalisms for a quark-gluon plasma “brick”, Phys. Rev. C 86, 064904 (2012).
  78. B. Betz and M. Gyulassy, Constraints on the path-length dependence of jet quenching in nuclear collisions at RHIC and LHC, J. High Energy Phys. 08 (2014) 090; 10 (2014) 043(E).

Outline

Information

Phys. Rev. D 111, 126019– Published 26 June, 2025
  • Received 16 April 2025
  • Accepted 4 June 2025
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