- 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

Deciphering the viscous properties and the Bjorken expansion of the QGP medium at finite angular velocity

Shubhalaxmi Rath1,2,* and Nicolás A. Neill1,†

  • *Contact author: shubhalaxmirath@gmail.com
  • †Contact author: naneill@outlook.com
PDF

Phys. Rev. D 112, 076017 – Published 14 October, 2025

DOI: https://doi.org/10.1103/w91p-n3k3

Abstract

We have studied the viscous properties as well as the Bjorken expansion of a rotating QGP medium. In the noncentral events of heavy-ion collisions, the produced medium can carry a finite angular momentum with a finite range of angular velocity. This rotation can significantly affect various properties, including viscous properties and the expansion of the QGP medium. Using a novel relaxation time approximation for the collision integral in the relativistic Boltzmann transport equation at finite angular velocity, we have calculated the shear and bulk viscosities and compared them with their counterparts in the standard relaxation time approximation within the kinetic theory approach. Our results show that the angular velocity increases both shear and bulk viscosities, suggesting an enhanced momentum transfer within the medium and greater fluctuations in local pressure. This rotational effect on viscosities is more evident at lower temperatures than at higher temperatures. Our analysis also shows that, compared to the standard relaxation time approximation, the shear viscosity is lower while the bulk viscosity is higher in the novel relaxation time approximation for all temperatures. Additionally, some observables related to the flow characteristic, fluid behavior, and conformal symmetry of the medium are markedly impacted due to rotation. We have also studied the hydrodynamic evolution of matter within the Bjorken boost-invariant scenario and have found that the energy density evolves faster in the presence of finite rotation than in the nonrotating case. Consequently, rapid rotation accelerates the cooling process of the QGP medium.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (91)

  1. W. T. Deng and X. G. Huang, Vorticity in heavy-ion collisions, Phys. Rev. C 93, 064907 (2016).
  2. Y. Jiang, Z. W. Lin, and J. Liao, Rotating quark-gluon plasma in relativistic heavy-ion collisions, Phys. Rev. C 94, 044910 (2016).
  3. X. Wang, M. Wei, Z. Li, and M. Huang, Quark matter under rotation in the NJL model with vector interaction, Phys. Rev. D 99, 016018 (2019).
  4. M. Wei, C. A. Islam, and M. Huang, Production rate and ellipticity of lepton pairs from a rotating hot and dense QCD medium, Phys. Rev. D 105, 054014 (2022).
  5. E. Berti, F. White, A. Maniopoulou, and M. Bruni, Rotating neutron stars: An invariant comparison of approximate and numerical space-time models, Mon. Not. R. Astron. Soc. 358, 923 (2005).
  6. A. L. Fetter, Rotating trapped Bose-Einstein condensates, Rev. Mod. Phys. 81, 647 (2009).
  7. Z. T. Liang and X. N. Wang, Spin alignment of vector mesons in non-central A+A collisions, Phys. Lett. B 629, 20 (2005).
  8. F. Becattini, F. Piccinini, and J. Rizzo, Angular momentum conservation in heavy-ion collisions at very high energy, Phys. Rev. C 77, 024906 (2008).
  9. D. E. Kharzeev and D. T. Son, Testing the chiral magnetic and chiral vortical effects in heavy ion collisions, Phys. Rev. Lett. 106, 062301 (2011).
  10. D. T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103, 191601 (2009).
  11. Y. Jiang, X. G. Huang, and J. Liao, Chiral vortical wave and induced flavor charge transport in a rotating quark-gluon plasma, Phys. Rev. D 92, 071501 (2015).
  12. K. Fukushima, D. E. Kharzeev, and H. J. Warringa, Chiral magnetic effect, Phys. Rev. D 78, 074033 (2008).
  13. D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, The effects of topological charge change in heavy ion collisions: “Event by event P and CP violation”, Nucl. Phys. A803, 227 (2008).
  14. D. E. Kharzeev and H. U. Yee, Chiral magnetic wave, Phys. Rev. D 83, 085007 (2011).
  15. Y. Burnier, D. E. Kharzeev, J. Liao, and H. U. Yee, Chiral magnetic wave at finite baryon density and the electric quadrupole moment of the quark-gluon plasma, Phys. Rev. Lett. 107, 052303 (2011).
  16. A. Ipp, A. Di Piazza, J. Evers, and C. H. Keitel, Photon polarization as a probe for quark-gluon plasma dynamics, Phys. Lett. B 666, 315 (2008).
  17. B. Betz, M. Gyulassy, and G. Torrieri, Polarization probes of vorticity in heavy ion collisions, Phys. Rev. C 76, 044901 (2007).
  18. F. Becattini and F. Piccinini, The ideal relativistic spinning gas: Polarization and spectra, Ann. Phys. (Amsterdam) 323, 2452 (2008).
  19. F. Becattini and M. A. Lisa, Polarization and vorticity in the quark-gluon plasma, Annu. Rev. Nucl. Part. Sci. 70, 395 (2020).
  20. M. N. Chernodub and S. Gongyo, Interacting fermions in rotation: Chiral symmetry restoration, moment of inertia and thermodynamics, J. High Energy Phys. 01 (2017) 136.
  21. S. Ebihara, K. Fukushima, and K. Mameda, Boundary effects and gapped dispersion in rotating fermionic matter, Phys. Lett. B 764, 94 (2017).
  22. Y. Fujimoto, K. Fukushima, and Y. Hidaka, Deconfining phase boundary of rapidly rotating hot and dense matter and analysis of moment of inertia, Phys. Lett. B 816, 136184 (2021).
  23. X. Chen, L. Zhang, D. Li, D. Hou, and M. Huang, Gluodynamics and deconfinement phase transition under rotation from holography, J. High Energy Phys. 07 (2021) 132.
  24. V. V. Braguta, A. Y. Kotov, D. D. Kuznedelev, and A. A. Roenko, Study of the confinement/deconfinement phase transition in rotating lattice SU(3) gluodynamics, JETP Lett. 112, 9 (2020).
  25. V. V. Braguta, A. Y. Kotov, D. D. Kuznedelev, and A. A. Roenko, Influence of relativistic rotation on the confinement-deconfinement transition in gluodynamics, Phys. Rev. D 103, 094515 (2021).
  26. Y. Jiang and J. Liao, Pairing phase transitions of matter under rotation, Phys. Rev. Lett. 117, 192302 (2016).
  27. B. R. Iyer, Dirac field theory in rotating coordinates, Phys. Rev. D 26, 1900 (1982).
  28. F. Becattini and L. Tinti, Thermodynamical inequivalence of quantum stress-energy and spin tensors, Phys. Rev. D 84, 025013 (2011).
  29. V. E. Ambruş and E. Winstanley, Rotating quantum states, Phys. Lett. B 734, 296 (2014).
  30. V. E. Ambruş and E. Winstanley, Rotating fermions inside a cylindrical boundary, Phys. Rev. D 93, 104014 (2016).
  31. H.-L. Chen, K. Fukushima, X.-G. Huang, and K. Mameda, Analogy between rotation and density for Dirac fermions in a magnetic field, Phys. Rev. D 93, 104052 (2016).
  32. B. McInnes, Angular momentum in QGP holography, Nucl. Phys. B887, 246 (2014).
  33. B. McInnes, A rotation/magnetism analogy for the quark-gluon plasma, Nucl. Phys. B911, 173 (2016).
  34. B. Singh, J. R. Bhatt, and H. Mishra, Probing vorticity in heavy ion collision with dilepton production, Phys. Rev. D 100, 014016 (2019).
  35. S. Rath and B. K. Patra, Revisit to electrical and thermal conductivities, Lorenz and Knudsen numbers in thermal QCD in a strong magnetic field, Phys. Rev. D 100, 016009 (2019).
  36. K. Tuchin, Magnetic contribution to dilepton production in heavy-ion collisions, Phys. Rev. C 88, 024910 (2013).
  37. S. Rath and B. K. Patra, One-loop QCD thermodynamics in a strong homogeneous and static magnetic field, J. High Energy Phys. 12 (2017) 098.
  38. A. Bandyopadhyay, B. Karmakar, N. Haque, and M. G. Mustafa, Pressure of a weakly magnetized hot and dense deconfined QCD matter in one-loop hard-thermal-loop perturbation theory, Phys. Rev. D 100, 034031 (2019).
  39. S. Rath and B. K. Patra, Thermomagnetic properties and Bjorken expansion of hot QCD matter in a strong magnetic field, Eur. Phys. J. A 55, 220 (2019).
  40. B. Karmakar, R. Ghosh, A. Bandyopadhyay, N. Haque, and M. G. Mustafa, Anisotropic pressure of deconfined QCD matter in presence of strong magnetic field within one-loop approximation, Phys. Rev. D 99, 094002 (2019).
  41. K. Hattori, Xu-G. Huang, D. H. Rischke, and D. Satow, Bulk viscosity of quark-gluon plasma in strong magnetic fields, Phys. Rev. D 96, 094009 (2017).
  42. K. Hattori and D. Satow, Electrical conductivity of quark-gluon plasma in strong magnetic fields, Phys. Rev. D 94, 114032 (2016).
  43. B. Feng, Electric conductivity and Hall conductivity of the QGP in a magnetic field, Phys. Rev. D 96, 036009 (2017).
  44. K. Fukushima and Y. Hidaka, Electric conductivity of hot and dense quark matter in a magnetic field with Landau level resummation via kinetic equations, Phys. Rev. Lett. 120, 162301 (2018).
  45. M. Kurian, S. Mitra, S. Ghosh, and V. Chandra, Transport coefficients of hot magnetized QCD matter beyond the lowest Landau level approximation, Eur. Phys. J. C 79, 134 (2019).
  46. S. Rath and B. K. Patra, Effect of magnetic field on the charge and thermal transport properties of hot and dense QCD matter, Eur. Phys. J. C 80, 747 (2020).
  47. S. Rath and S. Dash, Effects of weak magnetic field and finite chemical potential on the transport of charge and heat in hot QCD matter, Eur. Phys. J. A 59, 25 (2023).
  48. Seung-il Nam and Chung-W. Kao, Shear viscosity of quark matter at finite temperature under an external magnetic field, Phys. Rev. D 87, 114003 (2013).
  49. S. Li and Ho-U. Yee, Shear viscosity of the quark-gluon plasma in a weak magnetic field in perturbative QCD: Leading log, Phys. Rev. D 97, 056024 (2018).
  50. G. S. Denicol, X.-G. Huang, E. Molnár, G. M. Monteiro, H. Niemi, J. Noronha, D.  H. Rischke, and Qun Wang, Nonresistive dissipative magnetohydrodynamics from the Boltzmann equation in the 14-moment approximation, Phys. Rev. D 98, 076009 (2018).
  51. S. Rath and B. K. Patra, Momentum and its affiliated transport coefficients for hot QCD matter in a strong magnetic field, Phys. Rev. D 102, 036011 (2020).
  52. S. Rath and B. K. Patra, Viscous properties of hot and dense QCD matter in the presence of a magnetic field, Eur. Phys. J. C 81, 139 (2021).
  53. S. Rath and S. Dash, Momentum transport properties of a hot and dense QCD matter in a weak magnetic field, Eur. Phys. J. C 82, 797 (2022).
  54. K. Fukushima, K. Hattori, H.-U. Yee, and Y. Yin, Heavy quark diffusion in strong magnetic fields at weak coupling and implications for elliptic flow, Phys. Rev. D 93, 074028 (2016).
  55. H. van Hees, C. Gale, and R. Rapp, Thermal photons and collective flow at energies available at the BNL relativistic heavy-ion collider, Phys. Rev. C 84, 054906 (2011).
  56. K. A. Mamo, Enhanced thermal photon and dilepton production in strongly coupled N=4 SYM plasma in strong magnetic field, J. High Energy Phys. 08 (2013) 083.
  57. C. Shen, U. W. Heinz, J.-F. Paquet, and C. Gale, Thermal photons as a quark-gluon plasma thermometer reexamined, Phys. Rev. C 89, 044910 (2014).
  58. S. Rath and S. Dash, Analyzing the transport coefficients and observables of a rotating QGP medium in kinetic theory framework with a novel approach to the collision integral, Eur. Phys. J. C 85, 1034 (2025).
  59. G. S. Rocha, G. S. Denicol, and J. Noronha, Novel relaxation time approximation to the relativistic Boltzmann equation, Phys. Rev. Lett. 127, 042301 (2021).
  60. L. P. Csernai, J. I. Kapusta, and L. D. McLerran, Strongly interacting low-viscosity matter created in relativistic nuclear collisions, Phys. Rev. Lett. 97, 152303 (2006).
  61. S. Ryu, J.-F. Paquet, C. Shen, G. S. Denicol, B. Schenke, S. Jeon, and C. Gale, The importance of the bulk viscosity of QCD in ultrarelativistic heavy-ion collisions, Phys. Rev. Lett. 115, 132301 (2015).
  62. P. K. Kovtun, D. T. Son, and A. O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94, 111601 (2005).
  63. P. B. Arnold, C. Dogan, and G. D. Moore, Bulk viscosity of high-temperature QCD, Phys. Rev. D 74, 085021 (2006).
  64. S. Borsányi, G. Endrődi, Z. Fodor, A. Jakovác, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabó, The QCD equation of state with dynamical quarks, J. High Energy Phys. 11 (2010) 077.
  65. A. Bazavov et al., The equation of state in (2+1)-flavor QCD, Phys. Rev. D 90, 094503 (2014).
  66. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics (Pergamon Press, New York, 1981).
  67. K. Tuchin, On viscous flow and azimuthal anisotropy of the quark-gluon plasma in a strong magnetic field, J. Phys. G 39, 025010 (2012).
  68. C. Cercignani and G. M. Kremer, The Relativistic Boltzmann Equation: Theory and Applications (Birkhäuser, Basel, 2002).
  69. U. Gürsoy, D. Kharzeev, and K. Rajagopal, Magnetohydrodynamics, charged currents, and directed flow in heavy ion collisions, Phys. Rev. C 89, 054905 (2014).
  70. V. Roy and S. Pu, Event-by-event distribution of the ratio of magnetic field energy to initial fluid energy density in sNN=200  GeV Au-Au collisions, Phys. Rev. C 92, 064902 (2015).
  71. Y. Hirono, T. Hirano, and D. E. Kharzeev, The chiral magnetic effect in heavy-ion collisions from event-by-event anomalous hydrodynamics, arXiv:1412.0311.
  72. Long-Gang Pang, Gergely Endrődi, and Hannah Petersen, Magnetic-field-induced squeezing effect at energies available at the BNL relativistic heavy ion collider and at the CERN large hadron collider, Phys. Rev. C 93, 044919 (2016).
  73. S. Pu, V. Roy, L. Rezzolla, and D. H. Rischke, Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization, Phys. Rev. D 93, 074022 (2016).
  74. V. Roy, S. Pu, L. Rezzolla, and D. H. Rischke, Effect of intense magnetic fields on reduced-magnetohydrodynamics evolution in sNN=200  GeV Au+Au collisions, Phys. Rev. C 96, 054909 (2017).
  75. K. Kajantie, Hydrodynamics and approach to equilibrium in quark-gluon plasma, Nucl. Phys. A418, 41 (1984).
  76. G. Baym, Entropy production and the evolution of ultra-relativistic heavy ion collisions, Nucl. Phys. A418, 525 (1984).
  77. A. Hosoya and K. Kajantie, Transport coefficients of QCD matter, Nucl. Phys. B250, 666 (1985).
  78. A. Muronga, Second-order dissipative fluid dynamics for ultrarelativistic nuclear collisions, Phys. Rev. Lett. 88, 062302 (2002).
  79. F. Becattini and L. Tinti, The ideal relativistic rotating gas as a perfect fluid with spin, Ann. Phys. (Amsterdam) 325, 1566 (2010).
  80. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, New York, 1987).
  81. K. Dusling, G. D. Moore, and D. Teaney, Radiative energy loss and v2 spectra for viscous hydrodynamics, Phys. Rev. C 81, 034907 (2010).
  82. E. Calzetta and B. L. Hu, Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation, Phys. Rev. D 37, 2878 (1988).
  83. E. Braaten and R. D. Pisarski, Simple effective Lagrangian for hard thermal loops, Phys. Rev. D 45, R1827 (1992).
  84. A. Peshier, B. Kämpfer, and G. Soff, From QCD lattice calculations to the equation of state of quark matter, Phys. Rev. D 66, 094003 (2002).
  85. J.-P. Blaizot, A. Ipp, A. Rebhan, and U. Reinosa, Asymptotic thermal quark masses and the entropy of QCD in the large-Nf limit, Phys. Rev. D 72, 125005 (2005).
  86. J. I. Kapusta and C. Gale, Finite Temperature Field Theory Principles and Applications (Cambridge University Press, Cambridge, England, 2006).
  87. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley and Sons, New York, 1972).
  88. W. Israel and J. M. Stewart, Transient relativistic thermodynamics and kinetic theory, Ann. Phys. (N.Y.) 118, 341 (1979).
  89. R. Baier, P. Romatschke, and U. A. Wiedemann, Dissipative hydrodynamics and heavy-ion collisions, Phys. Rev. C 73, 064903 (2006).
  90. H. Kouno, M. Maruyama, F. Takagi, and K. Saito, Relativistic hydrodynamics of quark-gluon plasma and stability of scaling solutions, Phys. Rev. D 41, 2903 (1990).
  91. A. Kisiel, W. Broniowski, M. Chojnacki, and W. Florkowski, Azimuthally sensitive femtoscopy in hydrodynamics with statistical hadronization from the BNL relativistic heavy ion collider to the CERN large hadron collider, Phys. Rev. C 79, 014902 (2009).

Outline

Information

Phys. Rev. D 112, 076017– Published 14 October, 2025
  • Received 9 May 2025
  • Accepted 26 September 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