- Open Access
Transport coefficients of strongly interacting quark-gluon plasma including elastic and inelastic scattering within the dynamical quasiparticle model
Phys. Rev. D 114, 056007 – Published 8 September, 2026
DOI: https://doi.org/10.1103/stk4-zk62
Abstract
We study the impact of inelastic gluon-radiation and absorption processes on the transport coefficients of the quark-gluon plasma within the dynamical quasiparticle model (DQPM) in the temperature–baryon-chemical-potential plane . Extending the baseline established in previous DQPM calculations, we include gluon-radiation and the inverse gluon-absorption scattering channels with massive partons and effective DQPM propagators and vertices. The corresponding momentum-dependent interaction rates and relaxation times are used to calculate the shear viscosity, bulk viscosity, electric conductivity, and baryon diffusion coefficient as functions of temperature and baryon chemical potential . Within the relaxation time approximation, we find that contributions systematically reduce all considered transport coefficients relative to the only results, in accordance with the decrease of the relaxation times. In the thermal regime explored here, however, this reduction remains moderate, since the investigated inelastic rates stay below the ones over the considered range. The inelastic channels become more relevant mainly for partonic scatterings at large momenta, which are thermally suppressed in the strongly interacting QGP. At , the resulting , , and are compatible with available lattice-QCD estimates within uncertainties. At finite , our results provide predictions for the transport properties of QCD matter relevant for beam-energy-scan programs.
Physics Subject Headings (PhySH)
Article Text
References (77)
- A. Bzdak, S. Esumi, V. Koch, J. Liao, M. Stephanov, and N. Xu, Mapping the phases of quantum chromodynamics with beam energy scan, Phys. Rep. 853, 1 (2020).
- T. Ablyazimov et al. (CBM Collaboration), Challenges in QCD matter physics–the scientific programme of the compressed baryonic matter experiment at fair, Eur. Phys. J. A 53, 60 (2017).
- V. Golovatyuk, V. Kekelidze, V. Kolesnikov, O. Rogachevsky, and A. Sorin, The multi-purpose detector (MPD) of the collider experiment, Eur. Phys. J. A 52, 212 (2016).
- C. Sasaki and K. Redlich, Bulk viscosity in quasi particle models, Phys. Rev. C 79, 055207 (2009).
- M. Bluhm, B. Kampfer, and K. Redlich, Bulk and shear viscosities of the gluon plasma in a quasiparticle description, Phys. Rev. C 84, 025201 (2011).
- R. Marty, E. Bratkovskaya, W. Cassing, J. Aichelin, and H. Berrehrah, Transport coefficients from the Nambu-Jona-Lasinio model for , Phys. Rev. C 88, 045204 (2013).
- Y.-P. Zhao, Thermodynamic properties and transport coefficients of QCD matter within the nonextensive Polyakov–Nambu–Jona-Lasinio model, Phys. Rev. D 101, 096006 (2020).
- A. Bandyopadhyay and S. Ghosh, Quantum version of transport coefficients in Nambu–Jona-Lasinio model at finite temperature and strong magnetic field, Eur. Phys. J. C 83, 489 (2023).
- D. Singh and A. Kumar, Finite size effects on the transport coefficients of strongly interacting QCD matter, Phys. Rev. D 111, 074017 (2025).
- S. Madni, A. Mukherjee, A. Jaiswal, and N. Haque, Shear and bulk viscosity of quark-gluon plasma with Gribov gluons and quasiparticle quarks, Phys. Rev. D 110, 116035 (2024).
- S. Madni, L. Thakur, and N. Haque, Electrical conductivity of QGP with quasiparticle quarks and Gribov gluon, Eur. Phys. J. C 86, 473 (2026).
- M. Greif, J. A. Fotakis, G. S. Denicol, and C. Greiner, Diffusion of conserved charges in relativistic heavy ion collisions, Phys. Rev. Lett. 120, 242301 (2018).
- J. A. Fotakis, M. Greif, C. Greiner, G. S. Denicol, and H. Niemi, Diffusion processes involving multiple conserved charges: A study from kinetic theory and implications to the fluid-dynamical modeling of heavy ion collisions, Phys. Rev. D 101, 076007 (2020).
- J. A. Fotakis, O. Soloveva, C. Greiner, O. Kaczmarek, and E. Bratkovskaya, Diffusion coefficient matrix of the strongly interacting quark-gluon plasma, Phys. Rev. D 104, 034014 (2021).
- A. Das, H. Mishra, and R. K. Mohapatra, Diffusion matrix associated with the diffusion processes of multiple conserved charges in a hot and dense hadronic matter, Phys. Rev. D 106, 014013 (2022).
- S. Dey, A. Jaiswal, and H. Mishra, Diffusion coefficient matrix for multiple conserved charges: A Kubo approach, J. High Energy Phys. 12 (2024) 192.
- O. Ohanaka and Z.-W. Lin, Chapman-Enskog calculation of the shear viscosity of quark-gluon plasma including all scatterings at finite temperature, arXiv:2604.25059.
- G. Parisi, V. Nugara, S. Plumari, and V. Greco, Shear viscosity of a binary mixture for a relativistic fluid at high temperature, Phys. Rev. D 113, 014001 (2026).
- G. Parisi, V. Nugara, S. U. Arfeen, S. Plumari, and V. Greco, Bulk viscosity of a binary mixture: The role of the intra-species interaction, arXiv:2606.06105.
- C. Shen, B. Schenke, and W. Zhao, Viscosities of the baryon-rich quark-gluon plasma from beam energy scan data, Phys. Rev. Lett. 132, 072301 (2024).
- S. A. Jahan, H. Roch, and C. Shen, Bayesian analysis of relativistic nuclear dynamics with the RHIC beam energy scan data, Phys. Rev. C 110, 054905 (2024).
- A. Peshier and W. Cassing, The hot non-perturbative gluon plasma is an almost ideal colored liquid, Phys. Rev. Lett. 94, 172301 (2005).
- W. Cassing, From Kadanoff-Baym dynamics to off-shell parton transport, Eur. Phys. J. Special Topics 168, 3 (2009).
- P. Moreau, O. Soloveva, L. Oliva, T. Song, W. Cassing, and E. Bratkovskaya, Exploring the partonic phase at finite chemical potential within an extended off-shell transport approach, Phys. Rev. C 100, 014911 (2019).
- O. Soloveva, P. Moreau, and E. Bratkovskaya, Transport coefficients for the hot quark-gluon plasma at finite chemical potential , Phys. Rev. C 101, 045203 (2020).
- O. Soloveva, A. Palermo, and E. Bratkovskaya, Extraction of the microscopic properties of quasiparticles using deep neural networks, Phys. Rev. C 110, 034908 (2024).
- I. Grishmanovskii, Attenuation of jet partons in strongly interacting quark-gluon plasma, Ph.D. thesis, Goethe U., Frankfurt (main), 2024.
- I. Grishmanovskii, T. Song, C. Greiner, and E. Bratkovskaya, Transport coefficients of heavy quarks by elastic and radiative scatterings in the strongly interacting quark-gluon plasma, Phys. Rev. D 112, 014042 (2025).
- W. Cassing and E. L. Bratkovskaya, Parton-hadron-string dynamics: An off-shell transport approach for relativistic energies, Nucl. Phys. A831, 215 (2009).
- O. Linnyk, E. L. Bratkovskaya, and W. Cassing, Effective QCD and transport description of dilepton and photon production in heavy-ion collisions and elementary processes, Prog. Part. Nucl. Phys. 87, 50 (2016).
- O. Soloveva, J. Aichelin, and E. Bratkovskaya, Transport properties and equation-of-state of hot and dense QGP matter near the critical endpoint in the phenomenological dynamical quasiparticle model, Phys. Rev. D 105, 054011 (2022).
- O. Soloveva, D. Fuseau, J. Aichelin, and E. Bratkovskaya, Shear viscosity and electric conductivity of a hot and dense QGP with a chiral phase transition, Phys. Rev. C 103, 054901 (2021).
- I. Grishmanovskii, O. Soloveva, T. Song, C. Greiner, and E. Bratkovskaya, Inelastic and elastic parton scattering in the strongly interacting quark-gluon plasma, Phys. Rev. C 109, 024911 (2024).
- J. Barata, J. G. Milhano, A. V. Sadofyev, and J. M. Silva, Early-time dynamics of heavy-ion collisions through energy correlators: Celestial blocks and the spacetime structure of out-of-equilibrium QCD matter, arXiv:2512.17009.
- W. Cassing, Dynamical quasiparticles properties and effective interactions in the sQGP, Nucl. Phys. A795, 70 (2007).
- W. Cassing, QCD thermodynamics and confinement from a dynamical quasiparticle point of view, Nucl. Phys. A791, 365 (2007).
- H. Berrehrah, E. Bratkovskaya, T. Steinert, and W. Cassing, A dynamical quasiparticle approach for the QGP bulk and transport properties, Int. J. Mod. Phys. E 25, 1642003 (2016).
- B. Vanderheyden and G. Baym, Selfconsistent approximations in relativistic plasmas: Quasiparticle analysis of the thermodynamic properties, J. Stat. Phys. 93, 843 (1998).
- J. P. Blaizot, E. Iancu, and A. Rebhan, Approximately selfconsistent resummations for the thermodynamics of the quark gluon plasma. 1. Entropy and density, Phys. Rev. D 63, 065003 (2001).
- M. L. Bellac, Thermal Field Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2011).
- H. Berrehrah, W. Cassing, E. Bratkovskaya, and T. Steinert, Quark susceptibility in a generalized dynamical quasiparticle model, Phys. Rev. C 93, 044914 (2016).
- S. Borsanyi, G. Endrodi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, QCD equation of state at nonzero chemical potential: Continuum results with physical quark masses at order , J. High Energy Phys. 08 (2012) 053.
- S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, Full result for the QCD equation of state with flavors, Phys. Lett. B 730, 99 (2014).
- C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro, and F. Sanfilippo, Curvature of the chiral pseudocritical line in QCD, Phys. Rev. D 90, 114025 (2014).
- O. Kaczmarek, F. Karsch, F. Zantow, and P. Petreczky, Static quark anti-quark free energy and the running coupling at finite temperature, Phys. Rev. D 70, 074505 (2004); 72, 059903(E) (2005).
- O. Kaczmarek and F. Zantow, Static quark anti-quark interactions in zero and finite temperature QCD. I. Heavy quark free energies, running coupling and quarkonium binding, Phys. Rev. D 71, 114510 (2005).
- O. Kaczmarek, Screening at finite temperature and density, Proc. Sci. CPOD07 (2007) 043 [arXiv:0710.0498].
- S. Plumari, W. M. Alberico, V. Greco, and C. Ratti, Recent thermodynamic results from lattice QCD analyzed within a quasiparticle model, Phys. Rev. D 84, 094004 (2011).
- H. Berrehrah, E. Bratkovskaya, W. Cassing, P. B. Gossiaux, J. Aichelin, and M. Bleicher, Collisional processes of on-shell and off-shell heavy quarks in vacuum and in the Quark-Gluon-Plasma, Phys. Rev. C 89, 054901 (2014).
- A. Peshier, HTL resummation of the thermodynamic potential, Phys. Rev. D 63, 105004 (2001).
- I. Grishmanovskii, T. Song, O. Soloveva, C. Greiner, and E. Bratkovskaya, Exploring jet transport coefficients by elastic scattering in the strongly interacting quark-gluon plasma, Phys. Rev. C 106, 014903 (2022).
- I. Grishmanovskii, O. Soloveva, T. Song, C. Greiner, and E. Bratkovskaya, Jet transport coefficients by elastic and radiative scatterings in the strongly interacting quark-gluon plasma, Phys. Rev. C 110, 014908 (2024).
- A. Hosoya and K. Kajantie, Transport coefficients of QCD matter, Nucl. Phys. B250, 666 (1985).
- P. Chakraborty and J. I. Kapusta, Quasi-particle theory of shear and bulk viscosities of hadronic matter, Phys. Rev. C 83, 014906 (2011).
- M. Albright and J. I. Kapusta, Quasiparticle theory of transport coefficients for hadronic matter at finite temperature and baryon density, Phys. Rev. C 93, 014903 (2016).
- S. Gavin, Transport coefficients in ultrarelativistic heavy-ion collisions, Nucl. Phys. A435, 826 (1985).
- R. Kubo, Statistical mechanical theory of irreversible processes. 1. General theory and simple applications in magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957).
- G. Aarts and J. M. M. Resco, Transport coefficients, spectral functions and the lattice, J. High Energy Phys. 04 (2002) 053.
- D. Fernandez-Fraile and A. Gomez Nicola, The electrical conductivity of a pion gas, Phys. Rev. D 73, 045025 (2006).
- W. Israel and J. M. Stewart, Transient relativistic thermodynamics and kinetic theory, Ann. Phys. (N.Y.) 118, 341 (1979).
- G. S. Denicol, H. Niemi, E. Molnar, and D. H. Rischke, Derivation of transient relativistic fluid dynamics from the Boltzmann equation, Phys. Rev. D 85, 114047 (2012); 91, 039902(E) (2015).
- X.-G. Huang and T. Koide, Shear viscosity, bulk viscosity, and relaxation times of causal dissipative relativistic fluid dynamics at finite temperature and chemical potential, Nucl. Phys. A889, 73 (2012).
- N. Y. Astrakhantsev, V. V. Braguta, and A. Y. Kotov, Temperature dependence of shear viscosity of SU(3)-gluodynamics within lattice simulation, J. High Energy Phys. 04 (2017) 101.
- H. B. Meyer, A calculation of the shear viscosity in SU(3) gluodynamics, Phys. Rev. D 76, 101701 (2007).
- A. Nakamura and S. Sakai, Transport coefficients of gluon plasma, Phys. Rev. Lett. 94, 072305 (2005).
- A. Nakamura and S. Sakai, Lattice calculation of the QGP viscosities: Present results and next project, Proc. Sci. LATTICE2007 (2007) 221 [arXiv:0710.3625].
- N. Y. Astrakhantsev, V. V. Braguta, and A. Y. Kotov, Temperature dependence of bulk viscosity within lattice simulation of SU(3) gluodynamics, Phys. Rev. D 98, 054515 (2018).
- H. B. Meyer, A calculation of the bulk viscosity in SU(3) gluodynamics, Phys. Rev. Lett. 100, 162001 (2008).
- Y. Yin, Electrical conductivity of the quark-gluon plasma and soft photon spectrum in heavy-ion collisions, Phys. Rev. C 90, 044903 (2014).
- S. Turbide, R. Rapp, and C. Gale, Hadronic production of thermal photons, Phys. Rev. C 69, 014903 (2004).
- Y. Akamatsu, H. Hamagaki, T. Hatsuda, and T. Hirano, Can transport peak explain the low-mass enhancement of dileptons at RHIC?, J. Phys. G 38, 124184 (2011).
- O. Linnyk, V. Konchakovski, W. Cassing, and E. Bratkovskaya, Photon elliptic flow in relativistic heavy-ion collisions: Hadronic versus partonic sources, Phys. Rev. C 88, 034904 (2013).
- H. Berrehrah, P.-B. Gossiaux, J. Aichelin, W. Cassing, and E. Bratkovskaya, Dynamical collisional energy loss and transport properties of on- and off-shell heavy quarks in vacuum and in the quark gluon plasma, Phys. Rev. C 90, 064906 (2014).
- N. Y. Astrakhantsev, V. V. Braguta, M. D’Elia, A. Y. Kotov, A. A. Nikolaev, and F. Sanfilippo, Lattice study of electromagnetic conductivity of quark-gluon plasma in external magnetic field, Phys. Rev. D 102, 054516 (2020).
- G. Aarts, C. Allton, A. Amato, P. Giudice, S. Hands, and J.-I. Skullerud, Electrical conductivity and charge diffusion in thermal QCD from the lattice, J. High Energy Phys. 02 (2014) 186.
- B. B. Brandt, A. Francis, B. Jaeger, and H. B. Meyer, Charge transport and vector meson dissociation across the thermal phase transition in lattice QCD with two light quark flavors, Phys. Rev. D 93, 054510 (2016).
- B. B. Brandt, A. Francis, H. B. Meyer, and H. Wittig, Two-flavour lattice QCD correlation functions in the deconfinement transition region, Proc. Sci. ConfinementX (2012) 186 [arXiv:1302.0675].