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Shear viscosity of a massless quark-gluon gas in chemical equilibrium in terms of all 2↔2 cross sections

Okey Ohanaka and Zi-Wei Lin*

  • *Contact author: linz@ecu.edu
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Phys. Rev. D 114, 034019 – Published 10 August, 2026

DOI: https://doi.org/10.1103/878b-dyqp

Abstract

The analytical expressions of the shear viscosity of both one and two particle species with Boltzmann statistics and 2→2 elastic scatterings are known from the Chapman-Enskog method and have been shown to be quite accurate. The expression for a multispecies hadronic gas under 2→2 elastic scatterings is also known. Here we use the Chapman-Enskog method to derive the explicit expression of shear viscosity of a massless quark-gluon gas of Nf quark flavors in chemical equilibrium subjected to all 2→2 parton scatterings including for the first time inelastic scatterings. We then verify the expression in a general single-species limit, where the shear viscosity of the quark-gluon gas should reduce to the result for a single particle species. In addition, we show the explicit analytical result in terms of the seven independent cross sections for the special case of isotropic and energy-independent cross sections. The analytical expressions derived here can be useful for determining the shear viscosity of parton transport models with any 2→2 scattering cross sections. They can also be coupled with finite temperature QCD cross sections to help study the shear viscosity of the quark gluon plasma.

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Phys. Rev. D 114, 034019– Published 10 August, 2026
  • Received 6 March 2026
  • Accepted 24 June 2026
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