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Description
We use the Chapman-Enskog method to investigate the shear viscosity of a quark-gluon plasma at finite temperature with a focus on its relation to parton cross sections. We use the recent analytical expression for the shear viscosity [1] of a massless quark-gluon gas at chemical equilibrium with Boltzmann statistics after including all $2\leftrightarrow 2$ parton scatterings. Applying the expression to scattering cross sections at finite temperature that are based on perturbative-QCD and screened with scaled thermal masses $m_D$ and $m_F$, we calculate the corresponding shear viscosity. We find [2] that our Chapman-Enskog results on $\eta g^4/T^3$ versus $m_D/T$ are similar to but higher than the leading-order results from the AMY framework. We also show that the shear viscosity-to-entropy density ratio $\eta/s$ is very sensitive to the choice of the momentum scale $Q$ used in the strong coupling, where a smaller $Q/T$ leads to a lower $\eta/s$ value. These results lay the foundation for mapping parton cross sections to given shear viscosity in parton transport models and QCD effective kinetic theory.
[1] O. Ohanaka and Z.W. Lin, Shear viscosity of a massless quark-gluon gas in chemical equilibrium in terms of all $2\leftrightarrow 2$ cross sections, arXiv:2602.08155 [hep-ph].
[2] O. Ohanaka and Z.W. Lin, Chapman-Enskog calculation of the shear viscosity of quark-gluon plasma including all $2\leftrightarrow 2$ scatterings at finite temperature, arXiv:2604.25059 [nucl-th].