Abstract
We compute the shear viscosity of QCD with matter, including almost all next-to-leading order corrections — that is, corrections suppressed by one power of g relative to leading order. We argue that the still missing terms are small. The next-to-leading order corrections are large and bring η/s down by more than a factor of 3 at physically relevant couplings. The perturbative expansion is problematic even at T ≃ 100 GeV. The largest next-to-leading order correction to η/s arises from modifications to the widehat{q} parameter, which determines the rate of transverse momentum diffusion. We also explore quark number diffusion, and shear viscosity in pure-glue QCD and in QED.
Highlights
The original idea of the Quark-Gluon Plasma phase [1,2,3] was that it would consist of weakly-interacting, nearly-free quarks and gluons
Let us start by briefly summarizing how the transport coefficients we investigate are defined and how they have been computed to leading order in the Effective Kinetic Theory (EKT)
We show our results for the shear viscosity over entropy η/s and quark number diffusion Dq as a function of mD/T for QCD with Nf = 3 flavors
Summary
The original idea of the Quark-Gluon Plasma phase [1,2,3] was that it would consist of weakly-interacting, nearly-free quarks and gluons (this assumption is implicit, for instance, in treatments of the cosmological QCD phase transition [4]). We are able to give a relatively simple determination of these effects by the use of lightcone techniques These methods typically keep track of the incoming and outgoing momentum of a particle, but lose track of the momentum which it transfers to the other participants. The plot shows that next-to-leading order corrections lower the shear viscosity by a factor of two at high temperatures T ∼ 1000 GeV, and by a factor of four for physically relevant temperatures, T ∼ 250 MeV This large change is suggestive that the true value of η/s is smaller than the leading-order perturbative estimate, but it signals severe convergence problems in the perturbative expansion, even for surprisingly large temperatures or, equivalently, small values of g. Together with fits for our NLO results as a function of the coupling, are postponed to the appendices
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