Hot QCD: transport coefficients in strong and weak coupling regimes

Abstract

We evaluate the transport coefficients, namely the shear viscosity $\eta$ and the spatial diffusion coefficient of heavy quarks $D_s$, within a Quasi-Particle Model (QPM). In particular, for the first time this has been done by exploiting novel lQCD data at $N_f=3+1$. In such a framework, in which the gluons are massive, the interactions among quarks and gluons have been evaluated via the scattering matrices evaluated from tree level Feynman diagrams. As far as the evaluation of $D_s$ is concerned, the Fokker-Planck approximation for the relativistic Boltzmann equation has been employed for the diffusion of both charm and bottom quarks in either a $N_f=3$ and a $N_f=3+1$ bulk. We have developed a dual-component Chapman-Enskog formalism for the ratio $\eta/s$ (being $s$ the entropy density) of a mixture of quarks and gluons. The temperature dependence of the shear viscosity is then compared to the results from a Green-Kubo approach, based on the numerical resolution of the relativistic Boltzmann equation with a stochastic implementation of the collision integral. Finally, using the above results, we compare the strong and weak coupling regimes for the ratio $(2\pi T D_s)/(4\pi \eta/s)$.