Charmonium Spectral Functions and Transport Properties of Quark-Gluon Plasma

We study vacuum masses of charmonia and the charm-quark diffusion coefficient in the quark-gluon plasma based on the spectral representation for meson correlators. To calculate the correlators, we solve the quark gap equation and the inhomogeneous Bethe-Salpeter equation in the rainbow-ladder approximation. It is found that the ground-state masses of charmonia in the pseudoscalar, scalar, and vector channels can be well described. For $1.5T_c<T<3.0T_c$, the value of the diffusion coefficient $D$ is comparable with that obtained by lattice QCD and experiments: $3.4<2\pi TD<5.9$. Relating the diffusion coefficient with the ratio of shear viscosity to entropy density $\eta \mathrm{/}s$ of the quark-gluon plasma, we obtain values in the range $0.09<\eta \mathrm{/}s<0.16$.