Charm and beauty in the deconfined plasma from quenched lattice QCD

We present continuum extrapolated results of charmonium and bottomonium correlators in the vector channel at several temperatures below and above $T_c$. The continuum extrapolation jointly performed with the interpolations to have physical values of $J/\psi$ and $\Upsilon$ masses in the confined phase is based on calculations on several large quenched isotropic lattices using clover-improved Wilson valence fermions carrying different quark masses. The extrapolated lattice correlators are confronted with perturbation theory results incorporating resummed thermal effects around the threshold from pNRQCD and vacuum asymptotics above the threshold. An additional transport peak is modelled below the threshold allowing for an estimate of the diffusion coefficients for charm and bottom quarks. We find that charmonium correlators in the vector channel can be well reproduced by perturbative spectral functions above $T_c$ where no resonance peaks for $J/\psi$ are needed at and above 1.1 $T_c$, while for bottomonium correlators a resonance peak for $\Upsilon$ is still needed up to 1.5 $T_c$. By analyzing the transport contribution to the correlators we find that the drag coefficient of a charm quark is larger than that of a bottom quark.