Heavy Flavours in Quark-Gluon Plasma

Recent progresses in lattice studies of heavy quark and quarkonium at non-zero temperature are discussed. Formulating a tail of spectral functions as a transport coefficient allows lattice determination of momentum diffusion coefficient ($\kappa$) for charm quark in the heavy quark mass limit and lattice determination of heavy quark/heavy anti-quark chemical equilibration rate in NRQCD. Quenched lattice study on a large volume gives $\kappa/T^3 = 1.8 \cdots 3.4$ in the continuum limit. A recent study with $N_f = 2+1$ configurations estimates the charmonium chemical equilibration rate $\Gamma_{\rm chem}$. At $T = 400$ MeV with $M \sim 1.5$ GeV, $\Gamma_{\rm chem}^{-1} \sim 150$ fm/c. Earlier results from the two studies (with different lattice setups and with different Bayesian priors) which calculate bottomonium correlators using NRQCD and employ Bayesian method to calculate spectral functions are summarized: $\Upsilon (1S)$ survives upto $T \sim 1.9 T_c$ and excited states of $\Upsilon$ are sequentially suppressed. The spectral functions of $\chi_{b1}$ channel shows a Bayesian prior dependence of its thermal behavior: the $\chi_{b1}$ spectral function with MEM prior shows melting above $T_c$ but that with a new Bayesian prior hints survival of $\chi_{b1}$ upto $\sim 1.6 T_c$. Preliminary results from the efforts to understand the difference in the behavior of $\chi_{b1}$ spectral function is given.