Medium Modifications and Production of Charmonia at LHC

A previously constructed transport approach to calculate the evolution of quarkonium yields and spectra in heavy-ion collisions is applied to Pb-Pb($\sqrt{s}$=2.76\,ATeV) collisions at the Large Hadron Collider (LHC). In this approach spectral properties of charmonia are constrained by euclidean correlators from thermal lattice QCD and subsequently implemented into a Boltzmann equation accounting for both suppression and regeneration reactions. Based on a fair description of SPS and RHIC data, we provide predictions for the centrality dependence of $J/\psi$ yields at LHC. The main uncertainty is associated with the input charm cross section, in particular its hitherto unknown reduction due to shadowing in nuclear collisions. Incomplete charm-quark thermalization and non-equilibrium in charmonium chemistry entail a marked reduction of the regeneration yield compared to the statistical equilibrium limit.