Effective Field Theory and Lattice QCD approaches for hard probes in QCD matter

Hard Probes are an essential tool to discover the properties of the quark-gluon plasma created in heavy-ion collisions. The study of hard probes always involves taking into account very different energy scales, and this is precisely the situation in which Effective Fields Theories (EFTs) are useful. EFTs can be used to separate the short-distance and perturbative physics from the long-distance and non-perturbative. This method combined with Lattice QCD evaluations of the long-distance effects can provide accurate and first principles results. In this proceeding, I will report recent advances in this direction. Results from an EFT computation of quarkonium $R_{AA}$ at $\sqrt{s_{NN}}=5.02\,\textit{TeV}$ are shown for the first time here.