Lattice studies of the charmonium spectrum

Many experiments have found evidence of charmonium-like states that do not fit into conventional models of quark-antiquark mesons. Non-perturbative insight provided by lattice simulations is required to fully understand the properties of those states. The computation of single and multiparticle correlators is the main challenge of the numerical investigation of unstable states on the lattice. The phase shift and the properties of the resonance are then extracted from the finite volume energy levels. We present our analysis based on the distillation method and preliminary results for the charmonium states near the threshold.