Existence of mesons after deconfinement

We investigate the possibility for a quark-antiquark pair to form a bound state at temperatures higher than the critical one (T > Tc), thus after deconfinement. Our main goal is to find analytical criteria constraining the existence of such mesons. Our formalism relies on a Schrödinger equation for which we study the physical consequences of using both the free energy and the internal energy as potential term, assuming a widely accepted temperature-dependent Yukawa form for the free energy and a recently proposed nonperturbative form for the screening mass. We show that using the free energy only allows for the 1S bottomonium to be bound above Tc, with a dissociation temperature around 1.5 × Tc. The situation is very different with the internal energy, where we show that no bound states at all can exist in the deconfined phase. But, in this last case, quasibound states could be present at higher temperatures because of a positive barrier appearing in the potential.