Heavy Quarkonia in a Potential Model: Binding Energy, Decay Width, and Survival Probability

Recently a lot of progress has been made in deriving the heavy quark potential within a QCD medium. In this article we have considered heavy quarkonium in a hot quark gluon plasma phase. The heavy-quark potential has been modeled properly for short as well as long distances. The potential at long distances is modeled as a QCD string which is screened at the same scale as the Coloumb field. We have numerically solved the 1+1-dimensional Schrodinger equation for this potential and obtained the eigen wavefunction and binding energy for the $1S$ and $2S$ states of charmonium and bottomonium. Further, we have calculated the decay width and dissociation temperature of quarkonium states in the QCD plasma. Finally, we have used our recently proposed unified model with these new values of decay widths to calculate the survival probability of the various quarkonium states with respect to centrality at relativistic heavy ion collider (RHIC) and large hadron collider (LHC) energies. This study provides a unified, consistent and comprehensive description of spectroscopic properties of various quarkonium states at finite temperatures along with their nuclear modification factor at different collision energies.