Calculation of dissociation temperature of quarkonium using Gaussian Expansion Method

The dissociation temperatures of quarkonium states in a thermal medium are obtained in the framework of the quark model with the help of the Gaussian Expansion Method (GEM). This is the first time this method has been applied to the dissociation problem of mesons. The temperature-dependent potential is obtained by fitting the lattice results. Solving the Schr?dinger equation with the GEM, the binding energies and corresponding wave functions of the ground states and the excited states are obtained at the same time. The accuracy and efficiency of the GEM provide a great advantage for the dissociation problem of mesons. The results show that the ground states 11 S 0 and 13 S 1 have much higher dissociation temperatures than other states, and the spin-dependent interaction has a significant effect on the dissociation temperatures of 13 S 1 and 11 S 0. We also suggest using the radius of the bound state as a criterion of quarkonium dissociation. This can help to avoid the inaccuracy caused by the long tail of quarkonium binding energy dependence on temperature.