Quarkonium states in a complex-valued potential

Abstract

We calculate quarkonium binding energies using a realistic complex-valued potential for both an isotropic and anisotropic quark-gluon plasma. We determine the disassociation temperatures of the ground and first excited states considering both the real and imaginary parts of the binding energy. We show that the effect of momentum-space anisotropy is smaller on the imaginary part of the binding energy than on the real part of the binding energy. In the case that one assumes an isotropic plasma, we find disassociation temperatures for the $J/\ensuremath{\psi}$, $\ensuremath{\Upsilon}$, and ${\ensuremath{\chi}}_{b}$ of $2.3{T}_{c}$, $2.9{T}_{c}$, and $1.8{T}_{c}$, respectively. We find that a finite oblate momentum-space anisotropy increases the disassociation temperature for all states considered and results in a splitting of the $p$-wave states associated with the ${\ensuremath{\chi}}_{b}$ first excited state of bottomonium.