Complex-energy spectrum and dissociation of heavy quarkonia in an anisotropic collisional quark-gluon plasma

Abstract

We solve the Schr\"odinger equation for heavy quarkonia using the full complex potential of a momentum-anisotropic, collisional quark-gluon plasma. The real and imaginary parts of the complex eigenvalue give the in-medium binding energy and thermal width, while the corresponding eigenfunction determines the spatial distribution of the state. The noncentral anisotropic interaction is treated by expanding the potential in Legendre multipoles and solving the resulting coupled radial equations at fixed magnetic quantum number. The collision rate is tied to the running coupling, with the pinch singularity of the imaginary potential used to restrict the allowed parameter domain. Along the resulting pinch-free trajectories, the dissociation temperature of the $1S$ charmonium and bottomonium states increases with anisotropy. The widths obtained from the full complex eigenvalue differ appreciably from first-order estimates based on the imaginary potential, while the corresponding $1S$ eigenfunctions remain dominated by their leading $S$-wave component. We compare the thermal widths with available lattice-QCD results and use them to illustrate a static survival probability.