Search for the Charmonium Dissociation Temperature with Variational Analysis in Lattice QCD

TL;DR

This study investigates the dissociation temperatures of charmonium states in lattice QCD, finding no clear evidence of dissociation up to 2.3 times the critical temperature using variational analysis and boundary condition methods.

Contribution

It introduces a combined approach using variational analysis, boundary condition comparison, and wave function studies to assess charmonium dissociation in lattice QCD.

Findings

No clear dissociation evidence for ground and excited states up to 2.3T_c

Effective masses and wave functions indicate bound states persist at high temperatures

Boundary condition sensitivity helps distinguish bound from scattering states

Abstract

Charmonium dissociation temperatures are studied in a quenched anisotropic lattice QCD with standard plaquette gauge action and O(a) improved Wilson fermion action. Simulations are carried out at temperatures in the range 0.88T_c to 2.3T_c. From the meson correlators, we first subtract the contribution of constant mode, which was reported to mislead the analysis of, in particular, P wave signals. We then calculate effective masses and Bethe-Salpeter wave functions for ground (1S, 1P) and excited states (2S, 2P) using the multi-state variational analysis. To distinguish between bound states and scattering states, we apply two methods: First, we compare effective masses for charmonium correlation functions with finite spatial momenta under different spatial boundary conditions. Since the scattering state energies are sensitive to the boundary conditions, we expect finite volume effects when the charmonium dissociates. Second, we study the Bethe-Salpeter wave function, which should become broad when the charmonium bound state turns into a scattering state. With both methods, we have fond no clear evidences of dissociation for the ground and exited charmonium states up to 2.3T_c so far.