Charmonium spectral functions with the variational method in zero and finite temperature lattice QCD

TL;DR

This paper introduces a variational method to evaluate charmonium spectral functions in lattice QCD at zero and finite temperatures, demonstrating improved accuracy over traditional methods and providing insights into quarkonium behavior near the deconfinement transition.

Contribution

The paper develops and tests a variational approach for calculating spectral functions in lattice QCD, offering a systematic improvement over existing methods like MEM, especially for excited states.

Findings

The variational method accurately reproduces analytic spectra for free Wilson quarks.

It yields charmonium spectral features closer to experimental data for excited states.

No clear evidence of J/ψ and η_c dissociation up to 1.4 T_c.

Abstract

We propose a method to evaluate spectral functions on the lattice based on a variational method. On a lattice with a finite spatial extent, spectral functions consist of discrete spectra only. Adopting a variational method, we calculate the locations and the heights of spectral functions at low-lying discrete spectra. We first test the method in the case of analytically solvable free Wilson quarks at zero and finite temperatures and confirm that the method well reproduces the analytic results for low-lying spectra. We find that we can systematically improve the results by increasing the number of trial states. We then apply the method to calculate the charmonium spectral functions for S and P-wave states at zero-temperature in quenched QCD and compare the results with those obtained using the conventional maximum entropy method (MEM). The results for the ground state are consistent with the location and the area of the first peak in spectral functions from the MEM, while the variational method leads to a mass which is closer to the experimental value for the first excited state. We also investigate the temperature dependence of the spectral functions for S-wave states below and above $T_c$. We obtain no clear evidences for dissociation of $J/\psi$ and $\eta_c$ up to 1.4$T_c$.