Thermal QCD Sum Rules Study of Vector Charmonium and Bottomonium States

TL;DR

This study uses thermal QCD sum rules to analyze how the masses and decay constants of vector charmonium and bottomonium states change with temperature, indicating signs of quark-gluon plasma formation.

Contribution

It introduces a method to calculate temperature-dependent properties of heavy quarkonia using thermal QCD sum rules, including additional operators at finite temperature.

Findings

Masses decrease by about 12% for $J/\psi$ and 2.5% for $\Upsilon$ at deconfinement.

Decay constants drop to roughly 45% of their vacuum values at deconfinement.

Results align with experimental data and other models at zero temperature.

Abstract

We calculate the masses and leptonic decay constants of the heavy vector quarkonia, $J/\psi$ and $\Upsilon$ mesons at finite temperature. In particular, considering the thermal spectral density as well as additional operators coming up at finite temperature, the thermal QCD sum rules are acquired. Our numerical calculations demonstrate that the masses and decay constants are insensitive to the variation of temperature up to $T\cong 100 ~MeV$, however after this point, they start to fall altering the temperature. At deconfinement temperature, the decay constants attain roughly to 45% of their vacuum values, while the masses are diminished about 12%, and 2.5% for $J/\psi$ and $\Upsilon$ states, respectively. The obtained results at zero temperature are in good consistency with the existing experimental data as well as predictions of the other nonperturbative models. Considerable decreasing in the values of the decay constants can be considered as a sign of the quark gluon plasma phase transition.