Thermal QCD sum rules study of vector charmonium and bottomonium states

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.