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Investigation of heavy-heavy pseudoscalar mesons in thermal QCD Sum Rules

We investigate the mass and decay constant of the heavy-heavy pseudoscalar, $B_c$, $η_c$ and $η_b$ mesons in the framework of finite temperature QCD sum rules. The annihilation and scattering parts of spectral density are calculated in the lowest order of perturbation theory. Taking into account the additional operators arising at finite temperature, the nonperturbative corrections are also evaluated. The masses and decay constants remain unchanged under $T\cong 100 ~MeV$, but after this point, they start to diminish with increasing the temperature. At critical or deconfinement temperature, the decay constants reach approximately to 35% of their values in the vacuum, while the masses are decreased about 7%, 12% and 2% for $B_c$, $η_c$ and $η_b$ states, respectively. The results at zero temperature are in a good consistency with the existing experimental values as well as predictions of the other nonperturbative approaches.