(Pseudo)scalar charmonium in finite temperature QCD

The hadronic parameters of pseudoscalar (η_c) and scalar (χ_c) charmonium are determined at finite temperature from Hilbert moment QCD sum rules. These parameters are the hadron mass, leptonic decay constant, total width, and continuum threshold (s₀). Results for s₀(T) in both channels indicate that s₀(T) starts approximately constant, and then it decreases monotonically with increasing T until it reaches the QCD threshold, s_th=4m_Q², at a critical temperature T=T_c≃180MeV interpreted as the deconfinement temperature. The other hadronic parameters behave qualitatively similarly to those of the J/ψ, as determined in this same framework. The hadron mass is essentially constant, the total width is initially independent of T, and after T/T_c≃0.80 it begins to increase with increasing T up to T/T_c≃0.90(0.95) for χ_c (η_c), and subsequently it decreases sharply up to T≃0.94(0.99)T_c, for χ_c (η_c), beyond which the sum rules are no longer valid. The decay constant of χ_c at first remains basically flat up to T≃0.80T_c, then it starts to decrease up to T≃0.90T_c, and finally it increases sharply with increasing T. In the case of η_c the decay constant does not change up to T≃0.80T_c where it begins a gentle increase up to T≃0.95T_c beyond which it increases dramatically with increasing T. This behavior contrasts with that of light-light and heavy-light quark systems, and it suggests the survival of the η_c and the χ_c states beyond the critical temperature, as already found for the J/ψ from similar QCD sum rules. These conclusions are very stable against changes in the critical temperature in the wide range T_c=180-260MeV.