(Pseudo)Scalar Charmonium in Finite Temperature QCD

Abstract

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 ($s_0$). Results for $s_0(T)$ in both channels indicate that $s_0(T)$ starts approximately constant, and then it decreases monotonically with increasing $T$ until it reaches the QCD threshold, $s_{th} = 4 m_Q^2$, at a critical temperature $T = T_c \simeq 180 \; \mbox{MeV}$ 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 $T/T_c \simeq 0.80$ it begins to increase with increasing $T$ up to $T/T_c \simeq 0.90 \; (0.95)$ for $χ_c$ ($η_c$), and subsequently it decreases sharply up to $T \simeq 0.94 \; (0.99) \; T_c$, for $χ_c$ ($η_c$), beyond which the sum rules are no longer valid.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 $T \simeq 0.80\; T_c$, then it starts to decrease up to $T \simeq 0.90 \;T_c$, and finally it increases sharply with increasing $T$. In the case of $η_c$ the decay constant does not change up to $T \simeq 0.80 \;T_c$ where it begins a gentle increase up to $T \simeq 0.95 \;T_c$ beyond which it increases dramatically with increasing $T$. This behaviour 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 $T_c = 180 - 260 \; \mbox{MeV}$.