(Pseudo)Scalar Charmonium in Finite Temperature QCD

Abstract

The hadronic parameters of pseudoscalar (${\eta }_c$) and scalar (${\chi }_c$) 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, $s_{th}=4m_Q^2$, 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 $J/\psi$, 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 ${\chi }_c$ (${\eta }_c$), and subsequently it decreases sharply up to $T\simeq 0.94(0.99)T_c$, for ${\chi }_c$ (${\eta }_c$), beyond which the sum rules are no longer valid. The decay constant of ${\chi }_c$ at first remains basically flat up to $T\simeq 0.80T_c$, then it starts to decrease up to $T\simeq 0.90T_c$, and finally it increases sharply with increasing $T$. In the case of ${\eta }_c$ the decay constant does not change up to $T\simeq 0.80T_c$ where it begins a gentle increase up to $T\simeq 0.95T_c$ 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 ${\eta }_c$ and the ${\chi }_c$ states beyond the critical temperature, as already found for the $J/\psi$ from similar QCD sum rules. These conclusions are very stable against changes in the critical temperature in the wide range $T_c = 180 - 260 \; \mbox{MeV}$.

12 pages, 5 figures. A wide range of critical temperatures has been considered. No qualitative changes to the conclusions

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• QCD determination of the magnetic field dependence of QCD and hadronic parameters
• Chiral symmetry restoration and deconfinement in QCD at finite temperature
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• In-medium properties of pseudoscalar $D_s$ and $B_s$ mesons
• Comparison between the continuum threshold and the Polyakov loop as deconfinement order parameters
• Charmonium ground and excited states at finite temperature from complex Borel sum rules
• Temperature dependence of dimension 6 gluon operators and their effects on Charmonium
• The $a_1(1260)$ meson and chiral symmetry restoration and deconfinment at finite temperature QCD
• Power corrections to the electromagnetic spectral function and the dilepton rate in QCD plasma within operator product expansion in D=4