The thermal evolution of the hadronic parameters of charmonium in the vector channel, i.e. the J/psi resonance mass, coupling (leptonic decay constant), total width, and continuum threshold is analyzed in the framework of thermal Hilbert moment QCD sum rules. The continuum threshold $s_0$, as in other hadronic channels, decreases with increasing temperature until the PQCD threshold s_0 = 4, m_Q^2 is reached at T simeq 1.22T_c (m_Q is the charm quark mass) and the J/psi mass is essentially constant in a wide range of temperatures. The other hadronic parameters behave in a very different way from those of light-light and heavy-light quark systems. The total width grows with temperature up to T simeq 1.04T_c beyond which it decreases sharply with increasing T. The resonance coupling is also initially constant beginning to increase monotonically around T simeq T_c. This behavior strongly suggests that the J/psi resonance might survive beyond the critical temperature for deconfinement, in agreement with lattice QCD results.
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