Critical behavior of charmonia across the phase transition: A QCD sum rule approach

Abstract

We investigate the medium-induced change of mass and width of $J/\ensuremath{\psi}$ and ${\ensuremath{\eta}}_{c}$ across the phase transition in hot gluonic matter using QCD sum rules. In the QCD sum rule approach, the medium effect on heavy quarkonia is induced by the change of both scalar and twist-2 gluon condensates, whose temperature dependencies are extracted from the lattice calculations of energy density and pressure. Although the stability of the operator product expansion side seems to break down at $Tg1.06{T}_{c}$ for the vector channel and $Tg1.04{T}_{c}$ for the pseudoscalar channel, we find a sudden change of the spectral property across the critical temperature ${T}_{c}$, which originates from an equally rapid change of the scalar gluon condensate characterized by $\ensuremath{\varepsilon}\ensuremath{-}3p$. By parametrizing the ground state of the spectral density by the Breit-Wigner form, we find that for both $J/\ensuremath{\psi}$ and ${\ensuremath{\eta}}_{c}$, the masses suddenly decrease maximally by a few hundreds of MeV and the widths broaden to $~100$ MeV slightly above ${T}_{c}$. The implications for recent and future heavy-ion experiments are discussed. We also carry out a similar analysis for charmonia in nuclear matter, which could serve as a testing ground for observing the precursor phenomena of the QCD phase transition. We finally discuss the possibility of observing the mass shift at nuclear matter at the FAIR project at GSI.