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Finite temperature lattice QCD indicates that the charmonium ground state J/psi can survive in a quark-gluon plasma up to 1.5 T_c or more, while the excited states chi_c and psi-prime are dissociated just above T_c. We assume that the chi_c suffers the same form of suppression as that observed for the psi-prime in SPS experiments, and that the directly produced J/psi is unaffected at presently available energy densities. This provides a parameter-free description of J/psi and psi-prime suppression which agrees quite well with that observed in SPS and RHIC data.

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