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The inclusive $J/\psi$ transverse momentum ($p_{T}$) spectra and nuclearmodification factors are reported at midrapidity ($|y|<1.0$) in Au+Aucollisions at $\sqrt{s_{NN}}=$ 39, 62.4 and 200 GeV taken by the STARexperiment. A suppression of $J/\psi$ production, with respect to{\color{black}the production in $p+p$ scaled by the number of binarynucleon-nucleon collisions}, is observed in central Au+Au collisions at thesethree energies. No significant energy dependence of nuclear modificationfactors is found within uncertainties. The measured nuclear modificationfactors can be described by model calculations that take into account bothsuppression of direct $J/\psi$ production due to the color screening effect and$J/\psi$ regeneration from recombination of uncorrelated charm-anticharm quarkpairs.

Energy dependence of $J/\psi$ production in Au+Au collisions at $\sqrt{s_{NN}} =$ 39, 62.4 and 200 GeV