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Proof of Factorization of $J/Ψ$ Production in Non-Equilibrium QCD at RHIC and LHC

$J/ψ$ suppression/production is one of the main signature of quark-gluon plasma detection at RHIC and LHC. In order to study $j/ψ$ suppression/production in high energy heavy-ion collisions at RHIC and LHC, one needs to prove the factorization theorem of $j/ψ$ production in non-equilibrium QCD medium, otherwise one will predict infinite cross section of $j/ψ$. In this paper we prove factorization theorem of $j/ψ$ production in non-equilibrium QCD at RHIC and LHC at all order in coupling constant.