Complete suppression of the heavy quarkonium due to the screening mechanism of the quark-gluon plasma is proposed in the literature to be a signature of the quark-gluon plasma detection at RHIC and LHC. However, since the heavy quarkonium $Upsilon$ production is experimentally measured in the Pb-Pb collisions by the ALICE collaboration at LHC one has to study the $Upsilon$ production from the quark-gluon plasma instead of studying the $Upsilon$ suppression due to the screening mechanism of the quark-gluon plasma. In this paper we derive the non-perturbative formula of the $Upsilon$ production amplitude from the quark-gluon plasma from the first principle in QCD which can be calculated by using the lattice QCD method at the finite temperature.
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