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Forward photoproduction of $J/\psi$ can be used to extract Generalized PartonDistributions(GPD's) of gluons. We analyze the process at twist-3 level andstudy relevant classifications of twist-3 gluon GPD's. At leading power ortwist-2 level the produced $J/\psi$ is transversely polarized. We find that attwist-3 the produced $J/\psi$ is longitudinally polarized. Our study shows thatin high energy limit the twist-3 amplitude is only suppressed by the inversepower of the heavy quark mass relatively to the twist-2 amplitude. Thisindicates that the power correction to the cross-section of unpolarized$J/\psi$ can have a sizeable effect. We have also derived the amplitude of theproduction of $h_c$ at twist-3, but the result contains end-pointsingularities. The production of other quarkonia has been briefly discussed.

Gluon GPDs and Exclusive Photoproduction of a Quarkonium in Forward Region