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The prediction of single-spin asymmetry in inelastic photoproduction of J=ψ in ep ↑ collision is presented. At next-to-leading order, the dominating process is photon-gluon fusion, γ þ g → J=ψ þ g for the production of J=ψ in e þ p ↑ → J=ψ þ X, which directly probes the gluon Sivers function.Using the nonrelativistic QCD based color octet model, the color octet states 3 S contribution to J=ψ production is calculated. Sizable asymmetry is estimated as a function of transverse momentum P T and energy fraction z of J=ψ in the range 0 < P T ≤ 1 GeV and 0.3 < z ≤ 0.9. The unpolarized differential cross section of inelastic J=ψ photoproduction is found to be in good agreement with H1 and ZEUS data.

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