The prediction of single-spin asymmetry in inelastic photoproduction of $J/\psi$ in $e{p}^{\uparrow }$ collision is presented. At next-to-leading order, the dominating process is photon-gluon fusion, $\gamma +g\to J/\psi +g$ for the production of $J/\psi$ in $e+p^{\uparrow }\to J/\psi +X$, which directly probes the gluon Sivers function. Using the nonrelativistic QCD based color octet model, the color octet states ${{}^{3}S}_1^{(8)}$, ${{}^{1}S}_0^{(8)}$ and ${{}^{3}P}_{J(0,1,2)}^{(8)}$ contribution to $J/\psi$ production is calculated. Sizable asymmetry is estimated as a function of transverse momentum $P_T$ and energy fraction $z$ of $J/\psi$ in the range $0<P_T\le 1\mathrm{GeV}$ and $0.3<z\le 0.9$. The unpolarized differential cross section of inelastic $J/\psi$ photoproduction is found to be in good agreement with H1 and ZEUS data.

• Received 7 March 2018

DOI:https://doi.org/10.1103/PhysRevD.98.014007

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Published by the American Physical Society