Sivers effect in Inelastic $J/\psi$ Photoproduction in $ep^\uparrow$ Collision in Color Octet Model

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