Gluon Sivers Function and Single Spin Asymmetry in $e+p^{\uparrow }\to e+J\mathrm{/}\psi +X$

We propose measurement of transverse single spin asymmetry (SSA) in charmonium production as a probe of gluon Sivers function. We estimate SSA in low virtuality electroproduction of $J\mathrm{/}\psi$ using color evaporation model of charmonium production and existing models of the gluon Sivers function and find sizable asymmetry at JLab, HERMES, COMPASS and eRHIC energies.