Accessing linearly polarized gluon distribution in J/ψ production at the electron-ion collider

We calculate the cos 2 phi(h) asymmetry in J/psi production in electron-proton collision for the kinematics of the planned electron-ion collider (EIC). This directly probes the Weiszacker-Williams type linearly polarized gluon distribution. Assuming generalized factorization, we calculate the asymmetry at next-to-leading-order when the energy fraction of the J/psi satisfies z < 1 and the dominating subprocess is gamma* + g -> c + <(c)over bar> + g. We use the nonrelativistic QCD based color singlet model for J/psi. production. We investigate the small x region which will be accessible at the EIC. We present the upper bound of the asymmetry, as well as estimate it using a (i) Gaussian-type parametrization for the transverse momentum dependent parton distributions and (ii) McLerran-Venugopalan model at small x. We find small but sizable asymmetry in all three cases.