Accessing Linearly Polarized Gluon Distribution in $J/\psi$ Production at the Electron-Ion Collider

Understand

We calculate the $cos~2 \phi$ asymmetry in $J/\psi$ production in electron-proton collision for the kinematics of the planned electron-ion collider (EIC).

• This directly probes the Weisz\"acker-Williams (WW) type linearly polarized gluon distribution.
• Assuming generalized factorization, we calculate the asymmetry at next-to-leading-order (NLO) when the energy fraction of the $J/\psi$ satisfies $z<1$ and the dominating subprocess is $\gamma^* +g \rightarrow c + {\bar c}+g$.
• We use non-relativistic QCD based color singlet model for $J/\psi$ production.