Azimuthal angular correlation of $J\mathrm{/}\psi$ plus jet production at the electron-ion collider

By investigating the soft gluon radiation in the $J\mathrm{/}\psi$ plus jet photoproduction at the electron-ion collider (EIC), we demonstrate that the azimuthal angular correlations between the leading jet and heavy quarkonium provide a unique probe to the production mechanism of the latter. In particular, a significant $\cos (\phi )$ asymmetry is found for the color-singlet channel, whereas it vanishes or has an opposite sign for color-octet production, depending on the jet transverse momentum. Numerical results of $\cos (\phi )$ and $\cos (2\phi )$ asymmetries employing both the color-singlet model and the nonrelativistic QCD approach are presented for typical kinematics at the future EIC.