Twist-3 gluon contribution to Sivers asymmetry in J/ψ production in semi-inclusive deep inelastic scattering

We carry out the first calculation for the twist-3 gluon contribution to the single transverse-spin asymmetry (SSA) in J/psi production in semi-inclusive deep inelastic scattering. Our result shows that the J/psi SSA is an ideal observable to pin down the C-even type twist-3 gluon distribution that has a direct relationship with the gluon transverse-momentum-dependent distribution function. We also perform some numerical simulations of the J/psi SSA for the kinematics accessible at the future electron-ion-collider experiment. For color-singlet contribution, the hadronization effect of J/psi is completely canceled at the level of the SSA, and the spin-dependent structure functions directly reflect the behavior of the C-even twist-3 gluon distribution.