Polarized gluon distribution function of nucleon in diffractive lepto-production of charmonium

We investigate the longitudinal double spin asymmetry in the diffractive lepto-production of charmonium off the proton, and study its relation to the polarized gluon distribution ΔG of the proton. It is found that the transverse momenta of the exchanged gluons and Fermi motion of charm quarks give a finite spin asymmetry. Our calculation for the photo-production indicates the asymmetry is small and of O(10-3) ∼ O(10-2) at HERA collider energy. On the other hand, at fixed-target energy (HERMES), the asymmetry is of O(10-2) for J/ψ production. The asymmetry for the ψ' is even large, of O(10-1), due to the large Fermi motion of cc-bar in ψ'