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

We investigate the longitudinal double spin asymmetry in the diffractive le pto-production of charmonium off the proton, and study its relation to the polarized gluon distribution DeltaG of the proton. It is found that the tra nsverse momenta of the exchanged gluons and Fermi motion of charm quarks gi ve a finite spin asymmetry. Our calculation for the photo-production indica tes the asymmetry is small and of O(10(-3)) similar to O(10(-2)) at HERA co llider energy. On the other hand, at fixed-target energy (HERMES), the asym metry is of O(10(-2)) for J/psi production. The asymmetry for the psi ' is even large, of O(10(-1)), due to the large Fermi motion of c (c) over bar i n psi '.