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 clarify its relation to the polarized gluon distribution $ΔG$ of the proton. The asymmetry is found to be finite even in the forward limit, if we properly deal with the Fermi motion of charm quarks and transverse momenta of the exchanged gluons. Our calculation for the photo-production of $J/ψ$ indicates the asymmetry is of $O(10−3)∼O(10−2)$ at HERA collider energy and of $O(10−2)$ at fixed-target energy (HERMES). The asymmetry for the ψ^′ is even large, of $O(10−1),$ due to the large Fermi motion of $cc̄$ in $ψ′.$