  The transverse momentum distributions for inclusive $\eta_{c,b}$ meson
described by gluon-gluon interactions from photoproduction processes in
relativistic heavy ion collisions are calculated. We considered the color
singlet (CS) and color octet (CO) components with the framework of
non-relativistic Quantum Chromodynamics (NRQCD) into the production of heavy
quarkonium. The phenomenological values of the matrix elements for the
color-singlet and color-octet components give the main contribution to the
production of heavy quarkonium from the gluon-gluon interaction caused by the
emission of additional gluon in the initial state. The numerical results
indicate that the contribution of photoproduction processes cannot be
negligible for mid-rapidity in p-p and Pb-Pb collisions at the Large Hadron
Collider (LHC) energies.
