Inclusive diffractive heavy quarkonium photoproduction including quark subprocesses

The inclusive $J/\Psi$, $\Psi(2S)$ and $\Upsilon(1S)$ direct and resolved photoproduction are investigated by including the quark subprocesses in the framework of non-relativistic quantum chromodynamics (NRQCD). We find that the theoretical total cross section of heavy quarkonium productions are in good agreement with the data available at HERA, once the $\gamma q$, $qg$ and $qq$ subprocesses in the heavy quark pair productions are taken into account. The inclusive diffractive rapidity and transverse momentum distributions of $J/\Psi$, $\Psi(2S)$ and $\Upsilon(1S)$ in $pp$, $pPb$ and $PbPb$ collisions at LHC are also studied by our quark improved NRQCD model combined with the resolved pomeron model. We find that the contributions from the quark involved subprocesses can reach to $8\%$ in the rapidity distribution and $6\%$ in the transverse momentum distribution. The numerical results show that the contributions from quark involved subprocesses are significant in heavy quarkonium photoprodution.