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

Inclusive diffractive heavy quarkonium photoproduction including quark subprocesses