Inclusive diffractive heavy quarkonium photoproduction including quark subprocesses

To test the contributions of the quark subprocesses to the inclusive diffractive heavy quarkonium photoproduction, we first investigate the inclusive nondiffractive direct and resolved photoproduction of $J/\mathrm{\ensuremath{\Psi}}$ in the framework of nonrelativistic 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 $\ensuremath{\gamma}q$, $qg$, and $qq$ subprocesses in the heavy quark pair productions are taken into account. Then we predict the inclusive diffractive rapidity and transverse momentum distributions of $J/\mathrm{\ensuremath{\Psi}}$, $\mathrm{\ensuremath{\Psi}}(2S)$, and $\mathrm{\ensuremath{\Upsilon}}(1S)$ in $pp$, $p\mathrm{Pb}$, and $\mathrm{PbPb}$ collisions at the CERN Large Hadron Collider by using our quark improved NRQCD model. We find that the contributions from the quark involved subprocesses to quarkonium photoproduction are about $6%\text{--}15%$. The numerical results show that the contributions from quark involved subprocesses are significant modification in inclusive diffractive heavy quarkonium photoproduction.