Inelastic heavy quarkonium photoproduction in <i>p</i>-<i>p</i> and <i>Pb</i>-<i>Pb</i> collisions at LHC energies

Abstract We study the inelastic charmonium ($J/\psi$, $\psi(2S)$) and bottomonium ($\Upsilon(nS)$) photoproduction and fragmentation processes in $p$-$p$ and $Pb$-$Pb$ collisions at LHC energies, where the ultra-incoherent photon emission is included. &amp;#xD;In the framework of the NRQCD factorization approach, an exact treatment is developed which recovers Weizs"{a}cker-Williams approximation (WWA) near the region $Q^{2}\sim0$, where the methods of Martin-Ryskin and BCCKL are used to avoid double counting. We calculate the $Q^{2}$, $y$, $z$, $\sqrt{s}$, $p_{T}$ dependent and the total cross sections.&amp;#xD;It turns out that the inelastic photoproduction and fragmentation processes provide valuable contributions to the heavy quarkonium production, especially in the large $p_{T}$ regions.&amp;#xD;While the relative contribution of ultra-incoherent photon channel is very important, which rapidly increases along with the growing quarkonium mass, and begins to dominate the photoproduction processes at large $p_{T}$ ranges.&amp;#xD;Moreover, we obtain the complete validity scopes of WWA in inelastic heavy quarkonium photoproduction in heavy-ion collisions.&amp;#xD;WWA has a much higher accuracy at high energies and in $Pb$-$Pb$ collisions.&amp;#xD;The existing photon spectra are generally derived beyond the applicable scopes of WWA, and the double counting exists when the different channels are considered simultaneously. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.