Elastic and inelastic $J/\psi$ photoproduction in $p$-$p$ collisions at LHC energies: the feature of Weizsäcker-Williams approximation

Abstract

The $J/\psi$ production originating from elastic and inelastic photoproduction processes in p-p collisions at LHC energies is investigated, where the fragmentation processes are involved. An exact treatment is performed, which adopts the Martin-Ryskin method to weight the contribution from different channels, and can return to Weizsäcker-Williams approximation (WWA) when $Q^2\to 0$. The relevant kinematical relations are also achieved. We present a comprehensive analysis for the feature of WWA by comparing with the exact treatment. The results are expressed in $Q^2$, $y$, $z$, $p_T$, and $y_r$ (rapidity) distributions, and the total cross sections are also estimated. The numerical results indicate that, the incoherent-photon emission can provide the meaningful contribution to elastic photoproduction, and starts to play a very important role in the inelastic processes. The photoproduction and fragmentation processes can improve the contribution of $J/\psi$ production in $p$-$p$ collisions at LHC energies. Moreover, the WWA is only effective in very restricted domains, and the exact treatment is needed to deal accurately with the $J/\psi$ photoproduction, which can naturally avoid double counting and WWA errors.

Comments: 19 pages, 8 figures