Two-gluon production of $\varphi$ and ${\eta }^{\mathrm{\prime }}$ mesons in proton-proton collisions at high energies

We discuss gluon-gluon mechanisms for production of mesons with hidden strangeness, such as ${\eta }^{\mathrm{\prime }}$ and $\varphi$ meson, in proton-proton collisions at large energies. The $g^{\ast }{g}^{\ast }\to {\eta }^{\mathrm{\prime }}$ and $g^{\ast }{g}^{\ast }\to \varphi g$ mechanisms are considered only and the corresponding cross sections are calculated in the $k_t$-factorization approach. The $F_{{\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }^{\mathrm{\prime }}}$ and $F_{g^* g^* \to \eta’}$formfactorsarecalculatedfromquark-antiquark$\eta’$ light-cone wave function including quark/antiquark transverse momenta. The result for two-photon transition form factor demonstrates that higher twists may survive even to large photon virtualities. The result is compared with the result of a recent leading-twist NLO analysis which uses phenomenological distribution amplitudes fitted to exclusive production of ${\eta }^{\mathrm{\prime }}$ in $e^+ e^- \to e^+ e^- \eta’$ reaction. We calculate transverse momentum distributions of both ${\eta }^{\mathrm{\prime }}$ and $\varphi$ mesons in proton-proton collisions for RHIC and LHC energies. The results are compared to experimental data whenever available. The results of the Lund string model are shown for comparison for ${\eta }^{\mathrm{\prime }}$ production at LHC energies. It seems that the two-gluon fusion is not the dominant mechanism for both $\varphi$ and ${\eta }^{\mathrm{\prime }}$ production, although the situation for ${\eta }^{\mathrm{\prime }}$, especially at larger energies, is less clear due to lack of experimental data.