Central exclusive production of $\eta$ and ${\eta }^{\mathrm{\prime }}$ mesons in diffractive proton-proton collisions at the LHC and the nature of the pomeron

Central exclusive production (CEP) of $\eta$ and ${\eta }^{\mathrm{\prime }}$ mesons in proton-proton collisions at high-energies is discussed. At the LHC the main mechanism for the production of these mesons should be double-pomeron ($\mathrm{I}\text{\hspace{0.17em}⁣}\mathrm{P}$-$\mathrm{I}\text{\hspace{0.17em}⁣}\mathrm{P}$) exchange, that is, the fusion reactions $\mathrm{I}\text{\hspace{0.17em}⁣}\mathrm{P}\mathrm{I}\text{\hspace{0.17em}⁣}\mathrm{P}\to \eta ,{\eta }^{\mathrm{\prime }}$. We show that for a scalar pomeron these fusion reactions are not possible. In contrast, in the tensor-pomeron model CEP of $\eta$ and ${\eta }^{\mathrm{\prime }}$ mesons via double-pomeron exchange is allowed. We discuss these reactions for the c.m. energy $\sqrt{s}=29.1$ GeV realised at the WA102 experiment and for $\sqrt{s}=13$ TeV corresponding to the LHC experiments. Cross sections and distributions are presented and discussed.