Central exclusive production of $η$ and $η'$ mesons in diffractive proton-proton collisions at the LHC and the nature of the pomeron

Central exclusive production (CEP) of $η$ and $η'$ 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 ($\rm I\!P$-$\rm I\!P$) exchange, that is, the fusion reactions ${\rm I\!P I\!P} \to η, η'$. We show that for a scalar pomeron these fusion reactions are not possible. In contrast, in the tensor-pomeron model CEP of $η$ and $η'$ 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.