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We study the exclusive production of $J^{PC}=0^{++}, 0^{--}$ charmoniumstates in proton-proton collisions at the LHC energies The $pp \to pp\eta_c$reaction is discussed for the first time. We observe a substantial contributionfrom the nonperturbative domain of gluon virtualities, especially for $\eta_c$production. To model the nonperturbative region better, we utilize models ofthe unintegrated gluon distribution based on parametrizations of the colordipole cross-section.

Central exclusive production of $\eta_c$ and $\chi_{c0}$ in the light-front k$_{\perp}$-factorization approach