We study exclusive production of scalar $chi_{c0}equiv chi_c(0^{++})$ and pseudoscalar $eta_c$ charmonia states in proton-proton collisions at the LHC energies. The amplitudes for $gg to chi_{c0}$ as well as for $gg to eta_c$ mechanisms are derived in the $k_{T}$-factorization approach. The $p p to p p eta_c$ reaction is discussed for the first time. We have calculated rapidity, transverse momentum distributions as well as such correlation observables as the distribution in relative azimuthal angle and $(t_1,t_2)$ distributions. The latter two observables are very different for $chi_{c0}$ and $eta_c$ cases. In contrast to the inclusive production of these mesons considered very recently in the literature, in the exclusive case the cross section for $eta_c$ is much lower than that for $chi_{c0}$ which is due to a special interplay of the corresponding vertices and off-diagonal UGDFs used to calculate the cross sections. We present the numerical results for the key observables in the framework of potential models for the light-front quarkonia wave functions. We also discuss how different are the absorptive corrections for both considered cases.
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