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Nonperturbative and spin effects in the central exclusive production of tensor $χ_c(2^+)$ meson

We discuss central exclusive production (CEP) of the tensor $χ_c(2^{+})$ meson in proton-(anti)proton collisions at Tevatron, RHIC and LHC energies. The amplitude for the process is derived within the $k_t$-factorisation approach. Differential and total cross sections are calculated for several unintegrated gluon distributions (UGDFs). We compare exclusive production of all charmonium states $χ_c(0^+),\,χ_c(1^+)$ and $χ_c(2^+)$. Equally good description of the recent Tevatron data is achieved both with Martin-Ryskin phenomenological UGDF and UGDF based on unified BFKL-DGLAP approach. Unlike for Higgs production, the main contribution to the diffractive amplitude of heavy quarkonia comes from nonperturbative region of gluon transverse momenta $Q_{\perp}<1\,\GeV$. At $y \approx$ 0, depending on UGDF we predict the contribution of $χ_c(1^+,2^+)$ to the $J/Ψ+ γ$ channel to be comparable or larger than that of the $χ_c(0^+)$ one. This is partially due to a significant contribution from lower polarization states $λ=0$ for $χ_c(1^+)$ and $λ=0,\,\pm 1$ for $χ_c(2^+)$ meson. Corresponding theoretical uncertainties are discussed.