Nonperturbative and spin effects in the central exclusive production of tensor ${\chi }_c(2^{+})$ meson

Abstract

We discuss central exclusive production (CEP) of the tensor ${\chi }_c(2^{+})$ 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 ${\chi }_c(0^{+}),{\chi }_c(1^{+})$ and ${\chi }_c(2^{+})$. 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 $Q_{\perp }<1\text{GeV}$. At $y\approx$ 0, depending on UGDF we predict the contribution of ${\chi }_c(1^{+},2^{+})$ to the $J/\Psi +\gamma$ channel to be comparable or larger than that of the ${\chi }_c(0^{+})$ one. This is partially due to a significant contribution from lower polarization states $\lambda =0$ for ${\chi }_c(1^{+})$ and $\lambda =0,\pm 1$ for ${\chi }_c(2^{+})$ meson. Corresponding theoretical uncertainties are discussed.

Comments: 18 pages, 12 figures, discrepancies with Durham group results clarified, numerics corrected, basic conclusions unchanged, acknowledgements added