Polarisation effects in the central exclusive $\chi_c$ production and the $J/\psi$ angular distributions

We discuss exclusive elastic double diffractive axial-vector $\chi_c(1^+)$ and tensor $\chi_c(2^+)$ mesons production for different meson polarisations in proton-(anti)proton collisions at the Tevatron energy. The amplitude for the process is derived within the $k_t$-factorisation approach using unintegrated gluon distributions (UGDFs). Differential cross sections for different $\chi_c$ polarisations are calculated. Angular distributions of $J/\psi$ meson from the radiative $\chi_c(1^+,2^+)$ decays are derived. Prospects for experimental selection of different spin states of $\chi_c$ mesons are discussed.