Polarized $\chi_{c2}$-charmonium production in antiproton-nucleus interactions

Starting from the Feynman diagram representation of multiple scattering we consider the polarized $\chi_c$(1P)-charmonia production in antiproton-nucleus reactions close to the threshold ($p_{\rm lab}=5-7$ GeV/c). The rescattering and absorption of the incoming antiproton and outgoing charmonium on nucleons are taken into account, including the possibility of the elastic and nondiagonal (flavor-conserving) scattering $\chi_{cJ} N \to \chi_{cJ^\prime} N$, $J,J^\prime=0,1,2$. The elementary amplitudes of the latter processes are evaluated by expanding the physical $\chi_c$-states in the Clebsch-Gordan series of the $c \bar c$ states with fixed values of internal orbital angular momentum ($L_z$) and spin projections on the $\chi_c$ momentum axis. The total interaction cross sections of these $c \bar c$ states with nucleons have been calculated in previous works using the QCD factorization theorem and the nonrelativistic quarkonium model and turned out to be strongly $L_z$-dependent due to the transverse size difference. This directly leads to finite values of the $\chi_c$-nucleon nondiagonal scattering amplitudes. We show that the $\chi_{c0} N \to \chi_{c2} N$ transitions significantly influence the $\chi_{c2}$-production with helicity zero at small transverse momenta. This can serve as a signal in future experimental tests of the quark structure of $\chi_c$-states by the PANDA collaboration at FAIR.