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

Starting from the Feynman diagram representation of multiple scattering we consider the polarized $χ_c$(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 $χ_{cJ} N \to χ_{cJ^\prime} N$, $J,J^\prime=0,1,2$. The elementary amplitudes of the latter processes are evaluated by expanding the physical $χ_c$-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 $χ_c$ 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 $χ_c$-nucleon nondiagonal scattering amplitudes. We show that the $χ_{c0} N \to χ_{c2} N$ transitions significantly influence the $χ_{c2}$-production with helicity zero at small transverse momenta. This can serve as a signal in future experimental tests of the quark structure of $χ_c$-states by the PANDA collaboration at FAIR.