$χ_{c2} \to ρρ$ and the $rho$ polarization in massless perturbative QCD: how to test the distribution amplitudes

We compute the helicity density matrix of $\rho$ vector mesons produced in the two-body decays of polarized $\chi_{c2}$'s in the framework of massless perturbative QCD. The $\chi_{c2}$'s are either exclusively or inclusively produced in $p \, \bar p$ or $p \, p$ interactions, via quark-antiquark annihilation or gluon fusion. Our results show unambiguous significant differences depending on the choice of the $\rho$ distribution amplitudes and allow to discriminate between different proposed models.