Angular distributions in the decays of the triplet D ₂ state of charmonium directly produced in polarized proton-antiproton collisions

Using the helicity formalism, we calculate the combined angular distribution function of the two gamma photons and the electron in the cascade process p̄p → ³ D ₂→χ _J +γ ₁ and χ _J →ψ+γ ₂ → (e⁺ + ^-) + γ1 + γ2 (J=0,1,2), when p̄ and p are arbitrarily polarized. We also present the partially integrated angular distribution functions in six different cases. Our results show that by measuring the two-particle angular distribution of γ ₁ and γ ₂ and that of γ ₁ and e ^-, one can determine the relative magnitudes as well as the relative phases of all the helicity amplitudes in the two radiative decay processes ³ D ₂→χ _J +γ ₁ and χ _J →ψ+γ ₂.