Polarized angular distributions in the decays of the ψ' charmonium state directly produced in unpolarized proton-antiproton collisions

Using the helicity formulism, we calculate the combined angular distribution function of the polarized gamma photons and electron in the cascade process pp→ψ' →χ_J +γ₁ →ψ+γ₂+γ₁ →e⁺+e^-+ γ₂+γ₁ (J = 0, 1, 2), when p and p are unpolarized. We also present the partially integrated angular distribution functions in different cases. Our results show that by measuring the two-particle angular distribution of γ₁ and γ₂ and that of γ₂ and e^- with the polarization of either one of the two particles, one can determine the relative magnitudes as well as the relative phases of the helicity amplitudes in the radiative decay processes ψ' →χ_J +γ₁ and χ_J →ψ+γ₂.