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

Abstract

Using the helicity formalism, we calculate the combined angular distribution function of the two gamma photons and the electron in the cascade process \({\bar{p}p}\to{}^{3}{D}_{2}\to\chi_{J}+\gamma_{1}\to(\psi +\gamma_{2})+\gamma_{1}\to({e}^{+}+{e}^{-})+\gamma_{1}+\gamma_{2}\) (J=0,1,2), when \({\bar{p}}\) 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 γ₁ and γ₂ and that of γ₁ 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 ³D₂→χ_J+γ₁ and χ_J→ψ+γ₂.