Polarized angular distributions in the decays of the 3D2 state of charmonium produced in unpolarized proton–antiproton annihilation

Abstract

Using the helicity formalism, we calculate the combined angular distribution functions of the polarized gamma photons and electron in the triple cascade process $\bar{\mathrm{p}}\mathrm{p}\to{}^{3}\mathrm{D}_{\mathrm{2}}\to\chi_{\mathrm{\mathrm{{J}}}}+\gamma_{\mathrm{1}}\to(\psi +\gamma_{\mathrm{2}})+\gamma_{\mathrm{1}}\to(\mathrm{e}^{+}+\mathrm{e}^{-})+\gamma_{\mathrm{1}}+\gamma_{\mathrm{2}}\ (\mathrm{{J}}=0,1,2)$ , when $\bar{\mathrm{p}}$ 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 γ 1 and γ 2 and that of γ 2 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 all the helicity amplitudes in the two radiative decay processes 3D2→χ J+γ 1 and χ J→ψ+γ 2.