Angular distribution functions in the decays of the 3 D 3 state of charmonium originating from unpolarized $\overline{p}p$ collisions

Abstract

Using the helicity formalism, we calculate the combined angular distribution function of the two photons (γ1 and γ2) and electron (e −) in the cascade process $\overline{p}p\to {}^3{D_3}\to {}^3{P_2}+{\gamma_1}\to \left( {\psi +{\gamma_2}} \right)+{\gamma_1}\to \left( {{e^{+}}+{e^{-}}} \right)+{\gamma_2}+{\gamma_1}$ ,when $\overline{p}$ and p are unpolarized. We also derive six different partially integrated angular distribution functions which give the angular distributions of one or two particles in the final state. Once the angular distributions are measured, our expressions will enable one to determine the relative magnitudes as well as the cosines of the relative phases of all the angular-momentum helicity amplitudes in the radiative decay processes 3 D 3 → 3 P 2 + γ1 and 3 P 2 → ψ + γ2.