Radiative angular distributions fromcc¯states directly produced bypp¯annihilation

We present formulas, based on the helicity formalism, for the angular distributions of the radiative decay products involving ${\eta }_c^{\mathcal{’}}$, ψ, ${\chi }_J$, and ${}_{}{}^1{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$ cc¯ states formed in pp¯ collisions. Normalized joint angular observables are expressed in terms of allowed multipole transitions and the ratio of pp¯ production helicity amplitudes.