Radiative angular distributions from charmonium states directly produced byp¯pannihilation

We calculate the combined angular distributions of the photon and the electron in the cascade process $p\overline{p}\to {\chi }_J\to \left(e^{+}{e}^{-}\right)\gamma$ ($J=2,1,0\mathrm{}$), in terms of the helicity or the multipole transition amplitudes in $\psi$. Our expressions for them differ from those found previously. We describe the origin of these differences. The effect of the motion of $\psi$ in the ${\chi }_J$ rest frame on the angular-distribution functions is taken into account.