Spin tests for intermediate states in radiativeψ′(3684)decay chains

Analysis of the multiple angular-correlation functions for the sequential decays ${\psi }^{\prime }\left(1^{-}\right)\to \gamma +\chi$,$\chi \to M\overline{M}$, where $M$ is a spinless meson, and ${\psi }^{\prime }\left(1^{-}\right)\to {\gamma }_1+\chi$,$\chi \to {\gamma }_2+\psi$, $\psi \left(1^{-}\right)\to l\overline{l}$, when the ${\psi }^{\prime }$ is formed in $e^{+}{e}^{-}$ collisions, shows that these can unambiguously distinguish between the spin assignments $s_{\chi }=0.\mathrm{} 1, or 2$ for the intermediate states occuring in these decays, as well as determine the multipole amplitudes contributing to the radiative transitions. No dynamical assumptions are made beyond the conservation of angular momentum and parity; recoils are fully taken into account.