\begin{document}$ \psi(2S) \to $\end{document}\begin{document}$ \gamma_1 \chi_{cJ},\; \chi_{cJ} \to \gamma_2 V (V=\rho^0,\; \phi,\; \omega) $\end{document} (subscripts 1 and 2 are used to distinguish the two radiative photons), and the polarization expressions of the P-wave charmonia \begin{document}$ \chi_{cJ} $\end{document} and the vector mesons \begin{document}$ \rho^0, \phi, \omega $\end{document} for experimental measurements at an electron-positron collider. In addition, we derive formulae for the angular distributions of \begin{document}$ \chi_{c1,2} \to \gamma V $\end{document} to extract the degree of transverse polarization \begin{document}$ P_T $\end{document} of \begin{document}$ e^+ e^- $\end{document} pairs with symmetric beam energy as well as the ratios of two helicity amplitudes x (in \begin{document}$ \chi_{c1} $\end{document} decays) and \begin{document}$ x,\; y $\end{document} (in \begin{document}$ \chi_{c2} $\end{document} decays), which represent the relative magnitudes of transverse to longitudinal polarization amplitude. The results are validated by Monte Carlo simulation. Finally, the statistical sensitivity of \begin{document}$ P_T $\end{document}, x, and y are estimated based on the large \begin{document}$ \psi(2S) $\end{document} data samples collected at current and proposed future \begin{document}$ e^+e^- $\end{document} collider experiments."> Polarization study of <i>P</i>-wave charmonium radiative decay into a light vector meson at <i>e</i><sup>+</sup><i>e</i><sup>−</sup> collider experiment -
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