Polarization study of P-wave charmonium radiative decay into a light vector meson at e ⁺ e ⁻ collider experiment*

Abstract In this paper, a formalism is presented for the helicity amplitude analysis of the decays (subscripts 1 and 2 are used to distinguish the two radiative photons), and the polarization expressions of the P-wave charmonia and the vector mesons for experimental measurements at an electron-positron collider. In addition, we derive formulae for the angular distributions of to extract the degree of transverse polarization of pairs with symmetric beam energy as well as the ratios of two helicity amplitudes x (in decays) and (in 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 , x , and y are estimated based on the large data samples collected at current and proposed future collider experiments.