Polarization study of the P-wave charmonium radiative decay into a light vector meson at $e^{+}e^{-}$ collider experiment

TL;DR

This paper develops a formalism for analyzing the polarization and angular distributions in P-wave charmonium radiative decays into light vector mesons at electron-positron colliders, enabling precise measurements of polarization states.

Contribution

It introduces a new helicity amplitude analysis formalism and derives angular distribution formulas for extracting polarization parameters in charmonium decays, validated by Monte Carlo simulations.

Findings

Derived formulas for angular distributions and polarization extraction.

Validated the formalism with Monte Carlo simulations.

Estimated statistical sensitivities for future experiments.

Abstract

In this work, a formalism is presented for the helicity amplitude analysis of the decays $\psi(2S) \to \gamma_1 \chi_{cJ},~ \chi_{cJ} \to \gamma_2 V (V=\rho^0,~\phi,~\omega)$~(the subscript 1,2 is used to distinguish the two radiative photons), and the polarization expressions of the P-wave charmonia $\chi_{cJ}$ and the vector mesons $\rho^0, \phi, \omega$ for experimental measurements at Electron-Positron Collider. In addition, we derive the formulae of the angular distributions of the $\chi_{c1,2} \to \gamma V$ to extract the degree of transverse polarization $P_T$ of $e^+ e^-$ pairs with symmetric beam energy as well as the ratios of two helicity amplitudes $x$ (in $\chi_{c1}$ decays) and $x,~y$ (in $\chi_{c2}$ decays) representing the relative magnitudes of transverse to longitudinal polarization amplitude, and validate it by performing the Monte Carlo simulation. Finally, the statistical sensitivity of $P_T$, $x$ and $y$ are estimated based on the large $\psi(2S)$ data samples collected at the current and proposed future $e^+e^-$ collider experiment.