# Helicity amplitude and branching fraction measurement of $\chi_{cJ} \rightarrow \Lambda\bar{\Lambda} $

## TL;DR

This study measures helicity amplitudes, angular distribution parameters, width, and branching fractions of $oldsymbol{ ext{chi}_{cJ}}$ decays to $oldsymbol{ ext{Lambda}ar{ ext{Lambda}}}$ using a large $oldsymbol{ ext{psi(3686)}}$ dataset, providing new insights into charmonium decay dynamics.

## Contribution

First measurement of the helicity amplitude ratio and phase for $ ext{chi}_{c2}
ightarrow ext{Lambda}ar{ ext{Lambda}}$ decay, along with precise branching fractions and angular distribution parameters.

## Key findings

- Helicity amplitude ratio $R_{ ext{chi}_{c2}}=0.575 \, ext{with uncertainties}
- Branching fractions for $ ext{chi}_{cJ}
ightarrow ext{Lambda}ar{ ext{Lambda}}$ measured with high precision
- Width of $ ext{chi}_{c0}$ determined to be 12.31 MeV

## Abstract

Utilizing $2712.4 \pm 14.3$ million $\psi(3686)$ events accumulated by the BESIII experiment, we perform a partial wave analysis of $\psi(3686)\rightarrow\gamma\chi_{cJ}\rightarrow\gamma\Lambda\bar{\Lambda}$ decay ($J=0,1,2$). The ratio of the helicity amplitudes with same (++) and opposite (+-) helicity for $\chi_{c2}\rightarrow\Lambda\bar{\Lambda}$ decay is determined for the first time to be $R_{\chi_{c2}}=0.575 \pm 0.048 \pm 0.018 $, with a relative phase angle $\Delta\Phi_{\chi_{c2}} = 0.37 \pm 0.15 \pm 0.05 $~rad. The parameters of the angular distribution of $\chi_{c2}$ are determined to be $\alpha_{\chi_{c2}} = -0.211 \pm 0.100 \pm 0.050 $ and $\beta_{\chi_{c2}} = -0.039 \pm 0.089 \pm 0.033 $, based on the distribution $dN / d\cos\theta = 1 + \alpha_{\chi_{c2}} \cos^2\theta + \beta_{\chi_{c2}} \cos^4\theta$. The width of $\chi_{c0}$ is determined to be $12.31 \pm 0.26 \pm 0.12 $~MeV. Additionally, the branching fractions for $\chi_{cJ} \rightarrow \Lambda\bar{\Lambda}$ are measured to be $(3.662 \pm 0.048 \pm 0.111) \times 10^{-4}$, $(1.182 \pm 0.026 \pm 0.042) \times 10^{-4}$, and $(1.704 \pm 0.035 \pm 0.057) \times 10^{-4}$ for $\chi_{c0}$, $\chi_{c1}$ and $\chi_{c2}$, respectively, where the first uncertainty is statistical and the second systematic.