Helicity amplitude and branching fraction measurement of ${\chi }_{cJ}\to \Lambda \bar{\Lambda }$

Abstract

Utilizing $2712.4\pm 14.3$ million $\psi (3686)$ events accumulated by the BESIII experiment, we perform a partial wave analysis of $\psi (3686)\to \gamma {\chi }_{cJ}\to \gamma \Lambda \bar{\Lambda }$ decay ($J=0,1,2$). The ratio of the helicity amplitudes with same (++) and opposite (+-) helicity for ${\chi }_{c2}\to \Lambda \bar{\Lambda }$ 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 ${\chi }_{cJ}\to \Lambda \bar{\Lambda }$ 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.

arXiv commentThis is the first submission of the manuscript. 13 pages, 15 figures

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