Helicity amplitude and branching fraction measurement of $χ_{cJ} \rightarrow Λ\barΛ $
Utilizing $2712.4 \pm 14.3$ million $ψ(3686)$ events accumulated by the BESIII experiment, we perform a partial wave analysis of $ψ(3686)\rightarrowγχ_{cJ}\rightarrowγΛ\barΛ$ decay ($J=0,1,2$). The ratio of the helicity amplitudes with same (++) and opposite (+-) helicity for $χ_{c2}\rightarrowΛ\barΛ$ decay is determined for the first time to be $R_{χ_{c2}}=0.575 \pm 0.048 \pm 0.018 $, with a relative phase angle $ΔΦ_{χ_{c2}} = 0.37 \pm 0.15 \pm 0.05 $~rad. The parameters of the angular distribution of $χ_{c2}$ are determined to be $α_{χ_{c2}} = -0.211 \pm 0.100 \pm 0.050 $ and $β_{χ_{c2}} = -0.039 \pm 0.089 \pm 0.033 $, based on the distribution $dN / d\cosθ= 1 + α_{χ_{c2}} \cos^2θ+ β_{χ_{c2}} \cos^4θ$. The width of $χ_{c0}$ is determined to be $12.31 \pm 0.26 \pm 0.12 $~MeV. Additionally, the branching fractions for $χ_{cJ} \rightarrow Λ\barΛ$ 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 $χ_{c0}$, $χ_{c1}$ and $χ_{c2}$, respectively, where the first uncertainty is statistical and the second systematic.