Observation of $Ξ^{-}$ Hyperon Transverse Polarization in $ψ(3686)\rightarrowΞ^{-}\barΞ^{+}$
Using a sample of $(448.1~\pm~2.9)$ $\times 10^{6}$ $ψ(3686)$ decays collected with the BESIII detector at BEPCII, we report an observation of $Ξ^{-}$ transverse polarization with a significance of $7.3 σ$ in the decay $ψ(3686)\rightarrowΞ^{-}\barΞ^{+}$ ($Ξ^{-}\rightarrowπ^{-}Λ$, $\barΞ^{+}\rightarrowπ^{+}\barΛ$, $Λ\to pπ^{-}$, $\barΛ\to\bar{p}π^{+}$). The relative phase of the electric and magnetic form factors is determined to be $ΔΦ= (0.667 \pm 0.111 \pm 0.058)$ rad. This is the first measurement of the relative phase for a $ψ(3686)$ decay into a pair of $Ξ^{-}\barΞ^{+}$ hyperons. The $Ξ^{-}$ decay parameters ($α_{Ξ^{-}}$, $ϕ_{Ξ^-}$) and their conjugates ($α_{\barΞ^{+}}$, $ϕ_{\barΞ^{+}}$), the angular-distribution parameter $α_ψ$, and the strong-phase difference $δ_{p}-δ_{s}$ for $Λ$-$π^-$ scattering are measured to be consistent with previous BESIII results.