Observation of ${\Xi }^{-}$ hyperon transverse polarization in $\psi \left(3686\right)\to {\Xi }^{-}{\overline{\Xi }}^{+}$

Using a sample of $\left(448.1±2.9\right)×{10}^{6}\text{}\text{}\psi \left(3686\right)$ decays collected with the BESIII detector at BEPCII, we report an observation of ${\Xi }^{-}$ transverse polarization with a significance of $7.3\sigma $ in the decay $\psi \left(3686\right)\to {\Xi }^{-}{\overline{\Xi }}^{+}$ (${\Xi }^{-}\to \Lambda {\pi }^{-}$, ${\overline{\Xi }}^{+}\to \overline{\Lambda }{\pi }^{+}$, $\Lambda \to p{\pi }^{-}$, $\overline{\Lambda }\to \overline{p}{\pi }^{+}$). The relative phase of the electric and magnetic form factors is determined to be $\Delta \Phi =\left(0.667±0.111±0.058\right)\text{}\text{}\mathrm{rad}$. This is the first measurement of the relative phase for a $\psi \left(3686\right)$ decay into a pair of ${\Xi }^{-}{\overline{\Xi }}^{+}$ hyperons. The ${\Xi }^{-}$ decay parameters (${\alpha }_{{\Xi }^{-}}$, ${\varphi }_{{\Xi }^{-}}$) and their conjugates (${\alpha }_{{\overline{\Xi }}^{+}}$, ${\varphi }_{{\overline{\Xi }}^{+}}$), the angular-distribution parameter ${\alpha }_{\psi }$, and the strong-phase difference ${\delta }_{p}-{\delta }_{s}$ for $\Lambda {\pi }^{-}$ scattering are measured to be consistent with previous BESIII results.