Observation of $\Xi^{-}$ Hyperon Transverse Polarization in $\psi(3686)\rightarrow\Xi^{-}\bar\Xi^{+}$

Using a sample of $(448.1~\pm~2.9)$ $\times 10^{6}$ $\psi(3686)$ 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 $\psi(3686)\rightarrow\Xi^{-}\bar\Xi^{+}$ ($\Xi^{-}\rightarrow\pi^{-}\Lambda$, $\bar\Xi^{+}\rightarrow\pi^{+}\bar\Lambda$, $\Lambda\to p\pi^{-}$, $\bar\Lambda\to\bar{p}\pi^{+}$). The relative phase of the electric and magnetic form factors is determined to be $\Delta\Phi = (0.667 \pm 0.111 \pm 0.058)$ rad. This is the first measurement of the relative phase for a $\psi(3686)$ decay into a pair of $\Xi^{-}\bar\Xi^{+}$ hyperons. The $\Xi^{-}$ decay parameters ($\alpha_{\Xi^{-}}$, $\phi_{\Xi^-}$) and their conjugates ($\alpha_{\bar\Xi^{+}}$, $\phi_{\bar{\Xi}^{+}}$), 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.