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

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 ${\mathrm{\Xi }}^{-}$ transverse polarization with a significance of $7.3\sigma$ in the decay $\psi (3686)\to {\mathrm{\Xi }}^{-}{\bar{\mathrm{\Xi }}}^{+}$ (${\mathrm{\Xi }}^{-}\to {\pi }^{-}\mathrm{\Lambda }$, ${\bar{\mathrm{\Xi }}}^{+}\to {\pi }^{+}\bar{\mathrm{\Lambda }}$, $\mathrm{\Lambda }\to p{\pi }^{-}$, $\bar{\mathrm{\Lambda }}\to \bar{p}{\pi }^{+}$). The relative phase of the electric and magnetic form factors is determined to be $\mathrm{\Delta }\mathrm{\Phi }=(0.667\pm 0.111\pm 0.058)$ rad. This is the first measurement of the relative phase for a $\psi (3686)$ decay into a pair of ${\mathrm{\Xi }}^{-}{\bar{\mathrm{\Xi }}}^{+}$ hyperons. The ${\mathrm{\Xi }}^{-}$ decay parameters (${\alpha }_{{\mathrm{\Xi }}^{-}}$, ${\phi }_{{\mathrm{\Xi }}^{-}}$) and their conjugates (${\alpha }_{{\bar{\mathrm{\Xi }}}^{+}}$, ${\phi }_{{\bar{\mathrm{\Xi }}}^{+}}$), the angular-distribution parameter ${\alpha }_{\psi }$, and the strong-phase difference ${\delta }_p-{\delta }_s$ for $\mathrm{\Lambda }$-${\pi }^{-}$ scattering are measured to be consistent with previous BESIII results.