Evidence of transverse polarization of ${\mathrm{\Xi }}^0$ hyperon in $\psi (3686)\to {\mathrm{\Xi }}^0{\bar{\mathrm{\Xi }}}^0$

Using $(2.712\pm 0.014)\times {10}^9$ $\psi (3686)$ events collected with the BESIII detector at the BEPCII collider, we report an evidence of ${\mathrm{\Xi }}^0$ transverse polarization with a significance of 4.4$\sigma$, a precise measurement of the branching fraction and the ratios between the $S$-wave and $D$-wave contributions of $\psi (3686)\to {\mathrm{\Xi }}^0{\bar{\mathrm{\Xi }}}^0$. The weak decay parameters (${\phi }_{{\mathrm{\Xi }}^0\mathrm{/}{\bar{\mathrm{\Xi }}}^0}$, ${\alpha }_{{\mathrm{\Xi }}^0\mathrm{/}{\bar{\mathrm{\Xi }}}^0}$) and the angular distribution (${\alpha }_{\psi }$) are also measured with higher precision compared to the previous measurements. Furthermore, two the $CP$ observables are also determined to be $A_{CP}^{{\mathrm{\Xi }}^0}=-0.014\pm 0.030\pm 0.010$ and $\mathrm{\Delta }{\phi }_{CP}^{{\mathrm{\Xi }}^0}=0.000\pm 0.028\pm 0.003$~rad, which are still consistent with $CP$ conservation at 1$\sigma$ level under the current statistics.