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

Using $(2.712\pm0.014)\times10^{9}$ $\psi(3686)$ events collected with the BESIII detector at the BEPCII collider, we report an evidence of $\Xi^{0}$ 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 $\psi(3686)\to\Xi^{0}\bar\Xi^{0}$. The weak decay parameters ($\phi_{\Xi^0/\bar{\Xi}^{0}}$, $\alpha_{\Xi^0/\bar{\Xi}^{0}}$) 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 $A^{\Xi^0}_{CP} = -0.014 \pm 0.030 \pm 0.010$ and $\Delta\phi^{\Xi^0}_{CP} = 0.000 \pm 0.028 \pm 0.003$~rad, which are still consistent with $CP$ conservation at 1$\sigma$ level under the current statistics.