Observation of a Doubly-strange Hyperon $\mathrm{\Xi }(1720)$ in $J\mathrm{/}\psi \to K^{-}{\mathrm{\Sigma }}^0{\bar{\mathrm{\Xi }}}^{+}+c\mathrm{.}c\mathrm{.}$

Based on a sample of $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events collected with the BESIII detector at BEPCII, we report the first observation of the decay $J\mathrm{/}\psi \to K^{-}{\mathrm{\Sigma }}^0{\bar{\mathrm{\Xi }}}^{+}+c\mathrm{.}c\mathrm{.}$. A partial wave analysis is performed to investigate the involved excited states. In addition to the well-established $\mathrm{\Xi }(1690)$, a new doubly-strange hyperon $\mathrm{\Xi }(1720)$ is observed decaying to $K^{-}{\mathrm{\Sigma }}^0$ with a mass of $1721.0\pm {5.2}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {3.4}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}}\mathrm{M}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$ and a width of $31.3\pm {18.3}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {15.4}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}}\mathrm{M}\mathrm{e}\mathrm{V}$, with a statistical significance exceeding $10\sigma$. The spin-parity hypothesis testing across various quantum number configurations reveals that the spin-parity of $\mathrm{\Xi }(1720)$ favors $J^P={\frac{3}{2}}^{+}$. Furthermore, the branching fraction of $J\mathrm{/}\psi \to K^{-}{\mathrm{\Sigma }}^0{\bar{\mathrm{\Xi }}}^{+}+c\mathrm{.}c\mathrm{.}$ is determined to be $(2.68\pm {0.04}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.17}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\times {10}^{-5}$.