Observation of ${\chi }_{c0}\to {\mathrm{\Sigma }}^{+}{\bar{\mathrm{\Sigma }}}^{-}\eta$ and evidence for ${\chi }_{c1,2}\to {\mathrm{\Sigma }}^{+}{\bar{\mathrm{\Sigma }}}^{-}\eta$

Using $(27.12\pm 0.14)\times {10}^8$ $\psi (3686)$ events collected with the BESIII detector, the decay ${\chi }_{c0}\to {\mathrm{\Sigma }}^{+}{\bar{\mathrm{\Sigma }}}^{-}\eta$ is observed for the first time with a statistical significance of $7.0\sigma$, and evidence for ${\chi }_{c1}\to {\mathrm{\Sigma }}^{+}{\bar{\mathrm{\Sigma }}}^{-}\eta$ and ${\chi }_{c2}\to {\mathrm{\Sigma }}^{+}{\bar{\mathrm{\Sigma }}}^{-}\eta$ is found with statistical significances of $4.3\sigma$ and $4.6\sigma$, respectively. The branching fractions are determined to be $\mathcal{B}({\chi }_{c0}\to {\mathrm{\Sigma }}^{+}{\bar{\mathrm{\Sigma }}}^{-}\eta )=(1.26\pm 0.20\pm 0.13)\times {10}^{-4},\mathcal{B}({\chi }_{c1}\to {\mathrm{\Sigma }}^{+}{\bar{\mathrm{\Sigma }}}^{-}\eta )=(5.10\pm 1.21\pm 0.67)\times {10}^{-5}$, and $\mathcal{B}({\chi }_{c2}\to {\mathrm{\Sigma }}^{+}{\bar{\mathrm{\Sigma }}}^{-}\eta )=(5.46\pm 1.18\pm 0.50)\times {10}^{-5}$, where the first uncertainties are statistical, and the second ones are systematic.