Search for the isospin-violating decays and

Using a sample of $(2712.4\pm 14.3)\times {10}^6$~$\psi (3686)$ events collected with the BESIII detector, we perform a search for the isospin-violating decays ${\chi }_{cJ}\to \mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0+c\mathrm{.}c\mathrm{.}(J=0,1,2)$ and ${\eta }_c\to \mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0+c\mathrm{.}c\mathrm{.}$ No significant signal for ${\chi }_{cJ}$ or ${\eta }_c$ is observed in the $\mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0$ invariant mass distribution. The upper limits on the branching fractions at the 90% confidence level are set to be $\mathcal{B}$(${\chi }_{c0}\to \mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0+c\mathrm{.}c\mathrm{.}$)$<1.5\times {10}^{-6}$, $\mathcal{B}$(${\chi }_{c1}\to \mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0+c\mathrm{.}c\mathrm{.}$)$<1.6\times {10}^{-6}$, $\mathcal{B}$(${\chi }_{c2}\to \mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0+c\mathrm{.}c\mathrm{.}$)$<1.7\times {10}^{-6}$ and $\mathcal{B}$(${\eta }_c\to \mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0+c\mathrm{.}c\mathrm{.}$)$<6.2\times {10}^{-5}$ for the first time.