Amplitude analysis and branching fraction measurement of $J\mathrm{/}\psi \to \mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0\eta +\mathrm{c}\mathrm{.}\mathrm{c}$

Based on a sample of $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events collected with the BESIII detector, a partial-wave analysis of $J\mathrm{/}\psi \to \mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0\eta +\mathrm{c}\mathrm{.}\mathrm{c}$ is performed for the first time. The dominant contributions are found to be excited $\mathrm{\Lambda }$ states with $J^P=1\mathrm{/}{2}^{-}$ and $J^P=1\mathrm{/}{2}^{+}$ in the $\eta \mathrm{\Lambda }$ mass spectra. The measured masses and widths are $M=1668.8\pm 3.1\pm 21.2$ MeV/$c^2$ and $\mathrm{\Gamma }=52.7\pm 4.2\pm 17.8$ MeV for the $\mathrm{\Lambda }(1670)$, and $M=1881.5\pm 16.5\pm 20.3$ MeV/$c^2$ and $\mathrm{\Gamma }=82.4\pm 18.2\pm 8.9$ MeV for the $\mathrm{\Lambda }(1810)$, respectively. The branching fraction is determined to be $\mathcal{B}(J\mathrm{/}\psi \to \mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0\eta +\mathrm{c}\mathrm{.}\mathrm{c})$ = $(3.44\pm 0.11\pm 0.13)\times {10}^{-5}$. The first uncertainties are statistical and the second systematic.