Observation of ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{a}_0(980{)}^{+}$ and Evidence for $\mathrm{\Sigma }(1380{)}^{+}$ in ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}\eta$

Based on $6.1{\mathrm{f}\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at center-of-mass energies from 4.600 to 4.843 GeV with the BESIII detector at the BEPCII collider, a partial wave analysis of ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}\eta$ is performed, and branching fractions and decay asymmetry parameters of intermediate processes are determined. The process ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{a}_0(980{)}^{+}$ is observed for the first time, and evidence for the pentaquark candidate $\mathrm{\Sigma }(1380{)}^{+}$ decaying into $\mathrm{\Lambda }{\pi }^{+}$ is found with statistical significance larger than $3\sigma$ with mass and width fixed to theoretical predictions. The branching fraction product $\mathcal{B}[{\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{a}_0(980{)}^{+}]\mathcal{B}[a_0(980{)}^{+}\to {\pi }^{+}\eta ]$ is determined to be $(1.05\pm {0.16}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.05}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.07}_{\mathrm{e}\mathrm{x}\mathrm{t}})\mathrm{\%}$, which is larger than theoretical calculations by 1-2 orders of magnitude. Here the third (external) systematic is from $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}\eta )$. Finally, we precisely obtain the absolute branching fraction $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}\eta )=(1.94\pm {0.07}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.11}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\mathrm{\%}$.