Measurement of $\psi \left(3686\right)\to \Lambda \overline{\Lambda }\eta $ and $\psi \left(3686\right)\to \Lambda \overline{\Lambda }{\pi }^{0}$ decays

Based on a sample of $448.1×{10}^{6}\psi \left(3686\right)$ events collected with the BESIII detector, a study of $\psi \left(3686\right)\to \Lambda \overline{\Lambda }{\pi }^{0}$ and $\psi \left(3686\right)\to \Lambda \overline{\Lambda }\eta $ is performed. Evidence of the isospin-violating decay $\psi \left(3686\right)\to \Lambda \overline{\Lambda }{\pi }^{0}$ is found for the first time with a statistical significance of $3.7\sigma $, the branching fraction $B\left(\psi \left(3686\right)\to \Lambda \overline{\Lambda }{\pi }^{0}\right)$ is measured to be $\left(1.42±0.39±0.59\right)×{10}^{-6}$, and its corresponding upper limit is determined to be $2.47×{10}^{-6}$ at 90% confidence level. A partial wave analysis of $\psi \left(3686\right)\to \Lambda \overline{\Lambda }\eta $ shows that the peak around $\Lambda \eta $ invariant mass threshold favors a ${\Lambda }^{*}$ resonance with mass and width in agreement with the $\Lambda \left(1670\right)$. The branching fraction of the $\psi \left(3686\right)\to \Lambda \overline{\Lambda }\eta $ is measured to be $\left(2.34±0.18±0.52\right)×{10}^{-5}$. The first uncertainties are statistical and the second are systematic.