First observation of the isospin violating decay $J/psirightarrow Lambdabar{Sigma}^{0}+c.c.$

Using a sample of $(225.2pm 2.8)times 10^6$ $J/psi$ events collected with the BESIII detector, we present results of a study of $J/psirightarrow gammaLambdabar{Lambda}$ and report the first observation of the isospin violating decay $J/psirightarrowLambdabar{Sigma}^{0}+c.c.$, in which $bar{Sigma}^{0}$ decays to $gamma bar{Lambda}$. The measured branching fractions are $mathcal{B}(J/psirightarrowbar{Lambda}Sigma^{0}$) = $(1.46pm0.11pm0.12) times10^{-5}$ and $mathcal{B}(J/psirightarrowLambdabar{Sigma^{0}}$) = $(1.37pm0.12pm0.11) times10^{-5}$. We search for $Lambda(1520) rightarrow gamma Lambda$ decay, and find no evident signal, and an upper limit for the product branching fraction $mathcal{B}(J/psirightarrowLambdabar{Lambda}(1520)+c.c.)times mathcal{B}(Lambda(1520)rightarrowgammaLambda)<4.1 times10^{-6}$ is set at the 90% confidence level. We also report the observation of $eta_{c}rightarrowLambdabar{Lambda}$ in $J/psi rightarrow gamma eta_{c}$, $eta_{c}rightarrowLambdabar{Lambda}$ and measure the branching fraction $mathcal{B}(eta_{c}rightarrowLambdabar{Lambda}) =(1.16pm0.12 (stat)pm0.19(syst)pm0.28(PDG))times10^{-3}$.