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Based on a data sample of $(10087\pm44)\times10^6$ $J/\psi$ events collectedwith the BESIII detector, the branching fraction of$J/\psi\rightarrow\bar{\Lambda}\pi^{+}\Sigma^{-}+c.c.$ is measured to be$(1.221\pm 0.002\pm 0.038)\times10^{-3}$, and the branching fraction of itsisospin partner mode $J/\psi\rightarrow\bar{\Lambda}\pi^{-}\Sigma^{+}+c.c.$ ismeasured to be $(1.244\pm 0.002\pm 0.045)\times10^{-3}$ with improvedprecision. Here the first uncertainties are statistical and the second onessystematic. The isospin symmetry of the $\Sigma$ baryon in charmonium hadronicdecay and the "$12\%$ rule" are tested, and no violation is found. Thepotential of using these channels as $\Sigma$ baryon sources for nuclearphysics research is studied, and the momentum and angular distributions ofthese sources are provided.

physical review. d/physical review. d.

Precise measurement of the branching fractions of  $J/\psi\rightarrow\bar{\Lambda}\pi^{+}\Sigma^{-}+c.c.$ and  $J/\psi\rightarrow\bar{\Lambda}\pi^{-}\Sigma^{+}+c.c.$