  A search for invisible decays of the $\Lambda$ baryon is carried out in the
process $J/\psi\to\Lambda\bar{\Lambda}$ based on
$(1.0087\pm0.0044)\times10^{10}$ $J/\psi$ events collected with the BESIII
detector located at the BEPCII storage ring. No signals are found for the
invisible decays of $\Lambda$ baryon, and the upper limit of the branching
fraction is determined to be $7.4 \times 10^{-5}$ at the 90% confidence level.
This is the first search for invisible decays of baryons; such searches will
play an important role in constraining dark sector models related to the baryon
asymmetry.
