Search for sub-GeV dark particles in $η\toπ^0+\rm{invisible}$ decay

Using (10087$\pm$44)$\times$10$^{6}$ $J/ψ$ events collected with the BESIII detector at the BEPCII collider at the center-of-mass energy of $\sqrt{s}=3.097~\rm{GeV}$, we report the first search for $η\toπ^0S\toπ^0χ\barχ$ with $S$ denotes an on-shell dark scalar boson and $χ$ an invisible dark matter particle. No significant signals are observed with $S$ mass ranging from 0 to 400 $\rm{MeV}/c^2$. The upper limits on the branching fractions and the new physics coupling strengths between $S$ and quarks are set to be $(1.8\sim5.5)\times10^{-5}$ and $(1.3\sim3.2)\times10^{-5}$ at the 90% confidence level, respectively. The constraints on the dark-matter-nucleon scattering cross section is improved by approximately 5 orders of magnitude over previous dark-matter-nucleon scattering experiments, providing unique insights into sub-GeV dark matter.