Search for the rare decay $etarightarrowpi^{0}pi^{0}pi^{0}pi^{0}$ at BESIII

Based on a sample of 1.31 billion $J/psi$ events collected with the BESIII detector, we perform a search for the rare decay $etarightarrow 4pi^{0}$ via $J/psirightarrowgammaeta$. No significant $eta$ signal is observed in the invariant mass spectrum of 4$pi^{0}$. With a Bayesian approach, the upper limit on the branching fraction of $etarightarrow 4pi^{0}$ is determined to be $mathcal{B}(etarightarrow 4pi^{0})$ $< 4.94times10^{-5}$ at the 90% confidence level, which is a factor of six smaller than the previous experimental limit.