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The NA62 experiment at the CERN SPS reports a study of a sample of $4\times10^{9}$ tagged $\pi^0$ mesons from $K^+ \to \pi^+ \pi^0 (\gamma)$,searching for the decay of the $\pi^0$ to invisible particles. No signal isobserved in excess of the expected background fluctuations. An upper limit of$4.4 \times10^{-9}$ is set on the branching ratio at 90% confidence level,improving on previous results by a factor of 60. This result can also beinterpreted as a model-independent upper limit on the branching ratio for thedecay $K^+ \to \pi^+ X$, where $X$ is a particle escaping detection with massin the range 0.110-0.155 GeV$/c^2$ and rest lifetime greater than 100 ps.Model-dependent upper limits are obtained assuming $X$ to be an axion-likeparticle with dominant fermion couplings or a dark scalar mixing with theStandard Model Higgs boson.

Search for $\pi^0$ decays to invisible particles