A search for $K_{\mathrm{S}(\mathrm{L})}^0\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ decays is performed using proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of $5.1{\mathrm{fb}}^{-1}$. No evidence for signal is found. The 90% confidence level upper limits are the first set for both decays and are $\mathcal{B}(K_{\mathrm{S}}^0\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-})<5.1\times {10}^{-12}$ and $\mathcal{B}(K_{\mathrm{L}}^0\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-})<2.3\times {10}^{-9}$.

• Received 22 December 2022
• Accepted 23 January 2023

DOI:https://doi.org/10.1103/PhysRevD.108.L031102

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