Improved limit on the branching fraction of the rare decay ${{K} ^0_{\mathrm { \scriptscriptstyle S}}} \rightarrow \mu ^+\mu ^-$

A search for the decay ${{K} ^0_{\mathrm { \scriptscriptstyle S}}} \rightarrow \mu ^+\mu ^-$ is performed, based on a data sample of proton-proton collisions corresponding to an integrated luminosity of $3\,\text{ fb }^{-1} $ , collected by the LHCb experiment at centre-of-mass energies of 7 and 8 $\mathrm {\,TeV}$ . The observed yield is consistent with the background-only hypothesis, yielding a limit on the branching fraction of $\mathcal{B}({{K} ^0_{\mathrm { \scriptscriptstyle S}}} \rightarrow \mu ^+\mu ^-) < 0.8~(1.0) \times 10^{-9}$ at $90\%~(95\%)$ confidence level. This result improves the previous upper limit on the branching fraction by an order of magnitude.