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

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