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

A search for the decay $K^0_{scriptscriptstyle S}tomu^+mu^-$ 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 ${cal B}(K^0_{scriptscriptstyle S}tomu^+mu^-) < 0.8~(1.0) times 10^{-9}$ at $90%~(95%)$ confidence level. This result improves the previous upper limit on the branching fraction by an order of magnitude.