Measurement of the branching fraction for the decay $K_S \to πμν$ with the KLOE detector

Based on a sample of 300 million $K_S$ mesons produced in $φ\to K_L K_S$ decays recorded by the KLOE experiment at the DA$Φ$NE $e^+e^-$ collider we have measured the branching fraction for the decay $K_S \to πμν$. The $K_S$ mesons are identified by the interaction of $K_L$ mesons in the detector. The $K_S \to πμν$ decays are selected by a boosted decision tree built with kinematic variables and by a time-of-flight measurement. Signal efficiencies are evaluated with data control samples of $K_L \to πμν$ decays. A fit to the reconstructed muon mass distribution finds $7223 \pm 180$ signal events. Normalising to the $K_S \to π^+ π^-$ decay events the result for the branching fraction is $\mathcal{B}(K_S \to πμν) = (4.56 \pm 0.11_{\rm stat} \pm 0.17_{\rm syst})\times10^{-4}$.