Measurement of the branching fraction for the decay $K_S to pi mu u$ with the KLOE detector

Based on a sample of 300 million $K_S$ mesons produced in $phi to K_L K_S$ decays recorded by the KLOE experiment at the DA$Phi$NE $e^+e^-$ collider we have measured the branching fraction for the decay $K_S to pi mu u$. The $K_S$ mesons are identified by the interaction of $K_L$ mesons in the detector. The $K_S to pi mu u$ 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 $K_L to pi mu u$ decays. A fit to the reconstructed muon mass distribution finds $7223 pm 180$ signal events. Normalising to the $K_S to pi^+ pi^-$ decay events the result for the branching fraction is $mathcal{B}(K_S to pi mu u) = (4.56 pm 0.11_{rm stat} pm 0.17_{rm syst})times10^{-4}$.