Measurement of the $K_S \to \pi e \nu$ branching fraction with the KLOE experiment

The branching fraction for the decay $K_S \to \pi e \nu$ has been measured with 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. Signal decays are selected by a boosted decision tree built with kinematic variables and time-of-flight measurements. Data control samples of $K_L \to \pi e \nu$ decays are used to evaluate signal selection efficiencies. A fit to the reconstructed electron mass distribution finds 49647$\pm$316 signal events. Normalising to the $K_S \to \pi^+\pi^-$ decay events the result for the branching fraction is $\mathcal{B}(K_S \to \pi e \nu) = (7.211 \pm 0.046_{\rm stat} \pm 0.052_{\rm syst}) \times10^{-4}$. The combination with our previous measurement gives $\mathcal{B}(K_S \to \pi e \nu) = (7.153 \pm 0.037_{\rm stat} \pm 0.043_{\rm syst}) \times10^{-4}$. From this value we derive $f_+(0)|V_{us}| = 0.2170 \pm 0.009$.