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$\mathrm{\Phi }$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 $\mathcal{B}(K_S\to \pi e\nu )=(7.211\pm {0.046}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.052}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\times {10}^{-4}$. The combination with our previous measurement gives $\mathcal{B}(K_S\to \pi e\nu )=(7.153\pm {0.037}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.043}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\times {10}^{-4}$. From this value we derive $f_{+}(0)\mathrm{\mid }{V}_{us}\mathrm{\mid }=0.2170\pm 0.009$.