Measurement of the branching ratio of the deca $K_{L} \to \pi^{\pm}e^{\mp}\nu$ and extraction of the CKM parameter $|V_{us}|$

We present a new measurement of the branching ratio $R$ of the decay $K_{L} \to \pi^{\pm}e^{\mp}\nu$, denoted as $K_{e3}$, relative to all charged $K_{L}$ decays with two tracks, based on data taken with the NA48 detector at the CERN SPS. We measure $R=0.4978 \pm 0.0035$. From this we derive the $K_{e3}$ branching fraction and the weak coupling parameter $|V_{us}|$ in the CKM matrix. We obtain $|V_{us}| f_{+}(0) = 0.2146 \pm 0.0016$, where $f_{+}(0)$ is the vector form factor in the $K_{e3}$ decay.