Measurement of $K_{e3}^{0}$ form factors

The semi-leptonic decay of the neutral K meson $K^{0}_{L} \to \pi^{\pm}e^{\mp}\nu (K_{e3})$, was used to study the strangeness-changing weak interaction of hadrons. A sample of 5.6 million reconstructed events recorded by the NA48 experiment was used to measure the Dalitz plot density. Admitting all possible Lorentz-covariant couplings, the form factors for vector $(f_{+}(q^{2}))$, scalar $(f_{S})$ and tensor $(f_{T})$ interactions were measured. The linear slope of the vector form factor $\lambda_{+} = 0.0284 \pm 0.0007 \pm 0.0013$ and values for the ratios $|f_{S}/f_{+}(0)|=0.015^{+0.007}_{-0.010} \pm 0.012$ and $|f_{T}/f_{+}(0)|=0.05^{+0.03}_{-0.04} \pm 0.03$ were obtained. The values for $f_{S}$ and for $f_{T}$ are consistent with zero. Assuming only vector-axial vector couplings, $\lambda_{+} = 0.02888 \pm 0.0004 \pm 0.0011$ and a good fit consistent with pure V-A couplings were obtained. Alternatively a fit to a dipole form factor yields a pole mass of $M = 859 \pm 18$ MeV, consistent with the $K^{*}(892)$ mass.