Experimental Study of the DecayKL0→π+e+ν

A wide-gap magnetic-field spark chamber spectrometer has been used to measure the pion-energy dependence of the form factor $f_{+}$ in $K_L^{}{}_{}{}^0\to {\pi }^{\pm }+e^{\mp }+{\nu }_e$ decay ($K_{e3\mathrm{}}^{}{}_{}{}^0$). Decays of neutral particles were detected in the 13° beam of the Princeton-Pennsylvania Accelerator, and $K_{e3\mathrm{}}^{}{}_{}{}^0$ decays were identified by kinematical reconstruction, time-of-flight, and by electromagnetic showers in Cerenkov shower counters. The distribution of events according to their pion energy in the $K_L^{}{}_{}{}^0$ rest frame was used to determine the energy-dependence parameter $\lambda$ in the form factor $f_{+}\left(q^2\right)=f_{+}\mathrm{}\left(0\right)(1+\frac{\lambda q^2}{m_{\pi }^{}{}_{}{}^2})$, where $q^2=M_K^{}{}_{}{}^2+m_{\pi }^{}{}_{}{}^2-2\mathrm{}{E}_{\pi }{M}_K$. Based on a comparison of the data with the distribution of a Monte Carlo sample of events generated with constant form factor, $\lambda$ was determined to be $\lambda =+0.020\mathrm{}\pm 0.013$. The data are consistent with the single-particle-dominance model, where the intermediate state is the $K^{*}\mathrm{}\left(890\right)\mathrm{}$. The results, taken together with the value of $\lambda$ in $K_{e3\mathrm{}}^{}{}_{}{}^{+}$ decay are consistent with the predictions of the $\left|\Delta \mathbf{I}\right|=\frac{1}{2}$ rule in semileptonic decays.