Measurement of theKL0form factors fromKL0→πμνdecays in the 12-foot bubble chamber

We report results of a measurement of the form factors in $K_L^0$ leptonic decay. We analyze both the Dalitz plot of the decay $K_L^0\to \pi \mu \nu$ and the branching ratio $\frac{\Gamma \left(K_{\mu }^0\right)}{\Gamma \left(K_{e3\mathrm{}}^0\right)}$. The experiment was performed in the Argonne 12-foot bubble chamber exposed to a monoenergetic $K_L^0$ beam. Simultaneous detection of $\pi \mu \nu$ and $\pi e\nu$ decays with large acceptance results in well understood systematic uncertainties. The results have been analyzed to give ${\lambda }_{+}$ and ${\lambda }_0$, the expansion parameters of the form factors dominated by $1^{-}$ and $0^{+}$ $K^{*}$ poles, respectively. From our branching-ratio measurement of $\frac{\Gamma \left(K_{\mu 3}^0\right)}{\Gamma \left(K_{e3\mathrm{}}^0\right)}=0.702\mathrm{}\pm 0.011$, we obtain ${\lambda }_0=0.041\mathrm{}\pm 0.008$. A fit to the $K_{\mu 3}^0$ Dalitz-plot density distribution gives ${\lambda }_0=0.050\mathrm{}\pm 0.008$ and ${\lambda }_{+}=0.028\mathrm{}\pm 0.010$. These numbers are in agreement with our analysis of the $K_{e3\mathrm{}}^0$ decay Dalitz plot and with other recent measurements. A combined fit to all of our data yields ${\lambda }_{+}=0.028\mathrm{}\pm 0.007$ and ${\lambda }_0=0.046\mathrm{}\pm 0.006$.