Measurement of $\Gamma (K_{\mu 3})/\Gamma (K_{e3})$ ratio using stopped positive kaons

Abstract

The ratio of the $K^{+}\to {\pi }^0{\mu }^{+}\nu$ ($K_{\mu 3}^{+}$) and $K^{+}\to {\pi }^0{e}^{+}\nu$ ($K_{e3}^{+}$) decay widths, $\Gamma (K_{\mu 3})/\Gamma (K_{e3})$, has been measured with stopped positive kaons. $K_{\mu 3}^{+}$ and $K_{e3}^{+}$ samples containing 2.4$\times 10^4$ and 4.0$\times 10^4$ events, respectively, were analyzed. The $\Gamma (K_{\mu 3})/\Gamma (K_{e3})$ ratio was obtained to be 0.671$\pm$0.007(stat.)$\pm$0.008(syst.) calculating the detector acceptance by a Monte Carlo simulation with the assumption of $\mu$-$e$ universality in $K_{l3}^{+}$ decay. The coefficient of the $q^2$ dependent term of the $f_0$ form factor was also determined to be ${\lambda }_0$=0.022$\pm$0.005(stat.)$\pm$0.004(syst.).

12 pages, 6 figures

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