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

TL;DR

This study precisely measured the ratio of muonic to electronic decay widths of stopped positive kaons, testing lepton universality and determining form factor parameters with high statistical accuracy.

Contribution

The paper provides a new, precise measurement of the $rac{ ext{Gamma}(K_{ ext{mu3}}^+)}{ ext{Gamma}(K_{e3}^+)}$ ratio and the $q^2$ dependence of the $f_0$ form factor, using stopped kaons and Monte Carlo simulations.

Findings

Measured $rac{ ext{Gamma}(K_{ ext{mu3}}^+)}{ ext{Gamma}(K_{e3}^+)}$ as 0.671±0.007(stat)±0.008(syst)

Determined $ ext{lambda}_0$ as 0.022±0.005(stat)±0.004(syst)

Confirmed lepton universality in $K_{l3}^+$ decays

Abstract

The ratio of the $K^{+}\to \pi^{0} \mu^{+} \nu$ ($K_{\mu3}^+$) 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. $K_{\mu3}^+$ and $K_{e3}^+$ samples containing 2.4$\times 10^4$ and 4.0$\times 10^4$ events, respectively, were analyzed. The $\Gamma(K_{\mu3})/\Gamma(K_{e3})$ 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.).