New Results on Rare and Forbidden Semileptonic $K^{+}$ Decays

Abstract

Experiment E865 at the Brookhaven AGS was set up primarily to search for the lepton flavour violating decay $K^{+}\to {\pi }^{+}{\mu }^{+}{e}^{-}$ ($K_{\pi \mu e}$) with high sensitivity. The flexibility of the apparatus allowed also to obtain more than an order of magnitude larger than previously available event samples on the following decay modes: ${\pi }^{+}{e}^{+}{e}^{-}(K_{\pi ee})$, ${\pi }^{+}{\mu }^{+}{\mu }^{-}(K_{\pi \mu \mu })$, ${\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e(K_{e4})$, ${\mu }^{+}{e}^{+}{e}^{-}{\nu }_{\mu }$, and $e^{+}{e}^{+}{e}^{-}{\nu }_e$. The report focusses on the $K_{\pi \mu e}$ results and those on other lepton flavour violating decays as well as the $K_{e4}$ data, from which a new, quite precise value for the s-wave $\pi \pi$ scattering length can be deduced.

15 pages, 6 figures