Rare $K$ decays

This article reviews the current situation in the field of rare $K$ decays: the relevant phenomenology, the present experimental situation, and prospects for the near future. Study of rare $K$ decays can make a significant contribution in a number of different frontier areas of research in high-energy physics. In the area of $\mathrm{CP}$ violation, study of such rare decays as $K_L^0\to {\pi }^0{e}^{+}{e}^{-}$, $K_L^0\to {\pi }^0{\mu }^{+}{\mu }^{-}$, $K_L^0\to {\pi }^0\nu \overline{\nu }$, and muon polarization in $K_L^0\to {\mu }^{+}{\mu }^{-}$ can provide important complementary information to what has been learned from the decay $K_L^0\to \pi \pi$. Even though experiments with sufficient accuracy to make a meaningful study of $\mathrm{CP}$ violation are still a few years away, significant progress has been made in this general area during the last decade. A second major area of interest in the field of rare $K$ decays is the search for processes forbidden in the Standard Model, e.g., $K_L^0\to \mu e$ and $K^{+}\to {\pi }^{+}{\mu }^{+}{e}^{-}$. Various extensions of the Standard Model predict that these processes will occur with branching fractions in the range of ${10}^{-10\mathrm{}}$ to ${10}^{-15\mathrm{}}$. Experiments of the last decade have pushed the limits into the ${10}^{-10\mathrm{}}$ to ${10}^{-11\mathrm{}}$ range, and further improvements in sensitivity of one to two orders of magnitude can be expected in the next few years. $K$ decays allow one also to study higher-order weak-interaction processes such as $K_L^0\to {\mu }^{+}{\mu }^{-}$, $K_L^0\to e^{+}{e}^{-}$, $K^{+}\to {\pi }^{+}\nu \overline{\nu }$, which are forbidden to first order in the Standard Model. Because of strong suppression, these decay modes offer potential windows on new physics; in addition, they may offer the most reliable measurement of $V_{\mathrm{td}}$, one of the elements of the weak mixing matrix in the quark sector. The studies of the ${\mu }^{+}{\mu }^{-}$ channel have achieved data samples of close to 1000 events; the other two modes should be observed for the first time in the next few years. Finally, as a byproduct of these studies, one has been able to look simultaneously for new light particles into which the $K$ meson could decay. Limits obtained for various hypothetical particles are summarized.