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 CP violation, study of such rare decays as Kl-+Tr°e + e~, K®-• 7r°/z + jL4~, K^-^rfivv, and muon polarization in K®->/j,~hfi~ can provide important complementary information to what has been learned from the decay K^-^rnr.Even though experiments with sufficient accuracy to make a meaningful study of 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® -+fie and K + ->TT + pi + e~.Various extensions of the Standard Model predict that these processes will occur with branching fractions in the range of 10~1 0 to 10~1 5 . Experiments of the last decade have pushed the limits into the 10 -10 to 10 -11 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 A^J-•^+/z~~, K®->e + e~, K + ->7r + vv, 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 td , one of the elements of the weak mixing matrix in the quark sector. The studies of the I*I + JJ>~ 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.
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