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# Rare kaon decays and CP violation

Abstract (Summary)
Rare kaon decays are an important testing ground of the electroweak flavor theory. They can provide new signals of CP-violating phenomena and open a window into physics beyond the Standard Model. The interplay of long-distance QCD effects in strangeness-changing transitions can be analyzed with Chiral Perturbation Theory techniques. Some theoretical predictions obtained within this framework for radiative kaon decays are reviewed, together with the present experimental status. In particular, two rare kaon decays are analyzed: the first decay, $K\sb{L} \to \pi\sp0 e\sp+ e\sp-$, is being searched for as a signal of direct $\Delta S$ = 1 CP violation. We provide a thorough updating of the analysis of the three components of the decay: (1) direct CP violation, (2) CP violation through the mass matrix and (3) CP-conserving (two-photon) contributions. First the chiral calculation of the $K\sb{S} \to \pi\sp0 e\sp+ e\sp-$ rate, due to Ecker, Pich and de Rafael, is updated to include recent results on the nonleptonic amplitude. Then we systematically explore the uncertainties in this method. These appear to be so large that they will obscure the direct CP violation unless it is possible to measure the $K\sb{S} \to \pi\sp0 e\sp+ e\sp-$ rate. The CP-conserving amplitude remains somewhat uncertain, but present indications are such that there may be a sizable CP-violating asymmetry in the $e\sp+, e\sp-$ energies from the interference of CP-conserving and CP-violating amplitudes and this may potentially be useful in determining whether direct CP violation is present. The second decay, $K\sb{L} \to \pi\sp0\gamma e\sp+ e\sp-$, which occurs at a higher rate than the nonradiative process $K\sb{L} \to \pi\sp0 e\sp+e\sp-$ can be a background to CP violation studies using the latter reaction. It also has interest in its own right in the context of chiral perturbation theory, through its relation to the decay $K\sb{L} \to \pi\sp0\gamma\gamma$. The leading order chiral loop contribution to $K\sb{L} \to \pi\sp0\gamma e\sp+ e\sp-$, including the $(q\sb{e\sp+} + q\sb{e\sp-})\sp2/m\sbsp{\pi}{2}$ dependence, is completely calculable. We present this result and also include the higher order modifications that are required in the analysis of $K\sb{L} \to \pi\sp0\gamma\gamma$.
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