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Rare muon- and pion-decay modes

Two kinds of processes must be distinguished: a) processes with a finite rate where precision experiments try to measure small deviations from the prediction of the Standard Model, b) processes which are absolutely forbidden within the Standard Model. Experimentally the latter have essential advantages: i) there is no Standard Model background. Therefore, if other backgrounds can be avoided the sensitivity improves linearly (not by square root) with measuring time, ii) there is no need for a very accurate absolute calibration. High particle fluxes at intermediate energies can be obtained at so-called particle factories (meson [pion]-, B-meson-, $\tau$-lepton factories). Especially at pion factories extremely high fluxes of muons are available, which are very useful for rare decay studies because of the following reasons: Presently two new experiments are being discussed, the interest coming from several theoretical papers predicting measurable rates on the basis of supersymmetric grand unification schemes. There is a letter of intent for a new $\mu$-e conversion experiment submitted to BNL which aims to reach a sensitivity of 10-16 and enjoys highest priority ranking. The other experiment is $\mu \rightarrow$ e$\gamma$. The design of a detector largely depends on the outcome of the MEGA experiment at the Los Alamos Meson Factory (LAMPF). The only place where enough muons with sufficient quality are available (>108/s) to obtain a sensitivity of 10-14 is PSI. The interest in pion decays concentrates on pion beta decay. Although other rare pion decays ( $\pi \rightarrow$$\nu \gamma$$\pi \rightarrow$ 3e$\nu$$\pi^{0} \rightarrow e^{+} e^{-}$) also yield valuable information, pion beta decay will eventually improve our knowledge of the Vud matrix element of the CKM matrix. To summarise, we find that rare decays and especially rare muon processes have a great discovery potential for fundamentally new physics. Thanks to progress in accelerator and detector technologies, they also have the possibility of achieving further important improvements in sensitivity. 
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