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\subsubsection{Rare decays}  The very large statistics accumulated at TLEP, including $3 \times 10^{10}$ tau pairs or muon pairs, and more than $2 \times 10^{11}$ b quarks or c quarks, should allow a new range of searches for rare phenomena and tests of conservation laws that remain to be investigated. As an illustration, more than 20,000 ${\rm B_s \to \tau^+\tau^-}$ decays would be produced, according to the Standard Model prediction: the few thousand events observed will bring stringent constraints on new physics, which may change this branching fraction by large factors. It will also be possible to probe small flavour-changing-neutral-current couplings of the Z to quarks and leptons with very high accuracy. (Flavour-changing-neutral-current couplings of the top quark can also be probed both in production and in decays by running at the $\ttbar$ threshold and above.) It will be the purpose of the upcoming design study to examine and develop further the immense physics potential of TLEP-Z. TLEP in the search for rare decays and their theoretical interpretation.