\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 in the search for rare decays and their theoretical interpretation.  