The $\tau$ challenges at FCC-ee

At FCC-ee, about $1.7 \times 10^{11} Z \rightarrow \tau^+ \tau^-$ events will be produced. This high statistics in the clean ${e}^+{e}^-$ environment opens the possibility of much improved determinations of $\tau$-lepton properties and, via the measurement of the $\uptau $ polarisation, of the neutral-current couplings of electrons and $\tau$s. Improved measurements of $\tau $-lepton properties—lifetime, leptonic branching fractions, and mass—allow important tests of lepton universality. The experimental challenge is to match as far as possible statistical uncertainties generally at the $10^{-5}$ level. This applies in particular to the lifetime measurement, which is derived from the 2.2-mm $\tau$ average flight distance, and for the branching fraction and polarisation measurements, where the cross-channel contamination is of particular concern. These issues raise strict detector requirements, in particular, on the accuracy of the construction and alignment of the vertex detector and of the precise calorimetric separation and measurement of photons and $\pi^0$s in the collimated $\tau$ decay topologies.