Projections of H$\rightarrow \tau \tau $ cross-section at FCC-ee

The Future Circular Collider (FCC) stands at the forefront of the European Strategy for Particle Physics as the future flagship project at CERN. The H$\rightarrow \tau \tau $ decay, featuring a large branching ratio, clean identification in the FCC-ee environment, and the possibility to reconstruct tau spin-related observables, is an excellent channel to measure Higgs boson properties. This work shows the expected precision for the H$\rightarrow \tau \tau $ cross-section measurement at the FCC-ee in the ZH production mechanism at $\sqrt{s}$ 240 GeV and $\sqrt{s}$ 365 GeV, as well as via the vector boson fusion process at $\sqrt{s}$ 365 GeV. Furthermore, we explore and evaluate a set of methods for reconstructing tau decays. These techniques are critical for unlocking the full physics potential of the FCC-ee and for improving the understanding of tau-related observables in both Standard Model measurements and New Physics searches. The obtained results significantly enhance the FCC-ee outlook in the H$\rightarrow \tau \tau $ channel, improving it by at least an order of magnitude compared to the current uncertainties on the cross-sections measured at the LHC.