Projections of H$\to\tau\tau$ 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$\to\tau\tau$ decay, featuring a large branching ratio, clean identification in the FCC-ee environment, and the possibility to reconstruct polarization information, is an excellent channel to measure Higgs boson properties. This work shows the expected precision for the H$\to\tau\tau$ 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}=$365 GeV. Furthermore, we explore and evaluate a set of methods for reconstructing tau decays. These techniques are critical for unlocking the full physics potential of the FCC-ee and for improving the understanding of tau-related observables in both Standard Model measurements and New Physics searches. The results obtained significantly enhance the FCC-ee outlook in the H$\to\tau\tau$ channel, improving it by at least an order of magnitude compared to the current sensitivity of measurements' performance at the LHC.