Prospects for $B_{c}^+\to \tau^+ \nu_\tau$ at FCC-ee

This paper presents the prospects for a precise measurement of the branching fraction of the leptonic $ {B}_c^{+} $→ τ$^{+}$ν$_{τ}$ decay at the Future Circular Collider (FCC-ee) running at the Z -pole. A detailed description of the simulation and analysis framework is provided. To select signal candidates, two Boosted Decision Tree algorithms are employed and optimised. The first stage suppresses inclusive $ b\overline{b} $, $ c\overline{c} $, and $ q\overline{q} $ backgrounds using event-based topological information. A second stage utilises the properties of the hadronic τ$^{+}$→ π$^{+}$π$^{+}$π$^{−} \overline{\nu} _{τ}$ decay to further suppress these backgrounds, and is also found to achieve high rejection for the B$^{+}$→ τ$^{+}$ν$_{τ}$ background. The number of $ {B}_c^{+} $→ τ$^{+}$ν$_{τ}$ candidates is estimated for various Tera-Z scenarios, and the potential precision of signal yield and branching fraction measurements evaluated. The phenomenological impact of such measurements on various New Physics scenarios is also explored.