This paper presents the prospects for a precise measurement of the branching fraction of the leptonic $B_{ c}^+\to \tau^+ \nu_\tau$ 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 $b\bar{ b}$, $c\bar{ c}$, and $q\bar{ q}$ backgrounds using event-based topological information. A second stage utilises the properties of the hadronic $\tau^{ +} \to \pi^+ \pi^+ \pi^- \bar{ \nu}_\tau$ decay to further suppress these backgrounds, and is also found to achieve high rejection for the $B^+\to \tau^+ \nu_\tau$ background. The number of $B_{ c}^+\to \tau^+ \nu_\tau$ 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.
Categories: hep-ex hep-ph