Prospects for $B_{c}^+\to τ^+ ν_τ$ at FCC-ee

This paper presents the prospects for a precise measurement of the branching fraction of the leptonic $B_{c}^+\to τ^+ ν_τ$ 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 $b\bar{b}$, $c\bar{c}$, and $q\bar{q}$ backgrounds using event-based topological information. A second stage utilises the properties of the hadronic $τ^{+} \to π^+ π^+ π^- \barν_τ$ decay to further suppress these backgrounds, and is also found to achieve high rejection for the $B^+\to τ^+ ν_τ$ background. The number of $B_{c}^+\to τ^+ ν_τ$ 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.

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