Prospects for $$B_c^+$$ B c + and $$B^+\rightarrow \tau ^+ \nu _\tau $$ B + → τ + ν τ at FCC-ee

Abstract

Abstract The prospects are presented for precise measurements of the branching ratios of the purely leptonic $$B_c^+ \rightarrow \tau ^+ \nu _\tau $$ B c + → τ + ν τ and $$B^+ \rightarrow \tau ^+ \nu _\tau $$ B + → τ + ν τ decays at the Future Circular Collider (FCC). This work is focused on the hadronic $$\tau ^{+} \rightarrow \pi ^+ \pi ^+ \pi ^- {\bar{\nu }}_\tau $$ τ + → π + π + π - ν ¯ τ decay in both $$B_c^+ \rightarrow \tau ^+ \nu _\tau $$ B c + → τ + ν τ and $$B^+ \rightarrow \tau ^+ \nu _\tau $$ B + → τ + ν τ processes. Events are selected with two Boosted Decision Tree algorithms to optimise the separation between the two signal processes as well as the generic hadronic Z decay backgrounds. The range of the expected precision for both signals are evaluated in different scenarios of non-ideal background modelling. This paper demonstrates, for the first time, that the $$B^+ \rightarrow \tau ^+ \nu _\tau $$ B + → τ + ν τ decay can be well separated from both $$B_c^+ \rightarrow \tau ^+ \nu _\tau $$ B c + → τ + ν τ and generic $$Z\rightarrow b{\bar{b}}$$ Z → b b ¯ processes in the FCC-ee collision environment and proposes the corresponding branching ratio measurement as a novel way to determine the CKM matrix element $$|V_{ub}|$$ | V ub | . The theoretical impacts of both $$B^+ \rightarrow \tau ^+ \nu _\tau $$ B + → τ + ν τ and $$B_c^+ \rightarrow \tau ^+ \nu _\tau $$ B c + → τ + ν τ measurements on New Physics cases are discussed for interpretations in the generic Two-Higgs-doublet model and leptoquark models.