Recently there has been interest in the correlation between $R(D^{*})$ and the branching ratio (BR) of $B_c^{-}\to \tau \overline{\nu }$ in models with a charged scalar $H^{\pm }$. Any enhancement of $R(D^{*})$ by $H^{\pm }$ alone (in order to agree with current data) also enhances $\mathrm{BR}(B_c^{-}\to \tau \overline{\nu })$, for which there has been no direct search at hadron colliders. We show that LEP data taken at the $Z$ peak requires $\mathrm{BR}(B_c^{-}\to \tau \overline{\nu })\lesssim 10\%$, and this constraint is significantly stronger than the recent constraint $\mathrm{BR}(B_c^{-}\to \tau \overline{\nu })\lesssim 30\%$ from considering the lifetime of $B_c$. In order to respect this new constraint, any explanation of the $R(D)$ and $R(D^{*})$ anomaly in terms of $H^{\pm }$ alone would require the future measurements of $R(D^{*})$ to be even closer to the Standard Model prediction. A stronger limit on $\mathrm{BR}(B_c^{-}\to \tau \overline{\nu })$ (or its first measurement) would be obtained if the L3 Collaboration used all its data taken at the $Z$ peak.

• Received 24 August 2017

DOI:https://doi.org/10.1103/PhysRevD.96.075011