Lifetime of $B_c^{-}$ Mesons Constrains Explanations for Anomalies in $B\to D^{(*)}\tau \nu$

We investigate a new constraint on new-physics interpretations of the anomalies observed in $B\to D^{(*)}\tau \nu$ decays making use of the lifetime of the $B_c^{-}$ meson. A constraint is obtained by demanding that the rate for $B_c^{-}\to {\tau }^{-}\overline{\nu }$ does not exceed the fraction of the total width that is allowed by the calculation of the lifetime in the standard model. This leads to a very strong bound on new-physics scenarios involving scalar operators since they lift the slight, but not negligible, chiral suppression of the $B_c^{-}\to {\tau }^{-}\overline{\nu }$ amplitude in the standard model. The new constraint renders a scalar interpretation of the enhancement measured in $R_{D^{*}}$ implausible, including explanations implementing extra Higgs doublets or certain classes of leptoquarks. We also discuss the complementarity of $R_{D^{(*)}}$ and a measurement of the longitudinal polarization of the $\tau$ in the $B\to D^{*}\tau \nu$ decay in light of our findings.

Figure 1

Left panel: Parametric dependence of $R_{D^{*}}$ and $\mathrm{Br}(B_c\to \tau \nu )$ for a pseudoscalar NP interaction (red line). The shaded areas are the $1\sigma$ band corresponding to the measurement of $R_{D^{*}}$ (vertical orange) and to the bound on the NP contribution to the lifetime of the $B_c$ assuming that the SM accounts for 70% of it (gray horizontal). Right panel: The (black) dashed line represents the parametric ${\epsilon }_T$-dependence of $R_{D^{*}}$ and $P_L^{*}$. The overlaid (red) solid line corresponds to values of ${\epsilon }_T$ for which $R_D$ is consistent with the experimental measurement at $1\sigma$. The shaded areas are the $1\sigma$ bands corresponding to the current data set (orange) and naïve experimental prospects discussed in the main text (purple).