The lifetime of the $B_c^-$ meson and the 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 $B_c^-\to\tau^-\bar\nu$ 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 $B_c^-\to\tau^-\bar\nu$ 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.