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We investigate a new constraint on new-physics interpretations of theanomalies observed in $B\to D^{(*)}\tau\nu$ decays making use of the lifetimeof 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 isallowed by the calculation of the lifetime in the standard model. This leads toa very strong bound on new-physics scenarios involving scalar operators sincethey lift the slight, but not negligible, chiral suppression of the$B_c^-\to\tau^-\bar\nu$ amplitude in the standard model. The new constraintrenders a scalar interpretation of the enhancement measured in $R_{D^*}$implausible, including explanations implementing extra Higgs doublets orcertain 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.

The lifetime of the $B_c^-$ meson and the anomalies in $B\to D^{(*)}\tau\nu$