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

Abstract

We investigate a new constraint on new-physics interpretations of the anomalies observed in $B\to D^{(\ast )}\tau \nu$ 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 $R_{D^{\ast }}$ implausible, including explanations implementing extra Higgs doublets or certain classes of leptoquarks. We also discuss the complementarity of $R_{D^{(\ast )}}$ and a measurement of the longitudinal polarization of the $\tau$ in the $B\to D^{\ast }\tau \nu$ decay in light of our findings.

arXiv comment6 pages, 2 figs

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