Remarks on the Standard Model predictions for $R(D)$ and $R(D^{\ast })$

Abstract

Semileptonic $b\to c$ transitions, and in particular the ratios $R(D^{(\ast )})=\frac{\Gamma (B\to D^{(\ast )}\tau \nu )}{\Gamma (B\to D^{(\ast )}\ell \nu )}$, can be used to test the universality of the weak interactions. In light of the recent discrepancies between the experimental measurements of these observables by BaBar, Belle and LHCb and the Standard Model predicted values, we study the robustness of the latter. Our analysis reveals that $R(D)$ might be enhanced by lepton mass effects associated to the mostly unknown scalar form factor. In constrast, the Standard Model prediction for $R(D^{\ast })$ is found to be more robust, since possible pollutions from $B^{\ast }$ contributions turn out to be negligibly small, which indicates that $R(D^{\ast })$ is a promising observable for searches of new physics.

Comments: 11 pages, 3 figures; v2: minor corrections, matches published version