New physics solutions for $R_D$ and $R_{D^{\ast }}$

Recent measurements of $R_{D^{\ast }}$ have reduced tension with the Standard Model prediction. Taking all the present data into account, we obtain the values of the Wilson coefficients of each new physics four-fermion operator of a given Lorentz structure. We find that the combined data rule out most of the solutions based on scalar/pseudoscalar operators. By studying the inter-relations between different solutions, we find that there are only four allowed solutions, which are based on operators with $(V-A)$, linear combination of $(V-A)$ and $(V+A)$, tensor and linear combination of scalar/pseudoscalar and tensor structure. We demonstrate that the need for new physics is driven by those measurement of $R_D$ and $R_{D^{\ast }}$ where the $\tau$ lepton is not studied. Further, we show that new physics only in $b\rightarrow c,\mu,\bar{\nu}$ is not compatible with the full set of observables in the decays $B\to Dl\bar{\nu }$ and $B\to D^{\ast }l\bar{\nu }$.