one-to-one correspondence to the basis given above.

To identify the allowed combination of Wilson coefficients at $\mu=m_b$, one should perform a fit to the experimental values in Eq. . Our working assumption will be that the NP couplings to light leptons are negligble, as suggested by current flavor data. The compact expressions for these observable are then given by [@Feruglio:2018fxo] $$\begin{aligned}
\label{eq:RD-RDst-compact}
\begin{split}
\dfrac{R_{D^{(\ast)}}}{R_{D^{(\ast)}}^{\mathrm{SM}}} =  |1+g_{V_L}^\tau|^2 &+ a^{D^{(\ast)}}_{S} \, |g_S^\tau|^2 + a^{D^{(\ast)}}_{P} \, |g_P^\tau|^2+ a_T^{D^{(\ast)}} \, |g_T^\tau|^2 + a^{D^{(\ast)}}_{SV_L}\,\mathrm{Re}\left[g_S^\tau \left(1+\left(g_{V_L}^{\tau}\right)^\ast \right)\right]\\[0.3em]
&+ a^{D^{(\ast)}}_{PV_L}\,\mathrm{Re}\left[g_P^\tau\left(1+\left(g_{V_L}^{\tau}\right)^\ast \right)\right]+ a_{TV_L}^{D^{(\ast)}}\,\mathrm{Re}\left[g_T^\tau\left(1+\left(g_{V_L}^{\tau}\right)^\ast \right)\right]\,,
\end{split}\end{aligned}$$ where $g_{S(P)}^\tau = g_{S_R}^\tau \pm g_{S_L}^\tau$, and the coefficients $a_i^D$ and $a_i^{D^\ast}$ are collected in Table \[tab:RD-RDst-compact\]. Interestingly, $R_D$ and $R_{D^\ast}$ are sensitive to a complementary set of NP operators. While $R_D$ is sensitive to both scalar and tensor contributions, $R_{D^\ast}$ only receives sizable contributions from the tensor ones. Furthermore, the scenario with only $g_{V_L}$ predicts $R_D/R_D^{\mathrm{SM}}=R_{D^\ast}/R_{D^\ast}^{\mathrm{SM}}$, since it corresponds to an overall shift of the SM. In this case, a viable explanation of $R_{D^{(\ast)}}$ can be obtained for $$\begin{aligned}
\label{eq:gvl-fit}
g_{V_L}^\tau \in (0.09,0.13)\,.\end{aligned}$$ to $1\sigma$ accuracy. Other viable solutions, which are not in the (current)$\times$(current) form, are not only possible but also well motivated by concrete NP scenarios, as we will discuss 