(\mu=m_b) \in (-1.14,0.68)$, where we have used $|V_{cb}|=0.0417(20)$ [@Bigi:2017njr; @Grinstein:2017nlq]. [^6] This constraint is illustrated in the left panel of Fig. \[fig:RD-RDst-1TeV\], where it can be seen that an explanation of $R_{D^{(\ast)}}$ via only (pseudo)scalar operators is ruled out. Scenarios providing a good fit to $R_{D^{(\ast)}}$, while avoiding the $B_c$-lifetime constraint, can be obtained by using a different set of operators. For instance, a scenario containing only $g_{S_L}$ and $g_T$ can provide a good description of current data, as illustrated in the right panel of Fig. \[fig:RD-RDst-1TeV\]. This combination of Wilson coefficient is well motivated by scenarios containing leptoquark bosons which predict certain correlations between $g_{S_L}$ and $g_T$. Furthermore, it is known that a non-negligible mixing of $g_T$ into $g_{S_L}$ is induced via electroweak quantum corrections [@Gonzalez-Alonso:2017iyc], cf. also Ref. [@Feruglio:2018fxo]. Finally, note that viable scenarios with complex Wilson coefficients have also been considered in the literature, providing an equally good fit to the experimental results Ref. [@Sakaki:2013bfa; @Hiller:2016kry; @Becirevic:2018uab; @Becirevic:2018afm].

![*Allowed regions by $R_D$ and $R_{D^\ast}$ in the planes $g_{S}^\tau$ vs. $g_P^\tau$ (left panel), and $g_{S_L}^\tau$ vs. $g_T^\tau$ (right panel) are shown to $1$, $2$ and $3\,\sigma$ accuracy in blue (darker to lighter). The black lines show the constraints 