vector LQ $U_1=(\mathbf{3},\mathbf{1},2/3)$ induces $C_{\ell q}^{(3)}$, which implies nonzero values of $g_{V_L}$ and $g_{S_R}$ [@Buttazzo:2017ixm].

Note that some of the models which predict $g_{V_L}^\ell$ in Table \[tab:states\] cannot accommodate $R_{D^{(\ast)}}$, as shown in Table \[tab:states\]. This is the case because $g_{V_L}^\tau$ is constrained to be negative in these scenarios, providing an interference term with the wrong sign for $R_{D^{(\ast)}}$, cf. Eq.  [@lqpaper]. Furthermore, a peculiarity of the viable models listed above is a different pattern of effective operators which imply very distinctive phenomenological consequences, as we will discuss in Section \[sec:pheno\].

Finally, a natural question is if the hint of New Physics in $R_{K^{(\ast)}}^{\mathrm{exp}}<R_{K^{(\ast)}}^{\mathrm{SM}}$ and $R_{D^{(\ast)}}^{\mathrm{exp}}>R_{D^{(\ast)}}^{\mathrm{SM}}$ can be simultaneously explained by the same NP scenario. Building such a model turns out be a very challenging task. The only mediator that can account for both anomalies at tree-level is the vector LQ $U_1$ [@Buttazzo:2017ixm]. The problem in this case is that a resulting model is nonrenormalible and an explicit UV-completion needs to be specified. This issue has been addressed in a series of papers with gauged models [@Assad:2017iib; @DiLuzio:2017vat; @Bordone:2017bld; @Barbieri:2017tuq; @Blanke:2018sro]. A far more minimalistic approach, in terms of number of parameters, is to consider models containing two scalar LQs. 