to evade nontrivial LHC constraints on di-tau production [@Greljo:2015mma; @Faroughy:2016osc; @Buttazzo:2017ixm]. [^7] The only minimalistic scenarios capable of explaining $R_{D^{(\ast)}}^{\mathrm{exp}}$ while satisfying other existing constraints are LQs.

In Table \[tab:states\] we list the LQ states that can contribute to $b\to c\tau \bar{\nu}$ in terms of their SM quantum numbers, $(SU(3)_c,SU(2)_L,Y)$, with $Q=Y+T_3$ [@Dorsner:2016wpm]. From this Table we learn that very few possibilities are still viable:

-   The scalar LQ $S_1=(\mathbf{\bar{3}},\mathbf{1},1/3)$ generates, at the matching scale, the effective coefficients $C_{\ell q}^{(3)}$ and $C_{\ell e q u}^{(1)} =  -4 \, C_{\ell e q u}^{(3)}$, which induce nonzero values of $g_{V_L}$ and $g_{S_L} \approx -8.1 \, g_T$ at $\mu=m_b$, after accounting for RGE effects. Both of these Wilson coefficients can accommodate for $R_{D^{(\ast)}}$, as discussed in Sec. \[sec:eft\]. See also Ref. [@Sakaki:2013bfa; @Bauer:2015knc; @Becirevic:2018uab; @Marzocca:2018wcf].

-   The scalar LQ $R_2=(\mathbf{3},\mathbf{2},7/6)$ produces $C_{\ell e q u}^{(1)} =  4 \, C_{\ell e q u}^{(3)}$, which implies $g_{S_L} \approx 8.1 \, g_T$ at $\mu=m_b$. Note that this particularl correlation of scalar and tensor coefficients lies outside of the allowed regions in Fig. \[fig:RD-RDst-1TeV\], where only real coefficients were considered. However, this problem can be overcome by considering complex Wilson coefficients [@Sakaki:2013bfa; @Hiller:2016kry; @Becirevic:2018uab; @Becirevic:2018afm].

-   The 