$B$ anomalies and the tauphilic leptoquark model

We suggest three scalar leptoquarks, $S_1$, ${\tilde{R}}_2$, and $S_3$ which couple exclusively to the 3rd generation of leptons to explain the $B$ anomalies. The scalar singlet $S_1$ can explain $R(D^{(\ast )})$, while the doublet ${\tilde{R}}_2$ is needed to fit the branching ratio $\mathrm{B}\mathrm{r}(B\to K^{(\ast )}\nu \bar{\nu })$ via the right-handed Wilson coefficients $C_R^{\nu }$. A strong constraint from $\mathrm{\Delta }{m}_{B_s}$ requires triplet $S_3$ where the mixing term between $S_1$ and $S_3$ is important. Our analysis suggests subdominant $C_{V_L}<0$ and dominant $C_{S_L}>0$ and lepton-flavor universality violating $C_9^{\mathrm{L}\mathrm{Q}}\approx +1$. The masses are expected to be $M_{S_1}\sim M_{{\tilde{R}}_2}<M_{S_3}\lesssim 3$ TeV, which can be probed in future colliders.