$R_{D^{(*)}}$ and survival of the fittest scalar leptoquark

Abstract: Motivated by the long-standing discrepancy in lepton flavor universality ratios $R_D$ and $R_{D^{\ast}}$ we assess the status of scalar leptoquark states $R_2$, $\widetilde R_2$ and $S_1$ which can in principle provide a desired enhancement of $\mathcal{B}(B\to D^{(\ast )}\tau \nu)$ in a minimal setup with two Yukawa couplings only. We consider unavoidable low-energy constraints, $Z$-pole measurements as well as high-$p_T$ constraints. After setting mass of each leptoquark to $1.5$ TeV we find that of all considered states only $S_1$ leptoquark, coupled to both chiralities of leptons and quarks, is still a completely viable solution while the scenario with $R_2$ is in growing tension with $\Gamma(Z \to \tau \tau)$ and with the LHC constraints on the di-tau tails at high-$p_T$. We comment on the future experimental tests of $S_1$ scenario.