On a model with two scalar leptoquarks -- $R_2$ and $S_3$

We discuss a model that can accommodate the $B$-physics anomalies, based on combining two scalar leptoquarks, $R_2$ and $S_3$, of mass $\mathcal{O}(1\,\mathrm{TeV})$, and that we proposed in our previous paper. We update the analysis of its parameter space and show that a model remains viable and consistent with a number of low energy and high energy flavor physics constraints. Since the model predicts a non-zero New Physics phase, we discuss the possibility to test its contribution to the neutron electric dipole moment and to the angular distributions of the exclusive $b\to c\tau \bar \nu$ decays. We find that the model can provide a significant enhancement to $\mathcal{B}(B\to K^{(\ast)}\nu\nu)$ and provides both the upper and lower bounds to $\mathcal{B}(B\to K^{(\ast)}\mu\tau)$.