Leptoquark models for the $B$-physics anomalies

Abstract: The $B$-physics experiments at LHCb, BaBar and Belle hint towards deviations from Lepton Flavor Universality in both the tree-level and loop-induced $B$ meson semileptonic decays. We propose a leptoquark model with light right-handed neutrinos which can accommodate both $R_K^\mathrm{exp}<R_K^\mathrm{SM}$ and $R_{D^{(\ast)}}^\mathrm{exp}>R_{D^{(\ast)}}^\mathrm{SM}$. We discuss several of its predictions which can be tested in modern day experiments. We also comment on the recent finding at LHCb, namely $R_{K^\ast}^{\mathrm{exp}}<R_{K^\ast}^\mathrm{SM}$.