Reconciling $B$-meson Anomalies, Neutrino Masses and Dark Matter

Abstract: We explore the connection of the leptoquark solution to the recently reported $B$-meson anomalies with a mechanism of neutrino mass generation and a viable dark matter candidate. We consider a model consisting of two scalar leptoquarks and three generations of triplet fermions: neutrino masses are radiatively generated at the 3-loop level and, by imposing a discrete $Z_2$ symmetry, one can obtain a viable dark matter candidate. We discuss the constraints on the flavour structure of this model arising from numerous flavour observables. The rare decay $K\to \pi^+\nu\bar\nu$ and charged lepton flavour violating $\mu-e$ conversion in nuclei are found to provide the most stringent constraint on this class of models.