One Leptoquark to unify them? Neutrino masses and unification in the light of $(g-2{)}_{\mu }$, $R_{D^{(\star )}}$ and $R_K$ anomalies

Leptoquarks have been proposed as a possible explanation of anomalies in $\bar{B}\mapsto D^{\ast }\tau \bar{\nu }$ decays, the apparent anomalies in $(g-2{)}_{\mu }$ experiments and a violation of lepton universality. Motivated by this, we examine other motivations of leptoquarks: radiatively induced neutrino masses in the presence of a discrete symmetry that prevents a tree level see-saw mechanism, gauge coupling unification, and vacuum stability at least up to the unification scale. We present a new model for radiatively generating a neutrino mass which can significantly improve gauge coupling unification at one loop. We discuss this, and other models in the light of recent work on flavour anomalies.