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

Abstract: Leptoquarks have been proposed as a possible explanation of anomalies in $\bar{B}\mapsto D^{*} \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.