A nonunitary interpretation for a single vector leptoquark combined explanation to the $B$-decay anomalies

In order to simultaneously account for both $R_{D^{(\ast)}}$ and $R_{K^{(\ast)}}$ anomalies in $B$-decays, we consider an extension of the Standard Model by a single vector leptoquark field, and study how one can achieve the required lepton flavour non-universality, starting from a priori universal gauge couplings. While the unitary quark-lepton mixing induced by $SU(2)_L$ breaking is insufficient, we find that effectively nonunitary mixings hold the key to simultaneously address the $R_{K^{(\ast)}}$ and $R_{D^{(\ast)}}$ anomalies. As an intermediate step towards various UV-complete models, we show that the mixings of charged leptons with additional vector-like heavy leptons successfully provide a nonunitary framework to explain $R_{K^{(\ast)}}$ and $R_{D^{(\ast)}}$. These realisations have a strong impact for electroweak precision observables and for flavour violating ones: isosinglet heavy lepton realisations are already excluded due to excessive contributions to lepton flavour violating $Z$-decays. Furthermore, in the near future, the expected progress in the sensitivity of charged lepton flavour violation experiments should allow to fully probe this class of vector leptoquark models.