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

Abstract

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.

34 pages, 6 figures, v2 matches the published version (includes some new references and refinements in the analysis)

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