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We introduce two scalar leptoquarks, the SU$(2)_L$ isosinglet denoted$\phi\sim(\mathbf{3}, \mathbf{1}, -1/3)$ and the isotriplet$\varphi\sim(\mathbf{3}, \mathbf{3}, -1/3)$, to explain observed deviationsfrom the standard model in semi-leptonic $B$-meson decays. We explore theregions of parameter space in which this model accommodates the persistenttensions in the decay observables $R_{D^{(*)}}$, $R_{K^{(*)}}$, and angularobservables in $b\to s \mu\mu$ transitions. Additionally, we exploit the roleof these exotics in existing models for one-loop neutrino mass generationderived from $\Delta L=2$ effective operators. Introducing the vector-likequark $\chi \sim (\mathbf{3}, \mathbf{2}, -5/6)$ necessary for lepton-numberviolation, we consider the contribution of both leptoquarks to the generationof radiative neutrino mass. We find that constraints permit simultaneouslyaccommodating the flavour anomalies while also explaining the relativesmallness of neutrino mass without the need for cancellation between leptoquarkcontributions. A characteristic prediction of our model is a rate ofmuon--electron conversion in nuclei fixed by the anomalies in $b \to s \mu \mu$and neutrino mass; the COMET experiment will thus test and potentially falsifyour scenario. The model also predicts signatures that will be tested at the LHCand Belle II.

A near-minimal leptoquark model for reconciling flavour anomalies and generating radiative neutrino masses