Reconsidering the One Leptoquark solution: flavor anomalies and neutrino mass

We reconsider a model introducing a scalar leptoquark $phi sim (mathbf{3}, mathbf{1}, -1/3)$ to explain recent deviations from the standard model in semileptonic $B$ decays. The leptoquark can accommodate the persistent tension in the decays $bar{B}rightarrow D^{(*)}tau bar{ u}$ as long as its mass is lower than approximately $10 text{ TeV}$, and we show that a sizeable Yukawa coupling to the right-chiral tau lepton is necessary for an acceptable explanation. Agreement with the measured $bar{B}rightarrow D^{(*)}tau bar{ u}$ rates is mildly compromised for parameter choices addressing the tensions in $b to s mu mu$, where the model can significantly reduce the discrepancies in angular observables, branching ratios and the lepton-flavor-universality observables $R_K$ and $R_{K^*}$. The leptoquark can also reconcile the predicted and measured value of the anomalous magnetic moment of the muon and appears naturally in models of radiative neutrino mass derived from lepton-number violating effective operators. As a representative example, we incorporate the particle into an existing two-loop neutrino mass scenario derived from a dimension-nine operator. In this specific model, the structure of the neutrino mass matrix provides enough freedom to explain the small masses of the neutrinos in the region of parameter space dictated by agreement with the anomalies in $bar{B}rightarrow D^{(*)}tau bar{ u}$, but not the $b to s$ transition. This is achieved without excessive fine-tuning in the parameters important for neutrino mass.