Light Resonances and the Low-$q^2$ Bin of $R_{K^*}$

LHCb has reported hints of lepton-flavor universality violation in the rare decays B → K$^{(*)}$ℓ$^{+}$ℓ$^{−}$, both in high- and low-q$^{2}$ bins. Although the high-q$^{2}$ hint may be explained by new short-ranged interactions, the low-q$^{2}$ one cannot. We thus explore the possibility that the latter is explained by a new light resonance. We find that LHCb’s central value of $ {R}_{K^{*}} $ in the low-q$^{2}$ bin is achievable in a restricted parameter space of new-physics scenarios in which the new, light resonance decays preferentially to electrons and has a mass within approximately 10 MeV of the di-muon threshold. Interestingly, such an explanation can have a kinematic origin and does not require a source of lepton-flavor universality violation. A model-independent prediction is a narrow peak in the differential B → K$^{*}$e$^{+}$e$^{−}$ rate close to the di-muon threshold. If such a peak is observed, other observables, such as the differential B → Ke$^{+}$e$^{−}$ rate and R$_{K}$ , may be employed to distinguish between models. However, if a low-mass resonance is not observed and the low-q$^{2}$ anomaly increases in significance, then the case for an experimental origin of the lepton-flavor universality violating anomalies would be strengthened. To further explore this, we also point out that, in analogy to J/ψ decays, e$^{+}$e$^{−}$ and μ$^{+}$μ$^{−}$ decays of ϕ mesons can be used as a cross check of lepton-flavor universality by LHCb with 5 fb$^{−1}$ of integrated luminosity.