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

Abstract

LHCb has reported hints of lepton-flavor universality violation in the rare decays $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$, 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 $R_{K^{\ast }}$ 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 $B\to K^{\ast }{e}^{+}{e}^{-}$ rate close to the di-muon threshold. If such a peak is observed, other observables, such as the differential $B\to K{e}^{+}{e}^{-}$ 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 $J/\psi$ decays, $e^{+}{e}^{-}$ and ${\mu }^{+}{\mu }^{-}$ decays of $\varphi$ mesons can be used as a cross check of lepton-flavor universality by LHCb with $5$ fb${}^{-1}$ of integrated luminosity.

Comments: 28 pages, 8 figures