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

TL;DR

This paper investigates whether a new light resonance near the di-muon threshold can explain the low-$q^2$ lepton-flavor universality violation hints in $B o K^{(*)} \, \ell^+\ell^-$ decays, proposing observable signatures and experimental tests.

Contribution

It introduces a model-independent explanation involving a light resonance near the di-muon threshold for the low-$q^2$ anomaly, and suggests experimental signatures to distinguish this from other models.

Findings

A light resonance can reproduce the $R_{K^*}$ low-$q^2$ value within a restricted parameter space.

A narrow peak in $B \to K^* e^+e^-$ near the di-muon threshold is predicted if the resonance exists.

If no such resonance is observed and the anomaly persists, an experimental origin of the violation is favored.

Abstract

LHCb has reported hints of lepton-flavor universality violation in the rare decays $B \to K^{(*)} \ell^+\ell^-$, 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 $R_{K^*}$ 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 $B \to K^* e^+e^-$ 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 $\phi$ mesons can be used as a cross check of lepton-flavor universality by LHCb with $5$ fb$^{-1}$ of integrated luminosity.