The $B$ Anomalies and New Physics in $b \to s e^+ e^-$

We investigate the implications of the latest LHCb measurement of $R_K$ for NP explanations of the $B$ anomalies. The previous data could be explained if the $b \to s \mu^+ \mu^-$ NP is in (I) $C_{9,{\rm NP}}^{\mu\mu}$ or (II) $C_{9,{\rm NP}}^{\mu\mu} = -C_{10,{\rm NP}}^{\mu\mu}$, with scenario (I) providing a better explanation than scenario (II). This continues to hold with the new measurement of $R_K$. However, for both scenarios, this measurement leads to a slight tension of $O(1\sigma)$ between separate fits to the $b \to s \mu^+ \mu^-$ and $R_{K^{(*)}}$ data. In this paper, we investigate whether this tension can be alleviated with the addition of NP in $b \to s e^+ e^-$. In particular, we examine the effect of adding such NP to scenarios (I) and (II). We find several scenarios in which this leads to improvements in the fits. $Z'$ and LQ models with contributions to both $b \to s \mu^+ \mu^-$ and $b \to s e^+ e^-$ can reproduce the data, but only within scenarios based on (II). If the tension persists in future measurements, it may be necessary to consider NP models with more than one particle contributing to $b \to s \ell^+ \ell^-$.