New physics in $b\to s{e}^{+}{e}^{-}$?

At present, the measurements of some observables in $B\to K^{*}{\mu }^{+}{\mu }^{-}$ and $B_s^0\to \varphi {\mu }^{+}{\mu }^{-}$ decays, and of $R_{K^{(*)}}\equiv \mathcal{B}(B\to K^{(*)}{\mu }^{+}{\mu }^{-})/\mathcal{B}(B\to K^{(*)}{e}^{+}{e}^{-})$, are in disagreement with the predictions of the standard model. While most of these discrepancies can be removed with the addition of new physics (NP) in $b\to s{\mu }^{+}{\mu }^{-}$, a difference of $\gtrsim 1.7\sigma$ still remains in the measurement of $R_{K^{*}}$ at small values of $q^2$, the dilepton invariant mass squared. In the context of a global fit, this is not a problem. However, it does raise the question: if the true value of $R_{K^{*}}^{\mathrm{low}}$ is near its measured value, what is required to explain it? In this paper, we show that, if one includes NP in $b\to s{e}^{+}{e}^{-}$, one can generate values for $R_{K^{*}}^{\mathrm{low}}$ that are within $\sim 1\sigma$ of its measured value. Using a model-independent, effective-field-theory approach, we construct many different possible NP scenarios. We also examine specific models containing leptoquarks or a $Z^{\prime }$ gauge boson. Here, additional constraints from lepton-flavor-violating observables, $B_s^0-{\overline{B}}_s^0$ mixing, and neutrino trident production must be taken into account, but we still find a number of viable NP scenarios. For the various scenarios, we examine the predictions for $R_{K^{(*)}}$ in other $q^2$ bins, as well as for the observable $Q_5\equiv P_5^{\prime \mu \mu }-P_5^{\prime ee}$.

Figure 1

Predicted range of values of $Q_5$ for each of the scenarios in Tables 2, 3, and 6, as well as scenarios (i), (ii), (iii), and (iv) [Eqs. (3), (4), and (6)]. The $1\sigma$ range of the present measurement of $Q_5$ [Eq. (26)] is superposed.