New physics in $b\to s{\mu }^{+}{\mu }^{-}$ after the measurement of $R_{K^{*}}$

The recent measurement of $R_{K^{*}}$ is yet another hint of new physics (NP) and supports the idea that it is present in $b\to s{\mu }^{+}{\mu }^{-}$ decays. We perform a combined model-independent and model-dependent analysis in order to deduce properties of this NP. Like others, we find that the NP must obey one of two scenarios: (I) $C_9^{\mu \mu }(\mathrm{NP})<0$ or (II) $C_9^{\mu \mu }(\mathrm{NP})=-C_{10}^{\mu \mu }(\mathrm{NP})<0$. A third scenario, (III) $C_9^{\mu \mu }(\mathrm{NP})=-C_9^{\prime \mu \mu }(\mathrm{NP})$, is rejected largely because it predicts $R_K=1$, in disagreement with experiment. The simplest NP models involve the tree-level exchange of a leptoquark (LQ) or a $Z^{\prime }$ boson. We show that scenario II can arise in LQ or $Z^{\prime }$ models, but scenario I is only possible with a $Z^{\prime }$. Fits to $Z^{\prime }$ models must take into account the additional constraints from $B_s^0\text{−}{\overline{B}}_s^0$ mixing and neutrino trident production. Although the LQs must be heavy, O(TeV), we find that the $Z^{\prime }$ can be light, e.g., $M_{Z^{\prime }}=10\mathrm{GeV}$ or 200 MeV.

Figure 1

Comparison of the experimental measurements of $R_K$ and $R_{K^{*}}$ with the predictions of the three scenarios.