Discriminating 1D new physics solutions in $b\to s\ell\ell$ decays

The recent measurements of $R_{K^+}$, $R_{K_S^0}$, $R_{K^{*+}}$, $B_s\to\mu^+\mu^-$, a set of CP-averaged angular observables for the $B^0\to K^{*0}\mu^+\mu^-$ decay, and its isospin partner $B^+\to K^{*+}\mu^+\mu^-$ by the LHCb Collaboration, consistently hint at lepton universality violation in the $b\to s\ell\ell$ transitions. In this work, we first perform global fits to the $b\to s\ell\ell$ data and show that five one-dimensional scenarios, i.e, $\delta C_9^{\mu}$, $\delta C_{10}^{\mu}$, $\delta C_L^{\mu}$, $\delta C_9^{\mu}=C_{10}^{\mu\prime}$, and $\delta C_9^{\mu}=-C_9^{\mu\prime}$ can best explain the so-called B anamolies. Furthermore, we explore how these scenarios can be distinguished from each other. For this purpose, we first study the combinations of four angular asymmetries $A_i$~$(i=3,4,5,9)$ and find that they cannot distinguish the five new physics scenarios. We then show that a newly constructed ratio $R_{S}$ can uniquely discriminate the five new physics scenarios in proper intervals of $q^2$ if it can be measured with a percent level precision.