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

Abstract

The recent measurements of $R_{K^{+}}$, $R_{K_S^0}$, $R_{K^{\ast +}}$, $B_s\to {\mu }^{+}{\mu }^{-}$, a set of CP-averaged angular observables for the $B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$ decay, and its isospin partner $B^{+}\to K^{\ast +}{\mu }^{+}{\mu }^{-}$ 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.

Comments: 16 pages, 6 figures; latest $R_{K_S^0}$, $R_{K^{\ast +}}$ data included