Diagnosing lepton-nonuniversality in $b \to s \ell \ell$

Ratios of branching fractions of semileptonic B decays, $(B \to H \mu \mu)$ over $(B \to H ee)$ with $H=K, K^*,X_s, K_0(1430), \phi, \ldots$ are sensitive probes of lepton universality. In the Standard Model, the underlying flavor changing neutral current process $b\rightarrow s \ell \ell$ is lepton flavor universal. However models with new flavor violating physics above the weak scale can give substantial non-universal contributions. The leading contributions from such new physics can be parametrized by effective dimension six operators involving left- or right-handed quarks. We show that in the double ratios $R_{X_s}/R_K$, $R_{K^*}/R_K$ and $R_\phi/R_K$ the dependence on new physics coupling to left-handed quarks cancels out. Thus a measurement of any of these double ratios is a clean probe of flavor nonuniversal physics coupling to right-handed quarks. We also point out that the observables $R_{X_s}$, $R_{K^*}$, $R_{K_0(1430)}$ and $R_\phi$ depend on the same combination of Wilson coefficients and therefore satisfy simple consistency relations.