Gauge-invariant implications of the LHCb measurements on lepton-flavor nonuniversality

Abstract

We study the implications of the recent measurements of ${R}_{K}$ and ${R}_{{K}^{*}}$ by the LHCb Collaboration. We do that by adopting a model-independent approach based on the Standard Model effective field theory (SMEFT), with the dominant new physics (NP) effects encoded in the coefficients of dimension-6 operators respecting the full Standard Model (SM) gauge symmetry. After providing simplified expressions for ${R}_{K}$ and ${R}_{{K}^{*}}$, we determine the implications of the recent LHCb results for these observables on the coefficients of the SMEFT operators at low and high energies. We also take into account all $b\ensuremath{\rightarrow}s\ensuremath{\ell}\ensuremath{\ell}$ data, which combined lead to effective NP scenarios with SM pulls in excess of $5\ensuremath{\sigma}$. Thus, the operators discussed in this paper would be the first dimension-6 terms in the SM Lagrangian to be detected experimentally. Indirect constraints on these operators are also discussed. The results of this paper transcend the singularity of the present situation and set a standard for future analyses in $b\ensuremath{\rightarrow}s$ transitions when the NP is assumed to lie above the electroweak scale.