Gauge-invariant implications of the LHCb measurements on Lepton-Flavour Non-Universality

Abstract

We study the implications of the recent measurements of $R_K$ and $R_{K^{\ast }}$ by the LHCb collaboration. We do that by adopting a model-independent approach based on the Standard Model Effective Field Theory (SMEFT), in which the dominant new physics effects are encoded in the coefficients of dimension-six operators respecting the full Standard Model (SM) gauge symmetry. After providing simplified expressions for $R_K$ and $R_{K^{\ast }}$, 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 $b\to s\ell \ell$ data, which combined lead to effective New Physics (NP) scenarios with SM pulls in excess of 5~$\sigma$. Thus the operators discussed in this paper would be the first dimension-six 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 $b\to s$ transitions when the NP is assumed to lie above the electroweak scale.

10 pages, 2 figures, 3 tables. v2: references added, typos corrected, improved discussion in Sec. V, corrected coefficient of C7 in formula for RKstar in the low-bin, new figure with global fit in terms of SMEFT coefficients. Conclusions unchanged. v3: minor addition, shorter version to be published in PRD

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