The measurements carried out at LEP and SLC projected us into the precision era of electroweak physics. This has also been relevant in the theoretical interpretation of LHCb and Belle measurements of rare B semileptonic decays, paving the road for new physics with the inference of lepton universality violation in RK(∗) ratios. The simplest explanation of these flavour anomalies — sizeable one-loop contributions respecting Minimal Flavour Violation — is currently disfavoured by electroweak precision data. In this work, we discuss how to completely relieve the present tension between electroweak constraints and one-loop minimal flavour violating solutions to RK(∗). We determine the correlations in the Standard Model Effective Field Theory that highlight the existence of such a possibility. Then, we consider minimal extensions of the Standard Model where our effective-field-theory picture can be realized. We discuss how these solutions to b → sll anomalies, respecting electroweak precision and without any new source of flavour violation, may point to the existence of a Z′ boson at around the TeV scale, within the discovery potential of LHC, or to leptoquark scenarios.
