Résumé
We investigate new-physics contributions to $b\rightarrow s \ell \ell $ transitions in the context of an effective field theory extension of the Standard Model, including operator mixing at one loop. We identify the few scenarios where a single Wilson coefficient, $C/\Lambda ^2 \sim 1/\mathrm{TeV}^2$, induces a substantial shift in the lepton flavour universality ratios $R_K$ and $R_{K^*}$ at one loop, while evading Z-pole precision tests, collider bounds, and other flavour constraints. Novel fits to the present data are achieved by a left-handed current operator with quark-flavour indices (2, 2) or (3, 3). Interestingly, the running of the Standard Model Yukawa matrices gives the dominant effect for these scenarios. We match the favoured effective-theory scenarios to minimal, single-mediator models, which are subject to additional stringent constraints. Notably, we recognise three viable instances of a leptoquark with one coupling to fermions only. If the anomalies were confirmed, it appears that one-loop explanations have good prospects of being directly tested at the LHC.