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Measurements of $b \rightarrow s \mu^+ \mu^-$ transitions indicate that theremay be a new physics field coupling to di-muon pairs associated with the $b$ to$s$ flavour transition. Including the 2022 LHCb reanalysis of $R_K$ and$R_{K^\ast}$, one infers that there may also be associated new physics in$b\rightarrow e^+ e^-$ transitions. Here, we examine the extent of thestatistical preference for $Z^\prime$ models coupling to di-electron pairstaking into account the relevant constraints, in particular from experiments atLEP-2. We identify an anomaly-free set of models which interpolates between the$Z^\prime$ not coupling to electrons at all, to one in which there is an equal$Z^\prime$ coupling to muons and electrons (but where in all models in the set,the $Z^\prime$ boson can mediate $b\rightarrow \mu^+ \mu^-$ transitions). A$3B_3-L_e-2L_\mu$ model provides a close-to-optimal fit to the pertinentmeasurements along the line of interpolation. We have (re-)calculatedpredictions for the relevant LEP-2 observables in terms of dimension-6 SMEFToperators and put them into the ${\tt flavio2.3.3}$ computer program, so thatthey are available for global fits.

Plan B: New ${Z^\prime}$ models for $b\rightarrow sl^+l^-$ anomalies