Flavour issues in warped custodial models: B anomalies and rare K decays

Abstract We explore the flavour structure of custodial Randall–Sundrum (RS) models in the context of semi-leptonic decay of the B mesons. Anomalies in the $$b\rightarrow s ll$$ b→sll processes can be easily fit with partially composite second generation leptons and third generation quarks. Given the explanations of the B anomalies, we obtain predictions for rare K- decays which are likely to be another candle for new physics (NP). Two scenarios are considered: (A) The source of non-universality is the right handed muons (unorthodox case). (B) Standard scenario, with anomalies explained primarily by non-universal couplings to the lepton doublets. The prediction for the rare K-decays are different according to the scenario, thereby serving as a useful discriminatory tool. We note that, in this setup $$R(D^*)$$ R(D∗) is at best consistent with the SM and increasing the compositeness of the $$\tau _L$$ τL generates a net contribution becoming below the SM expectation. Finally, we also comment on the implications of flavour violation in the lepton sector and present an explicit example with the implementation of bulk leptonic MFV which helps in alleviating the constraints