We consider an abelian extension of the Standard Model (SM) comprising a new gauge group U(1)′, with the neutral gauge boson Z′ having flavour violating couplings to quarks and leptons. The fermion content is the same as in SM except for the addition of three right-handed neutrinos. The model, proposed in [1], describes the couplings of Z′ to fermions in terms of three rational parameters ϵ1,2,3 that sum to zero imposing the cancellation of the gauge anomalies. Each ϵi is common to all fermions in a generation, a feature producing correlations among quark and lepton observables. We focus on \(b\to s{{\ell}}_{1}^{-}{{\ell}}_{2}^{+}\) transitions for the lepton flavour conserving ℓ1 = ℓ2 and lepton flavour violating case ℓ1 ≠ ℓ2. Small deviations with respect to the SM predictions are found in the first case, which reflects a feature of the model where quark and lepton sectors prevent each other to manifest large discrepancies with respect to SM. We investigate the correlations between rare B and Bs decays and the leptonic processes τ− → μ−μ+μ−, μ− → e−γ, μ− → e−e+e− and the μ− → e− conversion in nuclei. We show that the current experimental upper bounds on these four channels play an increasingly important role in constraining the branching fractions of lepton flavour violating B and Bs decays. While the present bound on τ− → μ−μ+μ− does not impose significant restrictions, the other three modes set progressively more stringent limits, an important information for the planned new experimental facilities.
