Z-Z″ mixing and Z-mediated FCNCs in SU(3) _C × SU(3) _L × U(1) _X models

Most of the existing analyses of flavour changing neutral current processes (FCNC) in the 331 models, based on the gauge group SU(3) _C × SU(3) _L × U(1) _X, are fully dominated by tree-level exchanges of a new heavy neutral gauge boson Z″. However, due to the Z - Z″ mixing also corresponding contributions from Z boson are present. As the Z - Z″ mixing is estimated generally in Z″ models to be at most O(10^-3), the latter contributions are usually neglected. The paucity of relevant parameters in 331 models allows to check whether this neglect is really justified in these concrete models. We calculate the impact of these contributions on ΔF = 2 processes and rare K, B _s and B _d decays for different values of a parameter β, which distinguishes between various 331 models and for different fermion representations under the SU(3) _L group. We find a general expression for the Z - Z″ mixing in terms β, M _Z, M _Z″ and tan β ̄, familiar from 2 Higgs Doublet models, that differs from the one quoted in the literature. We study in particular the models with β = ±n/ 3√ with n = 1, 2 which have recently been investigated by us in the context of new data on B _s,d → μ ⁺ μ ^- and B _d → K (K)μ ⁺ μ ^-. We find that these new contributions can indeed be neglected in the case of ΔF = 2 transitions and decays, like B _d → K μ ⁺ μ ^-, where they are suppressed by the small vectorial Z coupling to charged leptons. However, the contributions of tree-level Z exchanges to decays sensitive to axial-vector couplings, like B _s,d → μ ⁺ μ ^- and B _d → Kμ ⁺ μ ^-, and those with neutrinos in the final state, like b → sν ν ̄ transitions, K ⁺ → π ⁺ ν ν ̄ and K _L → π ⁰ ν ν ̄ cannot be generally neglected with size of Z contributions depending on β, tan β ̄ and M _Z″. We analyze how our recent results on FCNCs in 331 models, in particular correlations between various observables, are modified by these new contributions. As a byproduct we analyze for the first time the ratio ε″/ε in these models including both Z″ and Z contributions. Our analysis of electroweak precision observables within 331 models demonstrates transparently that the interplay of NP effects in electroweak precision observables and those in flavour observables could allow in the future to identify the favourite 331 model.