331 models facing new b → sμ⁺μ^- data

We investigate how the 331 models, based on the gauge group SU(3) _C × SU(3)_L × U(1)_X face new data on B_s,d → μ⁺μ^- and B_d → K*(K)μ+μ? taking into account present constraints from δF = 2 observables, low energy precision measurements, LEP-II and the LHC data. In these models new sources of flavour and CP violation originate dominantly through flavour violating interactions of ordinary quarks and leptons with a new heavy Z0 gauge boson. The strength of the relevant couplings is governed by four new parameters in the quark sector and the parameter β which in these models determines the charges of new heavy fermions and gauge bosons. We study the implications of these models for β = ±n/√3 with n = 1, 2, 3. The case β = ?√3 leading to Landau singularities for MZ′ ≈ 4 TeV can be ruled out when the present constraints on Z0 couplings, in particular from LEP-II, are taken into account. For n = 1, 2 interesting results are found for MZ′ < 4 TeV with largest NP effects for β < 0 in B_d → K*μ ⁺μ^- and the ones in B_s,d → μ⁺μ^- for β > 0. As Re(C^NP ₉ ) can reach the values ?0.8 and ?0.4 for n = 2 and n = 1, respectively the B_d → K*μ⁺μ^- anomalies can be softened with the size depending on δM _s/(δM_s)_SM and the CP-asymmetry S _ψφ. A correlation between Re(C^NP₉ ) and B̄(B_s → μ⁺μ^-), identified for β < 0, implies for negative Re(C^NP₉ ) uniquely suppression of B̄(B_s → μ⁺μ^-) relative to its SM value which is favoured by the data. In turn also S _ψφ < S_SMψφ is favoured with S_ψφ having dominantly opposite sign to S^SM _ψφ and closer to its central experimental value. Another triple correlation is the one between Re(C^NP₉ ), B̄(B_s → μ⁺μ^-) and B̄(B_d → Kμ⁺μ^-). NP effects in b → svv̄ transitions, K⁺ → π^o+vv̄ and K_L → π⁰vv̄ turn out to be small. We find that the absence of B_d → K*μ⁺μ ^- anomalies in the future data and confirmation of the suppression of B̄(B_s → μ⁺μ^-) relative to its SM value would favour β = 1/√3 and MZ′ ≈ 3 TeV Assuming lepton universality, we find an upper bound |C^NP₉ | ≤ 1.1(1.4) from LEP-II data for all Z0 models with only left-handed flavour violating couplings to quarks when NP contributions to δMs at the level of 10%(15%) are allowed.