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 Z′ 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 M Z′ ≈ 4 TeV can be ruled out when the present constraints on Z′ couplings, in particular from LEP-II, are taken into account. For n = 1, 2 interesting results are found for M Z′ < 4TeV with largest NP effects for β < 0 in B d → K ∗ μ + μ − and the one sin B s,d → μ + μ − for β > 0. As Re( C₉NP ) can reach the values −0.8and −0.4for n = 2and 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( C₉NP ) and B̄( Bₛ→ μ⁺μ⁻ ) , identified for β < 0,implies for negative Re( C₉NP ) uniquely suppression of B̄( Bₛ→ μ⁺μ⁻ ) relative to its SM value which is favoured by the data. In turn also S ψϕ < S_ψ φSM is favoured with S ψϕ having dominantly opposite sign to S_ψ φSM and closer to its central experimental value. Another triple correlation is the one between Re( C₉NP ) , B̄( Bₛ→ μ⁺μ⁻ ) and B( Bd→ Kμ⁺μ⁻ ) . NP effects in b→ sν ν̄ transitions, K⁺→ π⁺ν ν̄ and KL→ π⁰ν ν̄ 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( Bₛ→ μ⁺μ⁻ ) relative to its SM value would favour β =1 / √3 . and M Z′ ≈ 3 TeV. Assuming lepton universality, we find an upper bound | C₉NP | ≤ 1.1(1.4) from LEP-II data for all Z′ models with only left-handed flavour violating couplings to quarks when NP contributions to ΔM s at the level of 10%(15%) are allowed.