Abstract
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 \( \beta ={{{\pm n}} \left/ {{\sqrt{3}}} \right.} \) with n = 1, 2, 3. The case \( \beta =-\sqrt{3} \) 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 \( \mathrm{Re}\left( {\mathrm{C}_9^{\mathrm{NP}}} \right) \) 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 \( \mathrm{Re}\left( {\mathrm{C}_9^{\mathrm{NP}}} \right) \) and \( \overline{\mathcal{B}}\left( {{B_s}\to {\mu^{+}}{\mu^{-}}} \right) \), identified for β < 0,implies for negative \( \mathrm{Re}\left( {\mathrm{C}_9^{\mathrm{NP}}} \right) \) uniquely suppression of \( \overline{\mathcal{B}}\left( {{B_s}\to {\mu^{+}}{\mu^{-}}} \right) \) relative to its SM value which is favoured by the data. In turn also S ψϕ < \( S_{{\psi \phi}}^{\mathrm{SM}} \) is favoured with S ψϕ having dominantly opposite sign to \( S_{{\psi \phi}}^{\mathrm{SM}} \) and closer to its central experimental value. Another triple correlation is the one between \( \mathrm{Re}\left( {\mathrm{C}_9^{\mathrm{NP}}} \right) \), \( \overline{\mathcal{B}}\left( {{B_s}\to {\mu^{+}}{\mu^{-}}} \right) \) and \( \mathcal{B}\left( {{B_d}\to K{\mu^{+}}{\mu^{-}}} \right) \). NP effects in \( b\to s\nu \overline{\nu} \) transitions, \( {K^{+}}\to {\pi^{+}}\nu \overline{\nu} \) and \( {K_L}\to {\pi^0}\nu \overline{\nu} \) 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 \( \overline{\mathcal{B}}\left( {{B_s}\to {\mu^{+}}{\mu^{-}}} \right) \) relative to its SM value would favour \( \beta ={1 \left/ {{\sqrt{3}}} \right.} \) and M Z′ ≈ 3 TeV. Assuming lepton universality, we find an upper bound \( \left| {C_9^{\mathrm{NP}}} \right| \) ≤ 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.
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Buras, A.J., De Fazio, F. & Girrbach, J. 331 models facing new b → sμ + μ − data. J. High Energ. Phys. 2014, 112 (2014). https://doi.org/10.1007/JHEP02(2014)112
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DOI: https://doi.org/10.1007/JHEP02(2014)112