Abstract
Most of the existing analyses of FCNC processes in the 331 models, based on the gauge group SU(3)_C x SU(3)_L x U(1)_X, take only into account 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 that are usually neglected. We calculate the impact of these contributions on Delta F=2 processes and rare K, B_s and B_d decays for different values of a parameter beta, 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 beta, M_Z, M_Z' and tan(bar{beta}), familiar from 2 Higgs Doublet models, that differs from the one quoted in the literature. We study in particular the models with beta=+-n/sqrt{3} with n=1,2 which have recently been investigated by us in the context of new data on B_{s,d}->mu^+ mu^- and B_d->K^*(K)mu^+ mu^-. We find that these new contributions can indeed be neglected in the case of Delta F=2 transitions and decays, like B_d->K^*mu^+mu^-, 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}->mu^+ mu^- and B_d->K mu^+ mu^-, and those with neutrinos in the final state, like b->s nu bar{nu} transitions, K^+->pi^+ nu bar{nu} and K_L->pi^0 nu bar{nu} cannot be generally neglected with size of Z contributions depending on beta, tan(bar{beta}) and M_Z'. We analyze for the first time the ratio epsilon'/epsilon 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.
Highlights
Asymptotic freedom of QCD imposes that, for example, if two quark generations transform as triplets, the remaining one should be an antitriplet
The goal of the present paper is to investigate, whether the neglect of Z boson flavour changing neutral current processes (FCNC) generated by Z − Z mixing in the 331 models in question is really justified
And 11 we show various correlations between rare decay branching ratios for the four 331 models considered for the F1 case, three values of tan β = 1, 5, 0.2 and the case without Z − Z mixing which represents sole Z contributions
Summary
As already emphasized in [8, 14] the choice of β does not uniquely specify the phenomenology of the 331 model considered which further depends on the choice of fermion representations under SU(3)L. On the other hand as evident from the comparison of our compendium for Z couplings to fermions in [4] with table 4 of [14] the signs in front of β in these couplings are changed when going from F1 to F2 This property can be derived from the action of the relevant operator QW on triplet and antitriplet. The ratios Rk with known Z couplings to leptons are only functions of β and of the parameter a or equivalently tan β In addition they depend on whether the representation F1 or F2 is considered. In table 1 we show the values of sin ξ, Rk and W k relevant for the couplings ∆μVμ, ∆μAμ and ∆νLν in scenario F1 for fermion representations for the four values of β and two values of tan β = 1(5). We will investigate these new contributions numerically
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