ε^′/ε in 331 models

Abstract: Motivated by the recent findings that the ratio ε^′/ε in the Standard Model (SM) appears to be significantly below the data we investigate whether the necessary enhancement of ε^′/ε can be obtained in 331 models, based on the gauge group SU(3)_C × SU(3)_L × U(1)_X. In these models new physics (NP) contributions to ε^′/ε and other flavour observables are dominated by tree-level exchanges of a Z^′ with non-negligible contributions from tree-level Z exchanges generated through the Z − Z^′ mixing. NP contributions to ε^′/ε in these models are governed by the electroweak penguin operator Q₈ for which the hadronic matrix element is already rather well known so that our analysis of NP contributions is subject to much smaller theoretical uncertainties than within the SM. In particular strong cancelations between different contributions do not take place. The size of NP effects depends not only on M_Z′ but in particular on a parameter β, which distinguishes between various 331 models. Also a parameter tan (Formula presented.) present in the Z − Z′ mixing plays a role. We perform the analysis in seven 331 models characterized by different β, tan (Formula presented.) and fermion representations under the gauge group that have been selected in our earlier analysis on the basis of electroweak precision data. Imposing the constraints from ΔF = 2 transitions we find that only three of these models can provide a significant positive shift in ε^′/ε up to 6 × 10⁻⁴ for M_Z′ = 3 TeV. Two of them allow simultaneously a supression of the rate for B_s → μ⁺μ⁻ by 20% thereby bringing the theory closer to the data without any significant impact on the Wilson coefficient C₉. The third model provides simultaneous shift ΔC₉ = −0.6, softening the anomalies in B → K^∗μ⁺μ⁻, without any significant impact on B_s → μ⁺μ⁻. NP effects in rare K decays, in particular in (Formula presented.) , turn out to be small. This is also the case of (Formula presented.). Both predictions could be challenged by NA62 experiment and Belle II in this decade. The special flavour structure of 331 models implies that even for M_Z′ = 30 TeV a shift of ε^′/ε up to 8 × 10⁻⁴ and a significant shift in ε_K can be obtained, while the effects in other flavour observables are small. In this manner ε^′/ε and ε_K appear to be unique flavour observables in these models which provide the possibility of accessing masses of M_Z′ far beyond the LHC reach.