Abstract
Motivated by the recently improved results from the Fermilab Lattice and MILC Collaborations on the hadronic matrix elements entering ΔMs,d in B s , d 0 − B ¯ s , d 0 $$ {B}_{s,d}^0-{\overline{B}}_{s,d}^0 $$ mixings and the resulting increased tensions between ΔMs,d and εK in the Standard Model (SM) and CMFV models, we demonstrate that these tensions can be removed in 331 models based on the gauge group SU(3)C × SU(3)L × U(1)X both for MZ′ in the LHC reach and well beyond it. But the implied new physics (NP) patterns in ΔF = 1 observables depend sensitively on the value of |Vcb|. Concentrating the analysis on three 331 models that have been selected by us previously on the basis of their performance in electroweak precision tests and ε′/ε we illustrate this for |Vcb| = 0.042 and |Vcb| = 0.040. We find that these new lattice data still allow for positive shifts in ε′/ε up to 6 × 10−4 for MZ′ = 3 TeV and |Vub| = 0.0036 for both values of |Vcb| but for MZ′ = 10 TeV only for |Vcb| = 0.040 such shifts can be obtained. For |Vub| = 0.0042 maximal shifts in ε′/ε increase to ≃ 7×10−4. NP effects in Bs → μ+μ− and in the Wilson coefficient C9 are significantly larger in all three models for the case of |Vcb| = 0.040. In particular in two models the rate for Bs → μ+μ− can be reduced by NP by 20% for MZ′ = 3 TeV resulting in values in the ballpark of central values from CMS and LHCb. In the third model a shift in C9 up to C9NP − 0.5 is possible. For |Vcb| = 0.042, NP effects in Bs → μ+μ− and in C9 are by at least a factor of two smaller. For MZ′ = 10 TeV NP effects in Bs → μ+μ− and C9, independently of |Vcb|, are at most at the level of a few percent. We also consider the simplest 331 model, analyzed recently in the literature, in which X = Y , the usual hypercharge. We find that in this model NP effects in flavour observables are much smaller than in the three models with X ≠ Y , in particular NP contributions to the ratio ε′/ε are very strongly suppressed. Our analysis exhibits the important role of lattice QCD and of precise values of CKM parameters, in particular |Vcb|, for quark flavour phenomenology beyond the SM. It also demonstrates exceptional role of ΔF = 2 observables and of ε′/ε in testing high energy scales beyond the LHC.