Abstract
Motivated by the recently improved results from the Fermilab Lattice and MILC Collaborations on the hadronic matrix elements entering ΔM s,d in \( {B}_{s,d}^0-{\overline{B}}_{s,d}^0 \) mixings and the resulting increased tensions between ΔM s,d and ε K 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 M Z ′ 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 |V cb |. 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 |V cb | = 0.042 and |V cb | = 0.040. We find that these new lattice data still allow for positive shifts in ε ′ /ε up to 6 × 10−4 for M Z ′ = 3 TeV and |V ub | = 0.0036 for both values of |V cb | but for M Z ′ = 10 TeV only for |V cb | = 0.040 such shifts can be obtained. For |V ub | = 0.0042 maximal shifts in ε′ /ε increase to ≃ 7×10−4. NP effects in B s → μ + μ − and in the Wilson coefficient C 9 are significantly larger in all three models for the case of |V cb | = 0.040. In particular in two models the rate for B s → μ + μ − can be reduced by NP by 20% for M Z ′ = 3 TeV resulting in values in the ballpark of central values from CMS and LHCb. In the third model a shift in C 9 up to C NP9 − 0.5 is possible. For |V cb | = 0.042, NP effects in B s → μ + μ − and in C 9 are by at least a factor of two smaller. For M Z ′ = 10 TeV NP effects in B s → μ + μ − and C 9, independently of |V cb |, 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 |V cb |, 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.
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Buras, A.J., De Fazio, F. 331 Models Facing the Tensions in ΔF = 2 Processes with the Impact on ε ′ /ε, B s → μ + μ − and B →K ∗ μ + μ − . J. High Energ. Phys. 2016, 115 (2016). https://doi.org/10.1007/JHEP08(2016)115
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DOI: https://doi.org/10.1007/JHEP08(2016)115