## Abstract

Motivated by the recently improved results from the Fermilab Lattice and MILC Collaborations on the hadronic matrix elements entering ΔM_{s,d} in Bs,d0−B¯s,d0 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_{9} ^{NP} − 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.

Original language | English |
---|---|

Article number | 115 |

Journal | Journal of High Energy Physics |

Volume | 2016 |

Issue number | 8 |

DOIs | |

State | Published - 1 Aug 2016 |

## Keywords

- Beyond Standard Model
- CP violation
- Heavy Quark Physics
- Kaon Physics

## Fingerprint

Dive into the research topics of '331 Models Facing the Tensions in ΔF = 2 Processes with the Impact on ε^{′}/ε, B

_{s}→ μ

^{+}μ

^{−}and B →K

^{∗}μ

^{+}μ

^{−}'. Together they form a unique fingerprint.