The anatomy of quark flavour observables in 331 models in the flavour precision era

The coming flavour precision era will allow to uncover various patterns of flavour violation in different New Physics (NP) scenarios that are presently washed out by hadronic and experimental uncertainties. We illustrate this by performing the anatomy of flavour violation in the 331 models, based on the gauge group SU(3) _C ×SU(3) _L ×U(1) _X that are among the simplest NP scenarios with new sources of flavour and CP violation. The latter originate dominantly through the flavour violating interactions of ordinary quarks and leptons with a new heavy Z′ gauge boson. After discussing first these models in some generality, we present a detailed study of ΔF = 2 observables and of rare K and B meson decays in the specific "β=1/3" model (to be called ̄331 model) assuming significantly smaller uncertainties in CKM and hadronic parameters than presently available. The most prominent roles in our analysis play ε _K, ΔM _q (q = d, s), the mixing induced CP asymmetries SψK_Sand S_ψφ, rare decays B _s,d → μ ⁺ μ ^- and in particular the CP-asymmetry Sμ+μ-^s in B _s → μ ⁺ μ ^-. As the phenomenology of Z′ contributions is governed only by M _Z′ and four new parameters ̃s ₁₃,̃s₂₃, δ₁ and δ₂, we identify a number of correlations between various observables that differ from those known from CMFV models. While, the δF = 2 observables allow still for four oases in the new parameter space, we demonstrate how the inclusion of δF = 1 observables can in the future identify the optimal oasis for this model. Favouring the inclusive value of |V _ub |, for 1 TeV ≤ M _Z′ ≤ 3 TeV, the ̄331 model is in good agreement with the recent data for B ⁺ → τ ⁺ ν _τ, it removes the it removes the epsi;_K-SψK _Stension present in the SM and the ε _K - ΔM _s,d tension present in CMFV models. Simultaneously, while differing from the SM, it is consistent with the present data on B(B_s,d → μ+μ- and S _ψφ . We identify the triple correlation B(B_s,d → μ+} μ-)-{Sψφ -Sμ+μ-^sthat constitutes an important test of this NP scenario.