331 model predictions for rare B and K decays, and ∆F = 2 processes: an update

Motivated by the improved results from the HPQCD lattice collaboration on the hadronic matrix elements entering ∆M_s,d in Bs,d0−B¯s,d0 mixings and the increase of the experimental branching ratio for B_s→ μ⁺μ⁻, we update our 2016 analysis of various flavour observables in four 331 models, M1, M3, M13 and M16 based on the gauge group SU(3)_C× SU(3)_L× U(1)_X. These four models, which are distinguished by the quantum numbers, are selected among 24 331 models through their consistency with the electroweak precision tests and simultaneously by the relation C9NP=−bC10NP with 2 ≤ b ≤ 5, which after new result on B_s→ μ⁺μ⁻ from CMS is favoured over the popular relation C9NP=−C10NP predicted by several leptoquark models. In this context we investigate in particular the dependence of various observables on |V_cb|, varying it in the broad range [0.0386, 0.043], that encompasses both its inclusive and exclusive determinations. Imposing the experimental constraints from ε_K, ∆M_s, ∆M_d and the mixing induced CP asymmetries SψKS and SψKS, we investigate for which values of |V_cb| the four models can be made compatible with these data and what is the impact on B and K branching ratios. In particular we analyse NP contributions to the Wilson coefficients C₉ and C₁₀ and the decays B_s,d→ μ⁺μ⁻, K⁺→ π⁺νν¯ and K_L→ πνν¯. This allows us to illustrate how the value of |V_cb| determined together with other parameters of these models is infected by NP contributions and compare it with the one obtained recently under the assumption of the absence of NP in ε_K, ∆M_s, ∆M_d and SψKS.