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Abstract Motivated by the improved results from the HPQCD lattice collaboration on the hadronic matrix elements entering ∆M s,d in B s , d 0 − B ¯ s , d 0 $$ {B}_{s,d}^0-{\overline{B}}_{s,d}^0 $$ 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 C 9 NP = − bC 10 NP $$ {C}_9^{\textrm{NP}}=-{bC}_{10}^{\textrm{NP}} $$ with 2 ≤ b ≤ 5, which after new result on B s → μ + μ − from CMS is favoured over the popular relation C 9 NP = − C 10 NP $$ {C}_9^{\textrm{NP}}=-{C}_{10}^{\textrm{NP}} $$ 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 S ψ K S $$ {S}_{\psi {K}_S} $$ and S ψ K S $$ {S}_{\psi {K}_S} $$ , 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 C 9 and C 10 and the decays B s,d → μ + μ − , K + → π + ν ν ¯ $$ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $$ and K L → π 0 ν ν ¯ $$ {K}_L\to {\pi}^0\nu \overline{\nu} $$ . 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 S ψ K S $$ {S}_{\psi {K}_S} $$ . |
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