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

Abstract

Abstract Motivated by the improved results from the HPQCD lattice collaboration on the hadronic matrix elements entering ∆Ms,d in $$ {B}_{s,d}^0-{\overline{B}}_{s,d}^0 $$ B s , d 0 − B ¯ s , d 0 mixings and the increase of the experimental branching ratio for Bs→ 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 $$ {C}_9^{\textrm{NP}}=-{bC}_{10}^{\textrm{NP}} $$ C 9 NP = − bC 10 NP with 2 ≤ b ≤ 5, which after new result on Bs→ μ+μ− from CMS is favoured over the popular relation $$ {C}_9^{\textrm{NP}}=-{C}_{10}^{\textrm{NP}} $$ C 9 NP = − C 10 NP predicted by several leptoquark models. In this context we investigate in particular the dependence of various observables on |Vcb|, varying it in the broad range [0.0386, 0.043], that encompasses both its inclusive and exclusive determinations. Imposing the experimental constraints from εK, ∆Ms, ∆Md and the mixing induced CP asymmetries $$ {S}_{\psi {K}_S} $$ S ψ K S and $$ {S}_{\psi {K}_S} $$ S ψ K S , we investigate for which values of |Vcb| 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 Bs,d→ μ+μ−, $$ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $$ K + → π + ν ν ¯ and $$ {K}_L\to {\pi}^0\nu \overline{\nu} $$ K L → π 0 ν ν ¯ . This allows us to illustrate how the value of |Vcb| 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 εK, ∆Ms, ∆Md and $$ {S}_{\psi {K}_S} $$ S ψ K S .