Minimal mixing of quarks and leptons in the SU(3) theory of flavour

Abstract

We argue that flavour mixing, both in the quark and lepton sector, follows the minimal mixing pattern, according to which the whole of this mixing is basically determined by the physical mass generation for the first family of fermions. So, in the chiral symmetry limit when the masses of the lightest (u and d) quarks vanish, all the quark mixing angles vanish. This minimal pattern is shown to fit extremely well the already established CKM matrix elements and to give fairly distinctive predictions for the as yet poorly known ones. Remarkably, together with generically small quark mixing, it also leads to large neutrino mixing, provided that neutrino masses appear through the ordinary "see-saw" mechanism. It is natural to think that this minimal flavour mixing pattern presupposes some underlying family symmetry, treating families of quarks and leptons in a special way. Indeed, we have found a local chiral SU(3) F family symmetry model which leads, through its dominant symmetry breaking vacuum configuration, to a natural realization of the proposed minimal mechanism. It can also naturally generate the quark and lepton mass hierarchies. Furthermore spontaneous CP violation is possible, leading to a maximal CP violating phase δ = π 2 , in the framework of the MSSM extended by a high-scale SU(3) F chiral family symmetry.

Constraining supersymmetric models fromBd−Bdmixing and theBGabrielli1, Khalil2 2003Phys. Rev. D261130View full textAdd to dashboardCite

“…It has been shown that these models are free from the EDM constraints and the off-diagonal phases lead to significant contribution to the observed CP violation in the kaon system, in particular to ε ′ /ε [5]. Let us consider, for instance, the case of Hermitian and hierarchical quark mass matrices with three zeros [21] …”

The origin of mass

“…The proportionality condition (43) is not so easy to generate from an underlying symmetry beyond the SM, but it is possible to realise it in a local chiral SU(3) family symmetry model [30].…”

“…3 Non-abelian SU(2) and SU(3) flavour symmetry groupshave also been considered, see for example Refs. [30,[40][41][42] for some recent examples. and obtain a realistic charged fermion spectrum in an SMG £ Uð1Þ f £ Uð1Þ f 0 model 4 [45].…”

Neutrino mass matrices from two zero 3 × 2 Yukawa textures and minimal d = 5 entries

“…It is also desirable to get texture zeros with the help of flavor symmetries in a spirit of Refs. [18], [32], [66][67][68][69][70][71][72][73][74][75][76][77][78]. These and related issues will be addressed elsewhere.…”