Family symmetries

In particle physics, family symmetries or horizontal symmetries are various discrete, global, or local symmetries between quark-lepton families or generations. While being conceptually useful, these symmetries are not yet finally confirmed. Some potentially relevant option considered in the literature is the local chiral SU(3)_F symmetry introduced by J.L. Chkareuli in 1980 and further developed.

The choice of the SU(3)_F as the underlying family symmetry beyond the Standard Model may be related to the following issues: (i) It provides a natural explanation of the number three of observed quark-lepton families; (ii) Its local nature conforms with the other local symmetries of the Standard Model, such as the weak isospin symmetry SU(2)_W or color symmetry SU(3)_C; (iii) Its chiral nature, according to which both left-handed and right-handed fermions are proposed to be fundamental triplets of the SU(3)_F symmetry, provides the hierarchical mass spectrum of quark-lepton families as a result of a spontaneous symmetry breaking; (iv) It admits a natural unification with conventional Grand unified theories (GUTs) in a direct product form, such as SU(5)⊗SU(3)_F, SO(10)⊗SU(3)_F or E(6)⊗SU(3)_F, and also as a subgroup of the family unified SU(8) or E(8) GUTs; (v) It has a straightforward extension to the supersymmetric Standard Model and GUTs. With these natural criteria accepted, other family symmetry candidates are turned out to be discriminated.

Among the applications of the SU(3)_F symmetry, the most interesting ones are the realistic description of the quark and lepton masses and mixings, neutrino masses and oscillations, rare processes etc. with a natural suppression of all dangerous flavor-changing transitions. The special sector of applications is related to a new type of topological defects - flavored cosmic strings and monopoles appearing during the spontaneous violation of the SU(3)_F which may be considered as possible candidates for the cold dark matter in the Universe.

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