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^{[1]}^{[2]}^{[3]} may be associated with the local chiral SU(3)_{F} family symmetry introduced in 1980^{[4]} and further developed.^{[5]} ^{[6]}^{[7]}^{[8]}^{[9]}

## SU(3)

The choice of the SU(3)_{F} as the underlying family symmetry beyond the Standard Model appears 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 extended (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 have turned out to be at least partially discriminated.^{[clarification needed]}

## Applications

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^{[clarification needed]} flavor-changing transitions. The special sector of applications is related to a newly described 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.^{[10]}

## References

**^**Khlopov, Maxim Yu (1999).*Cosmoparticle Physics*. Singapore: World Scientific. p. 577. ISBN 9810231881.**^**King, S.F.; Ross, G.G. (November 2001). "Fermion masses and mixing angles from SU(3) family symmetry".*Physics Letters B*.**520**(3–4): 243–253. arXiv:hep-ph/0108112. Bibcode:2001PhLB..520..243K. doi:10.1016/S0370-2693(01)01139-X. S2CID 6510221.**^**Appelquist, Thomas; Bai, Yang; Piai, Maurizio (15 August 2005). "Breaking discrete symmetries in broken gauge theories".*Physical Review D*.**72**(3): 036005. arXiv:hep-ph/0506137. Bibcode:2005PhRvD..72c6005A. doi:10.1103/PhysRevD.72.036005. S2CID 119330778.**^**Chkareuli, J. L. (1 December 1980). "Quark-lepton families: from SU(5) to SU(8) symmetry" (PDF).*Soviet Journal of Experimental and Theoretical Physics Letters*.**32**(11): 671–674. Bibcode:1980JETPL..32..671C. ISSN 0021-3640. DESY-L-TRANS-253.**^**Wilczek, Frank (1983). "Thoughts on family symmetries preprint NSF-ITP-83-08".*AIP Conference Proceedings*.**96**: 313. Bibcode:1983AIPC...96..313W. doi:10.1063/1.33949.**^**Z.G. Berezhiani; J.L. Chkareuli (1983). "Quark-Lepton Families in a Model with SU(5)⊗SU(3) Symmetry".*Sov. J. Nucl. Phys*.**37**(4): 618.**^**Berezhiani, Z.G. (September 1983). "The weak mixing angles in gauge models with horizontal symmetry — A new approach to quark and lepton masses".*Physics Letters B*.**129**(1–2): 99–102. Bibcode:1983PhLB..129...99B. doi:10.1016/0370-2693(83)90737-2.**^**P. Ramond (1998). "The Family Group in Grand Unified Theories". arXiv:hep-ph/9809459. Bibcode:1998hep.ph....9459R. Cite journal requires`|journal=`

(help)**^**Chkareuli, J.L.; Froggatt, C.D.; Nielsen, H.B. (April 2002). "Minimal mixing of quarks and leptons in the SU(3) theory of flavour".*Nuclear Physics B*.**626**(1–2): 307–343. arXiv:hep-ph/0109156. Bibcode:2002NuPhB.626..307C. CiteSeerX 10.1.1.346.7711. doi:10.1016/S0550-3213(02)00032-9. S2CID 9421103.**^**Spergel, David; Pen, Ue-Li (20 December 1997). "Cosmology in a String-Dominated Universe".*The Astrophysical Journal*.**491**(2): L67–L71. arXiv:astro-ph/9611198. Bibcode:1997ApJ...491L..67S. doi:10.1086/311074. S2CID 388418.