The $S_3$ symmetry: Flavour and texture zeroes

Abstract

We use the permutational symmetry group $S_3$ as a symmetry of flavour, which leads to a unified treatment of masses and mixings of the quarks and leptons. In this framework all mass matrices of the fermions in the theory have the same form with four texture zeroes of class of I. Also, with the help of six elements of real matrix representation of $S_3$ as transformation matrices of similarity classes, we make a classification of the sets of mass matrices with texture zeroes in equivalence classes. This classification reduce the number of phenomenologically viable textures for the non-singulars mass matrices of $3\times 3$, from thirty three down to only eleven independent sets of matrices. Each of these sets of matrices has exactly the same physical content.

Presented at XIV Mexican School on Particles and Fields, 4-13 November 2010, Morelia México

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Cited by in corpus (10)

• Quark sector of S3 models: classification and comparison with experimental data
• The $S_3$ flavour symmetry: Neutrino masses and mixings
• Non-Minimal Flavored ${\mathbf{S}}_3\otimes {\mathbf{Z}}_2$ Left-Right Symmetric Model
• Super Flavorsymmetry with Multiple Higgs Doublets
• Majorana neutrino mass matrices with three texture zeros and the sterile neutrino
• Flavored Non-Minimal Left-Right Symmetric Model Fermion Masses and Mixings
• Neutrino mass determination from a four-zero texture mass matrix
• The minimal adjoint-SU(5)xZ_4 GUT model
• Nearest-Neighbour-Interactions from a minimal discrete flavour symmetry within SU(5) Grand Unification
• A non-renormalizable neutrino mass model with ${\mathbf{S}}_3\otimes {\mathbf{Z}}_2$ symmetry