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A model with flavor-triplet Higgs scalars \phi_i (i=1,2,3)is investigatedunder a permutation symmetry S_3 and its symmetry breaking. A possible S_3breaking form of the Higgs potential whose vacuum expectation values v_i=<\phi_i> satisfy a relation v_1^2 +v_2^2 +v_3^2 ={2/3}(v_1 +v_2 +v_3)^2 isinvestigated, because if we suppose a seesaw-like mass matrix model M_e = mM^{-1} m with m_{ij} \propto \delta_{ij} v_i and M_{ij} \propto \delta_{ij},such a model can lead to the well-known charged lepton mass relation m_e +m_\mu+m_\tau = {2/3} (\sqrt{m_e}+\sqrt{m_\mu} +\sqrt{m_\tau})^2.Comment: 7 pages, 1 figure, final version to appear in PR

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Permutation symmetry<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi mathvariant="normal">S</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>and vacuum expectation value structure of flavor-triplet Higgs scalars

Permutation symmetryS3and vacuum expectation value structure of flavor-triplet Higgs scalars