Flavor Symmetry and Vacuum Aligned Mass Textures

Abstract

The mass matrix forms of quarks and leptons are discussed in theory with permutation flavor symmetry. The structure of scalar potential is analyzed in case that electroweak doublet Higgs fields have non-trivial flavor symmetry charges. We find that realistic forms of mass matrices are obtained dynamically in the vacuum of the theory, where some of Higgs bosons have vanishing expectation values which lead to vanishing elements in quark and lepton mass matrices. Mass textures are realized in the true vacuum and their positions are controlled by flavor symmetry. An interesting point is that, due to the flavor group structure, the up and down quark mass matrices are automatically made different in the vacuum, which lead to non-vanishing generation mixing. It is also discussed that flavor symmetry is needed to be broken in order not to have too light scalars. The lower bounds of Higgs masses are derived from the experimental data of flavor-changing rare processes such as the neutral K meson mixing.