Yukawa Textures from Family Symmetry and Unification

Abstract

In this letter, we show how the combination of both a gauged U(1)_X family symmetry and an extended vertical gauge symmetry in a single model, allows for the presence of additional Clebsch texture zeroes in the fermion mass matrices. This leads to new structures for the textures, with increased predictivity, as compared to schemes with enhanced family symmetries only. We illustrate these ideas in the context of the Pati-Salam gauge group SU(4)xSU(2)_LxSU(2)_R$ supplemented by a U(1)_X gauged family symmetry. In the case of symmetric mass matrices, two of the solutions of Ramond, Roberts and Ross that may not be obtained by family symmetries only, are accurately reproduced. For non-symmetric textures, new structures arise in models of this type. To distinguish between the solutions in this latter case, we performed a numerical fit to the charged fermion mass and mixing data. The best solution we found allows a fit with a total chi^2 of 0.39, for three degrees of freedom.