Analysis of the right-handed Majorana neutrino mass in an SU(4) × SU(2)_L × SU(2)_R Pati-Salam model with democratic texture

摘要

In this paper, we attempt to build a unified model with the democratic texture, that has some unification between up-type Yukawa interactions Y_v and Y_u. Since the S_(3L) × S_(3R) flavor symmetry is chiral, the unified gauge group is assumed to be Pati-Salam type SU(4)_c × SU(2)_L × SU(2)_R. The breaking scheme of the flavor symmetry is considered to be S_(3L) × S_(3R) → S_(2L) × S_(2R) → 0. In this picture, the four-zero texture is desirable for realistic masses and mixings. This texture is realized by a specific representation for the second breaking of the S_(3L) × S_(3R) flavor symmetry. Assuming only renormalizable Yukawa interactions, type-Ⅰ seesaw mechanism, and neglecting CP phases for simplicity, the right-handed neutrino mass matrix M_R can be reconstructed from low energy input values. Numerical analysis shows that the texture of M_R basically behaves like the “waterfall texture.” Since M_R tends to be the “cascade texture” in the democratic texture approach, a model with type-Ⅰ seesaw and up-type Yukawa unification Y_v - Y_u basically requires fine-tunings between parameters. Therefore, it seems to be more realistic to consider universal waterfall textures for both Y_f and M_R, e.g., by the radiative mass generation or the Froggatt-Nielsen mechanism. Moreover, analysis of eigenvalues shows that the lightest mass eigenvalue M_(R1) is too light to achieve successful thermal leptogenesis. Although the resonant leptogenesis might be possible, it also requires finetunings of parameters.