Analysis of right-handed Majorana neutrino mass in an $SU(4)\times SU(2{)}_L\times SU(2{)}_R$ Pati--Salam model with democratic texture

Abstract

In this paper, we attempt to build an unified model with democratic texture, that have some unification between $Y_{\nu }$ and $Y_u$. Since the $S_{3L}\times S_{3R}$ flavor symmetry is chiral, the unified gauge group is assumed to be Pati-Salam type $SU(4{)}_c\times SU(2{)}_L\times SU(2{)}_R$. The flavor symmetry breaking scheme is considered to be $S_{3L}\times S_{3R}\to S_{2L}\times S_{2R}\to 0$. In this picture, the four-zero texture is desirable for realistic mass and mixings. This texture is realized by a specific representation for the second breaking of the $S_{3L}\times S_{3R}$ 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 $Y_{\nu }\simeq Y_u$ 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 fine-tunings of parameters.

Comments: 14 pages, 3 tables, 8 figures, Final version for publication in Physical Review D