An SO(10) model with adjoint fermions for double seesaw neutrino masses

Abstract

An $SO(10)$ model where the $10_H$ and $120_H$ representations are used for generating fermion masses is quite predictive, though due to the absence of $SU(2{)}_{L,R}$ triplet/singlet fields it cannot give rise to neutrino masses through the usual type-I or type-II seesaw mechanisms. In this paper for neutrino masses we propose an extension of such an $SO(10)$ model by adding fermions in the adjoint representation (${45}_F$) and a symmetry breaking scalar ${\overline{16}}_H$. The ${\overline{16}}_H$ couples the adjoint fermions to the standard fermions in ${16}_F$ and induces neutrino masses through the `double seesaw' mechanism. In order to enhance the predictivity of the model we impose $\mu -\tau$ flavour symmetry on the Yukawa matrices for $10_H$ and ${\overline{16}}_H$ whereas for the $120_H$ it is assumed to be antisymmetric. We discuss the conditions that the mass matrices must obey so that the model can reproduce the tri-bimaximal mixing pattern.

13 pages, 1 figure

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