We present a supersymmetric grand unification model based on SO(10) group with $S4$ flavor symmetry. In this model, the fermion masses are from Yukawa couplings involving $\mathbf{10}$ and $\overline{\mathbf{126}}$ Higgs multiplets and the flavor structures of mass matrices of both quarks and leptons are determined by spontaneously broken $S4$. This model fits all of the masses and mixing angles of the quarks and leptons. For the most general $CP$-violation scenario, this model gives $\sin {\theta }_{13}$ a wide range of values from zero to the current bound with the most probable values 0.02–0.09. With certain assumptions where leptonic phases have same $CP$-violation source as CKM phase, one gets a narrower range 0.03–0.06 for $\sin {\theta }_{13}$ with the most probable values 0.04–0.08. This model gives leptonic Dirac $CP$ phase the most probable values 2–4 radians in the general $CP$-violation case.

• Received 14 August 2006

DOI:https://doi.org/10.1103/PhysRevD.74.115005