An SO(10)XS4 Model of Quark-Lepton Complementarity

The present observations of Cabbibo angle and solar mixing angle satisfy the empirical relation called Quark-Lepton Complementarity(QLC), namely $\theta_{12}^l\sim \pi/4-\theta_C$. It suggests the existence of correlation between quarks and leptons which is supported by the idea of grand unification. We propose a specific ansatz for the structure of Yukawa matrices in SO(10) unified theory which leads to such relation if neutrinos get masses through type-II seesaw mechanism. Viability of this ansatz is discussed through detailed analysis of fermion masses and mixing angles all of which can be explained in a model which uses three Higgs fields transforming as 10 and one transforming as $\bar{126}$ representations under SO(10). It is shown that the proposed ansatz can be derived from an extended model based on the two pairs of 16-dimensional vector-like fermions and an $S_4$ flavor symmetry. The model leads to the lepton mixing matrix that is dominantly bimaximal with ${\cal O}(\theta_C)$ corrections related to quark mixing. A generic prediction of the model is the reactor angle $\theta_{13}^l\sim \theta_C/\sqrt{2}$ which is close to its present experimental upper bound.