CP symmetry and fermion masses in O(10) grand unification models

Abstract

O(10) grand unification models which do not necessarily have an extra global symmetry are discussed, taking the model with one 10-plet in the Yukawa sector as an example. A strong correlation between mass ratios and CP is found. The mass relation $m_t/m_b=v_u/v_d$ is recovered when $G_W=0$; and another special relation $m_t/m_b=G_E/G_W$ appears when $v_d=0$, where $G_{E,W}$ are Yukawa coupling constants and $v_{u,d}$ are VEVs. To facilitate this discussion, a set of $O(10)$ $\gamma$- matrices is offered based on a physical representation of the spinors and that of the vector of the $SO(10)$ group. Flavor changing neutral currents in such models are also discussed.