The Mass Difference of F-bar{F} with SO(3) Family Gauge Symmetry

As a simple extension, a non-Abelian family gauge symmetry SO(3), as well as three family Majorana neutrinos, was introduced to explain the tri-bimaximal mixing matrix of neutrinos. We discuss the effect of the possible SO(3) family gauge interaction to the mass differences of $K-\bar{K}$, $B_d-\bar{B}_d$, $B_s-\bar{B}_s$ and $D-\bar{D}$, and get the constrains to the new gauge bosons.