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In this model, of nine U(3) family gauge bosons $A_i^{\\ j}$, those with $i=j$ are considerable heavy compared with those with $i \\neq j$, so that the model can be released from severe constraints due to the observed $K^0$-$\\bar{K}^0$ mixing, and so on. We speculate that the lightest gauge boson is $A_2^{\\ 3}$ and its mass is of $2 - 6$ TeV. Thereby, visible effects of the family gauge bosons are discussed. 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