  When we try to consider family gauge bosons with a lower energy scale, a
major obstacle is constraints from the observed $P^0$-$\bar{P}^0$ mixings
($P^0=K^0, D^0, B^0,B^0_s$). Against such a conventional view, we point out
that, in a U(3) family gauge boson model, the bosons are harmless to any
$P^0$-$\bar{P}^0$ mixings independently of explicit values of the family
mixings, if masses $M_{ij}$ of the gauge bosons $A_i^{\ j}$ ($i,j$ are family
indexes) satisfy a relation $2/M_{ij}^2=1/M_{ii}^2 +1/M_{jj}^2$. If such the
case can be realized together with an inverted mass hierarchy $M_{33}^2 \ll
M_{22}^2 \ll M_{11}^2$, we can consider family gauge bosons with a considerably
lower scale, so that we can expect rich signs for family gauge bosons in a TeV
scale.
