Can Mass of the Lightest Family Gauge Boson be of the Order of TeV?

The observed sign of a deviation from the $e$-$\mu$ universality in tau decays suggests family gauge bosons with an inverted mass hierarchy. Under the constraints from the observed $K^0$-$\bar{K}^0$ and $D^0$-$\bar{D}^0$ mixing, we investigate a possibility that a mass $M_{33}$ of the lightest gauge boson $A_3^3$ which couples with only the third generation quarks and leptons is of the order of TeV. It is concluded that $M_{33} \sim 1$ TeV is possible if we adopt a specific model phenomenologically.