Hint of family gauge bosons with an inverted mass hierarchy from the observed tau decays

The present data show a deviation from the e-m universality $\epsilon \equiv {\epsilon }_{\mu }-{\epsilon }_e=0.0020\pm 0.0016$. If we consider that the deviation originates in a mass difference between family gauge bosons $A_3^2$ and $A_3^1$, the sign of the observed deviation suggests ${\epsilon }_{\mu }>{\epsilon }_e$, i.e. mass relation $M\left(A_3^2\right)<M\left(A_3^1\right)$. A possibility of a family gauge boson model with an inverted mass hierarchy is discussed. It is concluded that, contrary to a conventional expectation, it is possible to take a considerably lower mass $M\left(A_3^3\right)\sim 1\text{TeV}$, even the constraint from $K^0-{\overline{K}}^0$ mixing is taken into consideration.