Leptonic Flavor Violations in the Presence of an Extra Z

Gauged extensions [$SU(2{)}_L\otimes U(1{)}_Y\otimes U(1{)}_X$] of the standard $SU(2{)}_L\otimes U(1{)}_Y$ model obtained without extending the fermion content of the model are studied. Models that are possible when $U(1{)}_X$ is identified with some combination of the family lepton numbers are systematically classified. Most of these contain flavor violations in the leptonic sector. These flavor violations are correlated to the mixing of the $U(1{)}_X$ gauge boson $Z^{\mathrm{\prime }}$ with the ordinary $Z$ in the models considered here. Detailed phenomenological implications of a typical model are discussed. Constraints on the $Z^{\mathrm{\prime }}$ mass and the $Z$-$Z^{\mathrm{\prime }}$ mixing following from ({\em i}) the observations at LEP, ({\em ii}) rare processes like $Z\to e\tau$ and ({\em iii}) flavor violating $\tau$ decays are presented. It is found that the constraints coming from the LEP allows the rare processes like $\tau \to eee$ at the level of the present limits on its branching ratio. Thus the future search could either improve on the existing LEP limits or would find such flavor violating decays.