Abstract
We show that {ital L}{sub 1}={ital L}{sub {ital e}}{minus}{ital L}{sub {mu}}, {ital L}{sub 2}={ital L}{sub {ital e}}{minus}{ital L}{sub {tau}}, and {ital L}{sub 3}={ital L}{sub {mu}}{minus}{ital L}{sub {tau}} (where {ital L}{sub {ital e},{mu},{tau}} are the family lepton numbers) are anomaly-free and can thus be gauged. Three simple theories featuring a flavor-conserving second {ital Z} boson ({ital Z}{sub 1,2,3}{sup {prime}}) result. Bounds on the {ital Z}{sub {ital i}}{sup {prime}} coupling constant ({ital g}{sub {ital i}}{sup {prime}}) and mass are derived. The mass of {ital Z}{sub 1}{sup {prime}} has a lower bound of 60--150 GeV at 90% confidence level for reasonable values of {ital g}{sub 1}{sup {prime}}. The mass of {ital Z}{sub 2}{sup {prime}} has a best-fit value of about 60 GeV. The physics of these bosons in the KEK TRISTAN and CERN LEP window of 63--87 GeV is discussed. Constraints on {ital Z}{sub 3}{sup {prime}} interactions are derived from ({ital g}{minus}2){sub {mu}}.
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