Model for a Light Z' Boson

A model of a light $Z'$ boson is constructed and phenomenological bounds are derived. This $Z'$ boson arises from a very simple extension to the Standard Model, and it is constrained to be light because the vacuum expectation values which generate its mass also break the electroweak gauge group. It is difficult to detect experimentally because it couples exclusively or primarily (depending on symmetry breaking details) to second and third generation leptons. However, if the $Z'$ boson is sufficiently light, then there exists the possibility of the two-body decay $\tau \rightarrow \mu Z'$ occuring. This will provide a striking signature to test the model.