The Measurement of Tri-Linear Gauge Boson Couplings at e^+e^- Colliders

We describe a detailed study of the process $e^+e^- \to \ell\nu_\ell q \bar{q}$ and the measurement of tri-linear gauge boson couplings (TGV's) at LEP200 and at a 500~GeV and 1~TeV NLC. We included all tree level Feynman diagrams contributing to the four-fermion final states including gauge boson widths and non-resonance contributions. We employed a maximum likelihood analysis of a five dimensional differential cross section of angular distributions. This approach appears to offer an optimal strategy for measurement of TGV's. LEP200 will improve existing measurements of TGV's but not enough to see loop contributions of new physics. Measurements at the NLC will be roughly 2 orders of magnitude more precise which would probe the effects of new physics at the loop level.