Tests on the Hierarchy of Trilinear and Quadrilinear Weak Bosons Couplings at the NLC and Comparison with the LHC/SSC

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I first review a few basic guiding principles that lead to the notion of a hierarchy of couplings in searches of New Physics involving weak bosons processes. The hierarchies within a linear and a non-linear realization of symmetry breaking are compared to the usual phenomenological parameterization of the WWV vertex. Limits that one expects to obtain at the NLC(500GeV) and LHC/SSC on the tri-linear and quadri-linear anomalous W couplings are compared. The cleanness of an gives the NLC a clear advantage in constraining the tri-linear couplings. However, with ``only" 500GeV, the is not competitive with pp colliders in probing the quadri-linear couplings. An interpretation in terms of scalar-like and vector-like models is given and I argue that in the presence of a light (or ``not-so-heavy") Higgs, the New Physics affecting the W sector would be easier to pin-down with a moderate energy machine.