Natural and model-independent conditions for evading the limits on the scale of new physics

I argue that the limits on this quantity obtained using model-independent parameterizations contain an tacit assumption that could be invalidated under a variety of situations. As a specific example, existing limits on $\Lambda $ would be decreased by at least an order of magnitude if the underlying physics has a symmetry under which all \sm particles are singlets but none of the heavy excitations are. In this case current experiments would see no clear indications of new physics using precision measurements while future colliders capable of directly producing the heavy particles would only occur in pairs.