Uses and abuses of effective Lagrangians

Motivated by past and recent analyses we critically reexamine the use of effective Lagrangians in the literature to constrain new physics and to determine the "physics reach" of future experiments. We demonstrate that many calculations, such as those involving anomalous trilinear gauge-boson couplings, either considerably overestimate loop-induced effects or give ambiguous answers. The source of these problems is the use of cutoffs to evaluate the size of such operators in loop diagrams. In contrast with other critiques of these loop estimates, we prove that the inclusion of nonlinearly realized gauge invariance into the low-energy Lagrangian is irrelevant to this conclusion. We use an explicit example using known multi-Higgs-boson physics above the weak scale to underline these points. We show how to draw conclusions regarding the nature of the unknown high-energy physics without making reference to low-energy cutoffs.