Loops , Cutoffs and Anomalous Gauge Boson Couplings †

We discuss several issues regarding analyses which use loop calculations to put constraints on anomalous trilinear gauge boson couplings (TGC's). Many such analyses give far too stringent bounds. This is independent of questions of gauge invariance, contrary to the recent claims of de Rújula et. al., since the lagrangians used in these calculations are gauge invariant, but the SU (2) L × U (1) Y symmetry is nonlinearly realized. The real source of the problem is the incorrect use of cutoffs – the cutoff dependence of a loop integral does not necessarily reflect the true dependence on the heavy physics scale M. If done carefully, one finds that the constraints on anomalous TGC's are much weaker. We also compare effective lagrangians in which SU (2) L × U (1) Y is realized linearly and nonlinearly, and discuss the role of custodial SU (2) in each formulation.