Amplitudes triangulares quadridimensionais anômalas

Abstract

A detailed study of the anomalous triangles amplitudes AVV, VAV, VVA and AAA is presented. The investigation is implemented using a strategy alternative to the traditional methods of regularization, for the treatment of (linearly) divergent amplitudes. The referred method allows the explicit forms of the amplitudes involved to be obtained without these being modified in the intermediate steps. The labeling for the moments of the inner lines is taken as arbitrary and with that the presence of possibly ambiguous terms is clearly identified and preserved, unlike what occurs in traditional procedures. No divergent integral is, in fact, calculated. Only finite integrals are performed. This allows clear and transparent conclusions to be taken in scenarios where regular regularizations present difficulties in doing so. The so-called anomalous amplitudes are calculated and their symmetry properties (Ward identities and low energy limits) are verified. We then realize that Ward's identities can be violated by two types of terms derived from the divergent parts: the so-called anomalous and the ambiguous terms. The anomalous terms also violates the linearity of the integration operation (relations among Green's functions) and the ambiguous terms are tied to surface terms, as expected. We then find that the possible interpretations available for specifying the values for the remaining quantities from the divergent parts of the amplitudes do not allow adequate description of the amplitudes. The mathematically honest option provides preserved Ward identities, only after convenient choices of label for the moments of inner lines, which eliminate ambiguous terms. Such a prescription violates the prediction for the low energy limit. The adoption of a prescription for the preservation of the low energy limit, allowing the retainment of the anomalous terms, produces the desired results for the AVV amplitude but does not produce consistent results when applied equally to all amplitudes. We conclude that, with the usual elements of the perturbative calculus (amplitudes constructed from the Feynman rules), there is no possibility of obtaining physical amplitudes having the desired properties; free of ambiguities, preserving the Ward Identities and exhibiting the correct low energy limit and, in this context, the so-called anomalous amplitudes can be characterized as exceptions.