Abstract
The off-shell and on-shell asymptotic behaviors of the three-point vertex function are examined for renormalizable theories with anomalous dimensions. A general argument based on the conformal-operator expansion is given, according to which the off-shell vertex function has the same asymptotic behavior as the on-shell vertex function if the field of minimal dimension related to the particle has dimension less than 2. If the dimension is larger than 2 the two asymptotic behaviors differ. This result is verified by an explicit calculation on a model with anomalous dimensions, and it is shown to be related to the occurrence of shadow singularities in a three-point function. A comparison with the different situation in superrenormalizable theories is given.
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