  Starting from the Schwinger--Dyson equation and the renormalization group
equation for the massless Wess--Zumino model, we compute the dominant
nonperturbative contributions to the anomalous dimension of the theory, which
are related by alien calculus to singularities of the Borel transform on
integer points. The sum of these dominant contributions has an analytic
expression. When applied to the two-point function, this analysis gives a tame
evolution in the deep euclidean domain at this approximation level, making
doubtful the arguments on the triviality of the quantum field theory with
positive \(\beta\)-function. On the other side, we have a singularity of the
propagator for time like momenta of the order of the renormalization group
invariant scale of the theory, which has a nonperturbative relationship with
the renormalization point of the theory. All these results do not seem to have
an interpretation in terms of semiclassical analysis of a Feynman path
integral.
