Higher loop corrections to a Schwinger--Dyson equation

TL;DR

This paper investigates higher-loop corrections to Schwinger--Dyson equations within the supersymmetric Wess--Zumino model, showing that the asymptotic behavior of the perturbative series remains unaffected by these corrections.

Contribution

It introduces efficient methods to analyze dominant higher-loop divergences without full calculations, extending understanding of perturbative series in quantum field theory.

Findings

Higher-loop divergences do not alter the asymptotic behavior of the series.

Dominant contributions at three and four loops can be obtained without full evaluation.

The asymptotic nature of the perturbative series is stable under higher-loop corrections.

Abstract

We consider the effects of higherloop corrections to a Schwinger--Dyson equations for propagators. This is made possible by the efficiency of the methods we developed in preceding works, still using the supersymmetric Wess--Zumino model as a laboratory. We obtain the dominant contributions of the three and four loop primitive divergences at high order in perturbation theory, without the need for their full evaluations. Our main conclusion is that the asymptotic behavior of the perturbative series of the renormalization function remains unchanged, and we conjecture that this will remain the case for all finite order corrections.