Asymptotic behavior in a model with Yukawa interaction from Schwinger-Dyson equations

TL;DR

This paper investigates the asymptotic behavior of a Yukawa interaction model using Schwinger-Dyson equations, proposing that full solutions may avoid non-physical singularities like the Landau pole and exhibit specific asymptotic properties.

Contribution

It introduces a method to analyze the full solutions of Schwinger-Dyson equations in a Yukawa model, suggesting they can be free from non-physical singularities and have a distinct asymptotic form.

Findings

Full solutions may be free from Landau poles.

Asymptotic behavior characterized by a logarithmic decay.

Approximate solutions support positivity of key constants.

Abstract

A system of Schwinger-Dyson equations for pseudoscalar four-dimensional Yukawa model in the two-particle approximation is investigated. The simplest iterative solution of the system corresponds to the mean-field approximation (or, equivalently, to the leading order of 1/N-expansion) and includes a non-physical Landau pole in deep-Euclidean region for the pseudoscalar propagator $\Delta$. It is argued, however, that a full solution may be free from non-physical singularities and has the self-consistent asymptotic behavior $p^2_e\Delta\simeq C\,\log^{-4/5}\frac{p^2_e}{M^2}$. An approximate solution confirms the positivity of $C$ and the absence of Landau pole.