Asymptotic behavior and critical coupling in scalar Yukawa model

TL;DR

This paper analyzes the asymptotic behavior of the phion propagator in a scalar Yukawa model, revealing a critical coupling where the behavior changes significantly in the deep Euclidean region.

Contribution

It provides an analytical study of the asymptotic behavior and critical coupling in the scalar Yukawa model using the leading order of the $1/N$ expansion.

Findings

Identification of a critical coupling constant.

Change in asymptotic behavior near the critical point.

Insights into the model's behavior in the Euclidean region.

Abstract

The solution of the equation for the phion propagator in the leading order of the $1/N$ -- expansion for a vector-matrix model with interaction $g(\phi_a)^*\phi_b\chi_{ab}$ in four dimensions shows a change of the asymptotic behavior in the deep Euclidean region in a vicinity of a certain critical value of the coupling constant.