Infrared Behaviour of Landau Gauge Yang-Mills Theory with a Fundamentally Charged Scalar Field

TL;DR

This paper investigates the infrared properties of Yang-Mills theory coupled with a fundamental scalar field using Dyson-Schwinger equations, revealing scaling behaviors and the significance of kinematic singularities especially for massive scalars.

Contribution

It provides a detailed analysis of the infrared scaling solutions of scalar Yang-Mills theory, highlighting the role of kinematic singularities and extending understanding beyond massless cases.

Findings

Scaling solutions similar to QCD for scalar Yang-Mills theory

Kinematic singularities are crucial for massive scalars

Uniform limit describes infrared behavior for massless scalars

Abstract

The infrared behaviour of the n-point functions of a Yang-Mills theory with a charged scalar field in the fundamental representation of SU(N) is studied in the formalism of Dyson-Schwinger equations. Assuming a stable skeleton expansion solutions in form of power laws for the Green functions are obtained. For a massless scalar field the uniform limit is sufficient to describe the infrared scaling behaviour of vertices. Not taking into account a possible Higgs-phase it turns out that kinematic singularities play an important role for the scaling solutions of massive scalars. On a qualitative level scalar Yang-Mills theory yields similar scaling solutions as recently obtained for QCD.