Infrared singularities and massive fields

TLDR

Gauge theories employing the Higgs mechanism aim to unify particle forces, and the linear and nonlinear σ models are related in the mσ→∞ limit. The study investigates how heavy fields influence the infrared structure of unbroken non‑Abelian gauge theories and examines the resulting mass‑shell behavior of fermion propagators via a decoupling theorem applied to general renormalizable theories. The authors apply the decoupling theorem to a simple gauge‑meson–fermion model and to general renormalizable theories to analyze infrared behavior. In a simple gauge‑meson–fermion model, heavy fields decouple at low momenta, contributing only to renormalization effects.

Abstract

We examine some problems associated with the low-momentum behavior of gauge theories and other renormalizable field theories. Our main interest is in the infrared structure of unbroken non-Abelian gauge theories and how this is affected by the presence of other heavy fields coupled to the massless gauge fields. It is shown in the context of a simple model of gauge mesons coupled to massive fermions that the heavy fields decouple at low momenta except for their contribution to renormalization effects. This result is used to discuss the mass-shell structure of the fermion propagator. The decoupling theorem is then stated for a general renormalizable theory and applied to some interesting examples. One is a more general gauge theory which makes use of the Higgs mechanism and attempts to unify the elementary particle forces. Another is the connection of the linear and nonlinear $\ensuremath{\sigma}$ models in the limit ${m}_{\ensuremath{\sigma}}\ensuremath{\rightarrow}\ensuremath{\infty}$.