A nonperturbative construction of massive Yang-Mills fields without Higgs fields

TL;DR

This paper constructs a nonperturbative, gauge-invariant massive vector field in a Higgsless Yang-Mills model, providing insights into gluon and ghost propagator decoupling in QCD.

Contribution

It introduces a nonlinear, local transformation to define a massive vector field in the Curci-Ferrari model, maintaining gauge invariance without Higgs fields.

Findings

Constructed a gauge-invariant massive vector field in a nonperturbative manner.

Formulated a local mass term and condensate invariant under key symmetries.

Provided a framework for understanding decoupling solutions in QCD.

Abstract

In order to understand the so-called decoupling solution for gluon and ghost propagators in QCD, we give a nonperturbative construction of a massive vector field describing a non-Abelian massive spin-one particle, which has the correct physical degrees of freedom and is invariant under a modified Becchi-Rouet-Stora-Tyutin transformation, in a massive Yang-Mills model without the Higgs field, i.e., the Curci-Ferrari model. The resulting non-Abelian massive vector boson field is written using a nonlinear but local transformation from the original fields in the Curci-Ferrari model. As an application, we write down a local mass term for the Yang-Mills field and a dimension-two condensate, which are exactly invariant under the modified Becchi-Rouet-Stora-Tyutin transformation, Lorentz transformation and color rotation.