Gauge-independent Brout-Englert-Higgs mechanism and Yang-Mills theory with a gauge-invariant gluon mass term

TL;DR

This paper presents a gauge-independent framework for the Brout-Englert-Higgs mechanism in Yang-Mills theory with a fundamental scalar, establishing a gauge-invariant mass term and connecting Higgs and confinement regimes.

Contribution

It introduces a gauge-invariant description of mass generation in Yang-Mills theory with a fundamental scalar, extending previous work with adjoint scalars, and relates it to lattice gauge theory concepts.

Findings

Gauge-invariant mass term derived from gauge-scalar model

Continuum realization of Fradkin-Shenker continuity

Gauge-independent approach to confinement investigation

Abstract

For the Yang-Mills theory coupled to a single scalar field in the fundamental representation of the gauge group, we present a gauge-independent description of the Brout-Englert-Higgs mechanism by which massless gauge bosons acquire their mass. The new description should be compared with the conventional gauge-dependent description relying on the spontaneous gauge symmetry breaking due to a choice of the non-vanishing vacuum expectation value of the scalar field. In this paper we focus our consideration on the fundamental scalar field which extends the previous work done for the Yang-Mills theory with an adjoint scalar field. Moreover, we show that the Yang-Mills theory with a gauge-invariant mass term is obtained from the corresponding gauge-scalar model when the radial degree of freedom (length) of the scalar field is fixed. The result obtained in this paper is regarded as a continuum realization of the Fradkin-Shenker continuity and Osterwalder-Seiler theorem for the complementarity between Higgs regime and Confinement regime which was given in the gauge-invariant framework of the lattice gauge theory. Moreover, we discuss how confinement is investigated through the gauge-independent Brout-Englert-Higgs mechanism by starting with the complementary gauge-scalar model.