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For the Yang-Mills theory coupled to a single scalar field in the fundamentalrepresentation of the gauge group, we present a gauge-independent descriptionof the Brout-Englert-Higgs mechanism by which massless gauge bosons acquiretheir mass. The new description should be compared with the conventionalgauge-dependent description relying on the spontaneous gauge symmetry breakingdue to a choice of the non-vanishing vacuum expectation value of the scalarfield. In this paper we focus our consideration on the fundamental scalar fieldwhich extends the previous work done for the Yang-Mills theory with an adjointscalar field. Moreover, we show that the Yang-Mills theory with agauge-invariant mass term is obtained from the corresponding gauge-scalar modelwhen the radial degree of freedom (length) of the scalar field is fixed. Theresult obtained in this paper is regarded as a continuum realization of theFradkin-Shenker continuity and Osterwalder-Seiler theorem for thecomplementarity between Higgs regime and Confinement regime which was given inthe gauge-invariant framework of the lattice gauge theory. Moreover, we discusshow confinement is investigated through the gauge-independentBrout-Englert-Higgs mechanism by starting with the complementary gauge-scalarmodel.

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