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We consider Yang–Mills theory with a compact gauge group <i>G</i> on Minkowski space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> and compare the introduction of masses of gauge bosons using the Stueckelberg and Higgs mechanisms. The Stueckelberg field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> is identified with a <i>G</i>-frame on the gauge vector bundle <i>E</i> and the kinetic term for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> leads to the mass of the gauge bosons. The Stueckelberg mechanism is extended to the Higgs mechanism by adding to the game a scalar field describing rescaling of metric on fibres of <i>E</i>. Thus, we associate Higgs fields as well as running coupling parameters with conformal geometry on fibres of gauge bundles. In particular, a running coupling tending to zero or to infinity is equivalent to an unbounded expansion of <i>G</i>-fibres or its contraction to a point. We also discuss scale connection, space-time dependent Higgs vacua and compactly supported gauge and quark fields as an attribute of confinement.