Derivation of spontaneously broken gauge symmetry from the consistency
of effective field theory II: Scalar field self-interactions and the
electromagnetic interaction
We extend our study of deriving the local gauge invariance with spontaneous
symmetry breaking in the context of an effective field theory by considering
self-interactions of the scalar field and inclusion of the electromagnetic
interaction. By analyzing renormalizability and the scale separation conditions
of three-, four- and five-point vertex functions of the scalar field, we fix
the two couplings of the scalar field self-interactions of the leading order
Lagrangian. Next we add the electromagnetic interaction and derive conditions
relating the magnetic moment of the charged vector boson to its charge and the
masses of the charged and neutral massive vector bosons to each other and the
two independent couplings of the theory. We obtain the bosonic part of the
Lagrangian of the electroweak Standard Model as a unique solution to the
conditions imposed by the self-consistency conditions of the considered
effective field theory.Comment: 11 pp, 3 fig