Massive vector-boson and scalar amplitudes through four points are uniquely fixed by two on-shell consistency conditions, forcing spontaneously-broken gauge theories — or Stueckelberg theory when scalar masses are equal — leaving only scalar self-couplings and mixing angles free.
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Massive Gauge Theories from Consistency Conditions of Amplitudes
Massive vector-boson and scalar amplitudes through four points are uniquely fixed by two on-shell consistency conditions, forcing spontaneously-broken gauge theories — or Stueckelberg theory when scalar masses are equal — leaving only scalar self-couplings and mixing angles free.