Higgs-Boson Low-Energy Theorem and Compatible Gauge-Fixing Conditions

Conventional gauge-fixing schemes such as R$_\xi$ gauges may lead to a violation of the Higgs-boson low-energy theorem beyond the tree level. To elucidate this fact, we study a simple model whose U(1) gauge symmetry is spontaneously broken, and show how the Higgs-boson low-energy theorem can consistently be extended to the gauge and Higgs sectors of the model. In this formulation, any gauge-fixing condition must comply with the requirement that it should be independent of the vacuum expectation value of the Higgs field in the symmetric limit of the theory. We give a diagrammatic proof of the Higgs-boson low-energy theorem to all orders in perturbation theory, within the context of a judiciously modified R$_\xi$ gauge compatible with the above constraint. The dependence of the kinematic parameters on the Higgs tadpole is found to be very important for the proof of the theorem.