Higgs-boson low-energy theorem and compatible gauge-fixing conditions

Conventional gauge-fixing schemes such as Rξ 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 Rξ 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.