Vacuum expectation value renormalization in the standard model and beyond

We show how the renormalization constant of the Higgs vacuum expectation value fixed by a tadpole condition is responsible for gauge dependences in various definitions of parameters in the $R_{\xi }$-gauge. Then we show the relationship of this renormalization constant to the Fleischer-Jegerlehner (FJ) scheme, which is used to avoid these gauge dependences. In this way, we also present a viewpoint on the FJ scheme complementary to the ones already existing in the literature. Additionally, we compare and discuss different approaches to the renormalization of tadpoles by identifying the similarities and relations between them. The relationship to the Higgs background-field renormalization is also discussed.

Figure 1

Feynman rules for calculating ${\widehat{\delta }}_{\varphi }$.

Figure 2

One-loop diagram for calculating ${\widehat{\delta }}_{\varphi }$.