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Integrating out the Standard Higgs Field in the Path Integral

Stefan Dittmaier·Carsten Grosse-Knetter
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Abstract

We integrate out the Higgs boson in the electroweak standard model at one loop and construct a low-energy effective Lagrangian assuming that the Higgs mass is much larger than the gauge-boson masses. Instead of applying diagrammatical techniques, we integrate out the Higgs boson directly in the path integral, which turns out to be much simpler. By using the background-field method and the Stueckelberg formalism, we directly find a manifestly gauge-invariant result. The heavy-Higgs effects on fermionic couplings are derived, too. At one loop the $\log\MH$-terms of the heavy-Higgs limit of the electroweak standard model coincide with the UV-divergent terms in the gauged non-linear $σ$-model, but vertex functions differ in addition by finite constant terms. Finally, the leading Higgs effects to some physical processes are calculated from the effective Lagrangian.

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Stefan Dittmaier, Carsten Grosse-Knetter. 1995-10-30. Integrating out the Standard Higgs Field in the Path Integral. https://doi.org/10.1016/0550-3213(95)00551-x

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