Integrating out the Standard Higgs Field in the Path Integral

Details Integrating out the Standard Higgs Field in the Path Integral Integrating out the Standard Higgs Field in the Path Integral

1995-05-09

arxiv.org/abs/hep-ph/9505266v2

Nucl.Phys. B459 (1996) 497-536

Physics

High Energy Physics

High Energy Physics - Phenomenology

39 pages, latex, 7 figures uuencoded postscript, revised version, to appear in Nucl. Phys. B

Scientific paper

10.1016/0550-3213(95)00551-X

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 $\sigma$-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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