Integrating out the standard Higgs field in the path integral |
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Institution: | 1. School of Engineering and Advanced Technology, Massey University, Private Bag 11222, Palmerston North, New Zealand;2. Department of Chemical Engineering and Environmental Technology, Valladolid University, Dr. Mergelina, s/n, 47011 Valladolid, Spain |
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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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