The Goldstone boson equivalence theorem with fermions

Abstract

The calculation of the leading electroweak corrections to physical transition matrix elements in powers of $M_H^2/v^2$ can be greatly simplified in the limit $M_H^2\gg M_W^2,M_Z^2$ through the use of the Goldstone boson equivalence theorem. This theorem allows the vector bosons $W^{\pm }$ and $Z$ to be replaced by the associated scalar Goldstone bosons $w^{\pm }$, $z$ which appear in the symmetry breaking sector of the Standard Model in the limit of vanishing gauge couplings. In the present paper, we extend the equivalence theorem systematically to include the Yukawa interactions between the fermions and the Higgs and Goldstone bosons of the Standard Model. The corresponding Lagrangian ${\mathcal{L}}_{EQT}$ is given, and is formally renormalized to all orders. The renormalization conditions are formulated both to make connection with physical observables and to satisfy the requirements underlying the equivalence theorem. As an application of this framework, we calculate the dominant radiative corrections to fermionic Higgs decays at one loop including the virtual effects of a heavy top quark. We apply the result to the decays $H\to t\bar{t}$ and $H\to b\bar{b}$, and find that the equivalence theorem results including fermions are quite accurate numerically for Higgs-boson masses $M_H>400(350)$ GeV, respectively, even for $m_t=175$ GeV.

32 pages, uses LaTeX2e, epsf and rotate, 7 figures included as separate uuencoded packed file. A complete PostScript version can also be obtained from http://www.physik.tu-muenchen.de/tumphy/d/T30d/PAPERS/TUM-HEP-227-95.ps.gz

References in corpus (6)

• Radiative Correction Effects of a Very Heavy Top
• Massive two--loop diagrams: The Higgs propagator
• Two-loop renormalization constants and high energy $2\to 2$ scattering amplitudes in the Higgs sector of the standard model
• Two--loop heavy Higgs corrections to the Higgs fermionic width
• Two-loop unitarity constraints on the Higgs boson coupling
• Two-loop $\mathrm{O}\left(G_F^2{M}_H^4\right)$ corrections to the fermionic decay rates of the Higgs boson

Cited by in corpus (2)

• The Higgs resonance in vector boson scattering
• Perturbative reliability of the Higgs-boson coupling in the standard electroweak model