Two-loop renormalization constants and high energy $2\rightarrow 2$ scattering amplitudes in the Higgs sector of the standard model

Details Two-loop renormalization constants and high energy $2\rightarrow 2$ scattering amplitudes in the Higgs sector of the standard model Two-loop renormalization constants and high energy $2\rightarrow 2$ scattering amplitudes in the Higgs sector of the standard model

1993-03-09

arxiv.org/abs/hep-ph/9303233v1

Phys.Rev.D48:1061,1993; Erratum-ibid.D52:553,1995

Physics

High Energy Physics

High Energy Physics - Phenomenology

47 pages, 7 figures available by request to LD, RevTEX 3.0, MAD/TH/93-1

Scientific paper

10.1103/PhysRevD.48.1061 10.1103

We calculate the complete matrix of two-body scattering amplitudes for the scattering of longitudinally polarized gauge bosons $W_L^\pm$, $Z_L$ and Higgs bosons to two loops in the high-energy, heavy-Higgs limit $\sqrt{s}\gg M_H\gg M_W$. Use of the Goldstone boson equivalence theorem reduces the problem to one involving only the scalar fields $w^\pm$, $z$ (the Goldstone bosons of the original theory) and the Higgs boson. Renormalization of the scattering amplitudes requires the calculation of the self-energy functions $\Pi _i^0(M_i^2)$, the renormalization constants $Z_i$, and the bare quartic Higgs coupling $\lambda _0$ to two loops. The results will be useful in other calculations. To facilitate the calculations, we introduce a powerful new technique for evaluating integrals over Feynman parameters in dimensional regularization which is based on a Barnes' type representation of the binomial expansion. We also collect some useful integrals which extend the tables given by Devoto and Duke.

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