2-LOOP RENORMALIZATION-CONSTANTS AND HIGH-ENERGY 2-]2 SCATTERING-AMPLITUDES IN THE HIGGS SECTOR OF THE STANDARD MODEL

We calculate the complete matrix of two-body scattering amplitudes for the scattering of longitudinally polarized gauge bosons W(L)+/-, Z(L) and Higgs bosons to two loops in the high-energy, heavy-Higgs-boson limit square-root s less much greater than M(H) much greater than M(W). Use of the Goldstone boson equivalence theorem reduces the problem to one involving only the scalar fields w+/-, 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 boson coupling lambda0 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.