W, Z and Higgs Scattering at SSC Energies

Abstract

The scattering of $W$, $Z$ and Higgs bosons in the Standard Model is investigated in the region $s,m_H^2\gg m_W^2$ with no restrictions on relative sizes of $s$ and $m_H^2$, so that our results are applicable at energies below as well as above $2m_H$. We have calculated, with the inclusion of the full one-loop corrections, the scattering matrix between the states $W_L^+W_L^-$, $Z_LZ_L$ and $HH$, and computed the S-wave amplitudes as functions of the center-of-mass energy $\sqrt{s}$ for $m_H=$500~GeV and 1000~GeV. The apparent violation of unitarity is avoided by unitarizing the amplitudes by the K-matrix and the Pad\'e methods. For the detection of the Higgs boson through gauge boson scattering in $pp$ collisions, we have used the unitarized amplitudes to obtain the invariant-mass distributions for the final $W_L^+W_L^-$ and $Z_LZ_L$ pairs at the SSC energy of $\sqrt{s}=$40~TeV by means of the effective-W approximation.