Abstract
We discuss the current picture of the standard model scalar sector at strong coupling. We compare the pattern observed in the scalar sector in perturbation theory up to two loops with the nonperturbative solution obtained by a next-to-leading order $1/N$ expansion. In particular, we analyze two resonant Higgs scattering processess $f\overline{f}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{H}{f}^{\ensuremath{'}}{f}^{\ensuremath{'}}$ and $f\overline{f}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{H}ZZ,WW.$ We describe the ingredients of the nonperturbative calculation, such as tachyonic regularization, higher order $1/N$ intermediate renormalization, and the numerical methods for evaluating the graphs. We discuss briefly the perspectives and usefulness of extending these nonperturbative methods to other theories.
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