Self-consistent dynamics of a light composite scalar Higgs boson.

Abstract

We apply a simple approximate relativistic amplitude-unitarization generalization of nonrelativistic Schr\"odinger-equation dynamics to the scattering of longitudinal mass-degenerate $W$ and $Z$ gauge bosons. The strong energy dependence of our amplitude near the $\mathrm{WW}$ threshold then makes possible a nonperturbative self-consistent nonelementary neutral Higgs scalar bound state ($H$) just below this threshold. We must, however, include a constant term approximating high-energy inelastic effects in addition to $H$ exchange. Everything, including the $H$ mass, can then be determined in terms of the small phenomenological $\mathrm{WWH}$ coupling and $W$ mass, which serves to set the energy scale of the problem; this is the same number of arbitrary parameters as in the underlying electroweak theory. The partial-wave amplitude containing the $H$ is then in approximate agreement at zero energy with the one given by the perturbative crossing-symmetric $H$-pole-only tree-graph amplitude. We find unacceptable zero-energy disagreement, however, if, instead of an inelasticity term, we insert a subtraction constant approximating the effect of short-range high-mass exchanges to obtain our $H$. Similar self-consistent $H$ bound-state solutions can also arise near the $t\overline{t}$ threshold in $t\overline{t}$ scattering with $H$ exchange.