Large width in the Lee model for the Higgs-Goldstone sector

Abstract

We discuss a variant of the unstable particle Lee model motivated by the problem of large width in Higgs meson decay. The essential result is that, in the point-interaction model, the width for decay into Goldstone bosons (W's and Z's), defined from the second-sheet unstable particle pole, obeys , where [Gamma]0 is the naive perturbative width, and the ordering is from weak coupling at the lower end to strong coupling at the upper end. If the point interaction of the Lee model is modified to make the tree scattering amplitude for Goldstone particles relativistically invariant, a large-coupling upper bound for the width results. [Gamma] mH, where by comparison, the naive perturbative width grows like mH3.We find that defining the renormalized coupling at the complex Higgs pole is reasonable in the Lee model, even when the pole moves far from the real axis. Furthermore, scattering effects remain strong, in the sense that the unitarity bound is roughly approached over a large range of energies, although the scattering amplitude never reaches more than about 80% of saturation in the point-interaction model, contrary to naive perturbation theory. We also point out, without discussing it in this paper, what appears to be a new fact about the Lee model, that the Higgs propagator has a bound-state pole in addition to the resonance pole.