A multi-scale perturbative approach to SU(2)-Higgs classical dynamics: stability of nonlinear plane waves and bounds of the Higgs field mass

TL;DR

This paper uses a multi-scale perturbative approach to analyze the classical dynamics of SU(2)-Higgs fields, deriving stability conditions for nonlinear plane waves and establishing bounds on the Higgs mass relevant for experiments.

Contribution

It introduces a novel multi-scale perturbation method to study SU(2)-Higgs dynamics and derives stability criteria for nonlinear plane waves in the broken phase.

Findings

Nonlinear plane waves are stable only when Higgs amplitude is much smaller than gauge field amplitude.

Higgs mass bounds are derived based on stability conditions.

Results may inform experimental searches for the Higgs particle.

Abstract

We study the classical dynamics of SU(2)-Higgs field theory using multiple scale perturbation theory. In the spontaneously broken phase, assuming small perturbations of the Higgs field around its vacuum expectation value, we derive a nonlinear Schroedinger equation and study the stability of its nonlinear plane wave solutions. The latter, turn out to be stable only if the Higgs amplitude is an order of magnitude smaller than that of the gauge field. In this case, the Higgs field mass possesses some bounds which may be relevant to the search for the Higgs particle at ongoing experiments.