Valley Instanton in the Gauge-Higgs System

The instanton configuration in the SU(2)-gauge system with a Higgs doublet is constructed by using the new valley method. This method defines the configuration by an extension of the field equation and allows the exact conversion of the quasi-zero eigenmode to a collective coordinate. It does not require ad-hoc constraints used in the current constrained instanton method and provides a better mathematical formalism than the constrained instanton method. The resulting instanton, which we call ``valley instanton'', is shown to have desirable behaviors. The result of the numerical investigation is also presented.