Valley Instanton in the Gauge-Higgs System

TL;DR

This paper introduces the valley instanton, a new gauge-Higgs system configuration derived using the valley method, which improves upon constrained instanton techniques by providing a more rigorous mathematical framework.

Contribution

The paper develops the valley instanton in the SU(2)-gauge system with a Higgs doublet, offering a novel, constraint-free method for constructing instanton solutions.

Findings

Valley instanton exhibits desirable behaviors.

Numerical results support the effectiveness of the valley method.

Method improves mathematical formalism over constrained instanton approach.

Abstract

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.