Valley Instanton versus Constrained Instanton

TL;DR

This paper introduces valley instantons, a new method for constructing instanton-like configurations in theories with a mass scale, and compares them to constrained instantons, highlighting differences crucial for baryon number violation calculations.

Contribution

The paper proposes valley instantons based on the valley equation, providing a novel approach to instanton-like configurations in theories with a mass scale.

Findings

Significant differences between valley and constrained instantons at large radii.

Differences impact calculations of baryon number violating processes.

Valley instantons offer a plausible alternative in certain quantum field theories.

Abstract

Based on the new valley equation, we propose the most plausible method for constructing instanton-like configurations in the theory where the presence of a mass scale prevents the existence of the classical solution with a finite radius. We call the resulting instanton-like configuration as valley instanton. The detail comparison between the valley instanton and the constrained instanton in $\phi^4$ theory and the gauge-Higgs system are carried out. For instanton-like configurations with large radii, there appear remarkable differences between them. These differences are essential in calculating the baryon number violating processes with multi bosons.