Valley instanton versus constrained instanton

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 the valley instanton. A detailed comparison between the valley instanton and the constrained instanton in phi(4) theory and the gauge-Higgs system is 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.