Sphaleron without shape mode and its oscillon

Abstract

We find that an oscillon can possess a characteristic double oscillation structure even though it results in a decay of a sphaleron which does not have any positive energy discrete vibrational mode (shape mode). We show that dynamics of such an oscillon can still be qualitatively captured by collective coordinates provided by the sphaleron. Namely, its unstable mode and its scaling deformation i.e., Derrick mode.