False-vacuum bubbles in sphaleron scattering

Abstract

We investigate the collision dynamics of two bright sphalerons in a (1+1)-dimensional deformed ${\varphi }^6$ scalar field theory with a symmetric potential possessing false vacua. Two one-parameter realizations of the model, referred to as the barrier and well models, are considered and their static and linear instability properties are first reviewed. We then study head-on collisions of boosted sphalerons over a broad range of initial velocities and deformation parameters. The scattering dynamics exhibit a rich variety of final states, including the production of kink-antikink pairs, long-lived oscillons in true and false vacuum, multiple oscillons propagating in false-vacuum regions, and radiative decay. A particularly remarkable outcome is the emergence of a long-lived bubble of the false broken vacuum bounded by a kink-antikink pair, which repeatedly collapses and re-expands before eventually decaying into an oscillon. These results demonstrate that deformed ${\varphi }^6$ theories with false vacua exhibit considerably richer sphaleron dynamics than previously known and provide new insight into the role of unstable localized configurations in nonlinear field theories.

15 pages, 14 figures