Long-Lived Oscillons as Closed Domain Walls in the $\mathbb Z_2$-Symmetric Two-Higgs-Doublet Model

Abstract: We identify an oscillatory solution that exists as a long-lived, bubble-like closed domain wall in the two-Higgs-doublet model (2HDM) under a $\mathbb{Z}_2$ symmetry constraint, and these structures emerge naturally during the late stages of domain wall decay. \ \ The longevity of these structures is attributed to a potential landscape characterized by two distinct vacuum regions, the oscillating region lies in one vacuum, while the constant outer region lies in the other. The lifetime of the structure depends on the parameter in the Lagrangian, we identify a specific parameter space where radiation is suppressed, the solution exhibits a maximum lifetime that goes up to infinity. \ \ The simpler two-complex-field system is first used to introduce the mathematical requirements of the structure before extending it to the more physical but complex 2HDM. Further Numerical verification via Floquet analysis shows these structures are stable under perturbation.