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

TL;DR

This work reveals long-lived oscillon-like closed domain walls in a $\ ext{Z}_2$-symmetric $2$HDM, forming as bubble-like remnants late in domain-wall decay. It develops a minimal four-field model that can be radiation-free under a specific parameter choice, and shows that the full eight-field $\mathbb{Z}_2$-2HDM realizes the same mechanism, validated by Floquet stability analysis. Lifetimes depend on the Lagrangian parameters, with a radiation-suppressed subspace allowing lifetimes to diverge to infinity, and comparisons across $2$-field, $4$-field, and $2$HDM indicate that the full model supports more long-lived bubbles. Boundary-condition strategies (sponge layers) and detailed frequency-domain analysis establish the robustness of these structures, suggesting potential relevance for early-universe dynamics and analogous condensed-matter systems. The results introduce a new class of nonperturbative, topologically flavored, radiation-suppressing configurations with possible implications beyond high-energy theory.

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.

Figures (7)

• Figure 1: Plot of how domain wall length(area) change in time, in 2D(a) and 3D(b) space. (c-e) and (f-h) show the plot of the domain wall structure at the timeslice 40(c,f), 240(d,g), 360(e,h). 2D graphs plot the $R^1$ distribution with values, while 3D plots only illustrate surface where $R^1=0$. The departure from the earlier period decay rate signals the formation of stable oscillon relics. The diameter of Bubbles in 3D was measured to be the same from different directions.
• Figure 2: Histogram of plot of 'lifetime' in 2-fields, 4-fields, 2HDM for comparison. Parameters used were given in Appendix 2. The probability is measured by the chance of falling in each bin, with the bin width is 40.
• Figure 3: Plot of $f_0$ and $f_1$ in 2D and 3D space, with choice of parameter $\mu= 0.5$, $\lambda= 1.78$, and $\lambda_4 = -2.56$ as in Appendix 2. When frequency is low, the oscillation has high amplitude and the system lies in the opposite vacuum manifold than the constant outer region. When the angular frequency $\omega$ is high, the system becomes a small-amplitude oscillation, there is no crossing of the domain wall, and all regions stay in the same vacuum. There is a maximum frequency $\omega_m=1.6$ where any system should have a frequency below that $\omega<\omega_m$. Solutions were found based on the Newton-Raphson method via Python 'fslove' code.
• Figure 4: The plot of time slice at rotating phase of fields in $0$, $\pi/2$, $\pi$, $3\pi/2$. with the $R^1$ distribution (left column), radial field distribution (middle column), and energy distribution (right column)plot. The plot use constant phase $\alpha=\pi/4$, and other parameters used are from Appendix 2 with full mixing. The sponge-layer absorbing boundary condition is used to replace periodic ones.
• Figure 5: 100 random chosen eigenvalues from the matrix of Floquet analysis. 'equal to 1' include values within $1\pm10^{-5}$ due to the consideration of decimal uncertainties from grids and iteration(though output range can narrow to $1\pm10^{-15}$). parameters and background are chosen from FIG. \ref{['f0f1']} with $\omega=0.45$.