Collapsing domain walls in the two-Higgs-doublet model and deep insights from the EDM

TL;DR

This paper investigates domain wall solutions in the two-Higgs-doublet model with CP violation, showing how explicit CP-violating terms can lead to domain wall collapse, with implications for gravitational waves and electric dipole moments.

Contribution

It provides a detailed analysis of domain wall solutions in the 2HDM with CP violation, constrains on CPV parameters from cosmology and EDM measurements, and estimates gravitational wave signals.

Findings

Domain walls with spontaneous CP violation are excluded by tension bounds.

Explicit CP violation can cause domain wall collapse, constrained by BBN.

Future EDM measurements can further restrict CPV parameter space.

Abstract

We study the domain wall solutions in the general two-Higgs-doublet model (2HDM) with a CP-violating phase. The 2HDM with the spontaneouse CP violation is found to have domain wall solutions whose tensions are $\mathcal{O}(10^6)\,{\rm GeV}^3$, which are excluded by the Zel'dovich-Kobzarev-Okun bound. With the explicit CP-violating (CPV) terms as the so-called biased term in the scalar potential, domain walls can collapse in the early Universe. The sizes of the explicit CP violation can be constrained from the Big Bang nucleosynthesis. This constraint is converted to the CPV mixing of $\alpha_c$, and is mostly sensitive to the mass splittings between two heavy neutral Higgs bosons. We estimate the possible gravitational wave signals and the electric dipole moment (EDM) predictions due to the domain wall collapsing. It turns out that the peak spectrum of the GW from the domain wall collapsing cannot be probed in any future program. In contrast, the untenable regions with very tiny explicit CPV parameter in the Higgs potential has been partially excluded by the latest electron EDM measurements at the ACME-II and will be further confirmed or excluded by the future ACME-III projection.