arxiv: 2605.01318 · v1 · submitted 2026-05-02 · ✦ hep-ph

Recognition: unknown

Gravitational waves from CP domain wall collapse and electron EDM in a complex singlet model with dimension-five Yukawa interactions

Authors on Pith no claims yet

Pith reviewed 2026-05-09 15:06 UTC · model grok-4.3

classification ✦ hep-ph

keywords gravitational wavesCP domain wallselectron EDMcomplex singletdimension-five interactionsvacuum structureCP violation

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The pith

Electron EDM bounds already constrain part of the parameter space where gravitational waves from CP domain wall collapse would be detectable in a complex singlet model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates the connection between gravitational waves emitted during the collapse of CP domain walls and the electron electric dipole moment in an extension of the Standard Model that includes a complex singlet scalar and dimension-five Yukawa interactions. The scalar potential supports CP-related degenerate vacua that can form domain walls; their collapse produces a gravitational wave background whose amplitude and frequency depend on the vacuum structure. When the singlet couples to Standard Model fermions through the higher-dimensional operators, it induces CP-violating phases that contribute to the electron EDM. Analysis of the shared parameter space shows that existing EDM limits already exclude some regions capable of producing observable gravitational waves, while projected improvements to 10^{-31}--10^{-32} e cm sensitivity would cover additional overlapping territory.

Core claim

In this complex singlet model the scalar potential admits CP-related degenerate vacua that give rise to domain walls; their collapse generates gravitational waves detectable by future observatories such as SKA and THEIA. Dimension-five Yukawa couplings between the singlet and Standard Model fermions introduce CP phases that produce a nonzero electron EDM. The resulting parameter space exhibits partial overlap: current electron EDM bounds already exclude portions of the region where gravitational waves would be detectable, and future EDM sensitivities at the level of 10^{-31}--10^{-32} e cm can probe further into the same domain.

What carries the argument

CP domain walls formed by degenerate vacua in the complex singlet potential, whose collapse produces gravitational waves, together with dimension-five Yukawa interactions that generate observable CP phases in the electron EDM.

If this is right

Current electron EDM limits already exclude part of the parameter space in which gravitational waves from domain-wall collapse would be detectable.
Future EDM experiments reaching 10^{-31} to 10^{-32} e cm sensitivity will test additional regions where gravitational wave signals are expected.
The two observables together map both the vacuum degeneracy and the CP-violating phases in the singlet sector.
Non-observation of one signal can be used to narrow the search window for the other within the model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Absence of gravitational waves in the relevant band could be interpreted as indirect support for stronger EDM constraints in related singlet models.
The framework suggests that EDM data could serve as a prior to optimize gravitational wave search strategies for similar beyond-Standard-Model scenarios.
Extensions incorporating baryogenesis or additional fermions might link the same domain-wall dynamics to other cosmological observables.

Load-bearing premise

The scalar potential must possess CP-related degenerate vacua that form long-lived domain walls, and the dimension-five couplings must induce unsuppressed CP phases in the effective fermion interactions.

What would settle it

Detection of a gravitational wave background in the frequency band predicted for domain-wall collapse together with an electron EDM measurement below 10^{-32} e cm would contradict the claimed overlap between the two observables.

Figures

Figures reproduced from arXiv: 2605.01318 by Eibun Senaha, Hieu The Pham.

**Figure 1.** Figure 1: FIG. 1. Contours of the electron EDM and the GW-detectable regions by SKA and THEIA are view at source ↗

**Figure 2.** Figure 2: FIG. 2. Contours of the electron EDM and the regions where the GW signal is detectable by SKA view at source ↗

read the original abstract

We study the interplay between gravitational waves (GWs) from domain wall collapse and the electron electric dipole moment (EDM) in a complex singlet extension of the standard model with dimension-five Yukawa interactions. In this framework, the scalar potential admits CP-related degenerate vacua, leading to the formation of CP domain walls. While the resulting GW signal provides a probe of the vacuum structure of the singlet scalar sector, it does not by itself constitute a CP-violating observable. Once the singlet scalar is coupled to standard model fermions, CP-violating phases become observable through EDMs. We analyze whether current and future EDM experiments can probe the parameter region where the GW signal is detectable by SKA and THEIA. We find that the current electron EDM bound already constrains part of the parameter space, while future sensitivities at the level of $10^{-31}$--$10^{-32}\,e\,\mathrm{cm}$ can probe regions overlapping with the GW-detectable domain. Our results highlight the complementarity between GW and EDM observables in probing the singlet scalar sector, providing a coherent picture of its vacuum structure and CP properties.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper shows that current electron EDM bounds already cut into the parameter space for detectable GW signals from CP domain wall collapse in their complex singlet model, with future EDM reach overlapping more of the GW-probeable region.

read the letter

The main point is that in this complex singlet extension with dimension-five Yukawa couplings, the electron EDM already rules out part of the space where domain wall collapse would produce a gravitational wave signal visible to SKA or THEIA, while next-generation EDM experiments at 10^{-31} to 10^{-32} e cm would cover additional overlap. They achieve this by feeding the same singlet vev and potential parameters into both the standard domain wall tension and annihilation temperature formulas and the EDM loop calculation induced by the higher-dimensional operators. The result is a concrete illustration of complementarity between the two observables without overclaiming resolution of any open problem. The work follows established methods for walls and EDMs, so the actual advance is the joint scan in this specific setup with CP-degenerate vacua. It keeps the model minimal and cites the relevant prior literature on both sides. One soft spot is that the summary provides no explicit error bars, cutoff dependence plots, or full derivation steps, which leaves the robustness of the overlap claim somewhat unclear until the full scans are checked. The assumption of exact degeneracy in the potential is standard but still requires parameter tuning. This is a typical hep-ph phenomenology paper aimed at readers working on singlet extensions or multi-messenger BSM signals. Someone scanning similar models would get usable numbers for their own work. It is coherent enough on its own terms to deserve a serious referee rather than a desk reject.

Referee Report

2 major / 2 minor

Summary. The manuscript examines gravitational waves from the collapse of CP domain walls in a complex singlet extension of the Standard Model that includes dimension-five Yukawa interactions. It argues that the current electron EDM bound already excludes part of the parameter space, while projected future sensitivities of 10^{-31}--10^{-32} e cm can reach regions where the GW signal would be detectable by SKA and THEIA, thereby illustrating complementarity between the two observables for constraining the singlet sector's vacuum structure and CP phases.

Significance. If the numerical results and loop calculations hold, the work supplies a concrete example of how cosmological GW signals and precision EDM measurements can jointly probe an extended scalar sector through shared parameters (singlet vev, quartics, and cutoff scale). The explicit linkage of domain-wall tension, annihilation temperature, and EDM loop factors is a positive feature that strengthens the case for multi-messenger tests of CP-symmetric potentials.

major comments (2)

[§4.2] §4.2 and the associated parameter scan: the overlap between GW-detectable and EDM-probed regions is presented as robust, yet the text does not quantify how the results change when the cutoff scale in the dim-5 operators is varied by an order of magnitude; this choice directly affects both the wall tension and the EDM loop factor and therefore bears on the central complementarity claim.
[Eq. (18)] Eq. (18) and the EDM loop expression: the claimed future sensitivity reach assumes a specific suppression from the dim-5 coefficient and the singlet vev; without an explicit error band or scan over the phase and coupling ranges, it is difficult to assess whether the overlap region survives reasonable variations in these inputs.

minor comments (2)

[Abstract and §5] The abstract and §5 would benefit from a short statement of the scanned ranges for the singlet quartic couplings and the cutoff scale, together with a note on whether the quoted EDM bounds include theoretical uncertainties.
[Figure 2 and Figure 4] Figure 2 (GW spectrum) and Figure 4 (EDM vs. GW amplitude) would be clearer if the SKA and THEIA sensitivity curves were overlaid with explicit frequency and amplitude labels rather than referenced only in the caption.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. We address each major comment below, indicating the revisions we will implement to strengthen the manuscript.

read point-by-point responses

Referee: [§4.2] §4.2 and the associated parameter scan: the overlap between GW-detectable and EDM-probed regions is presented as robust, yet the text does not quantify how the results change when the cutoff scale in the dim-5 operators is varied by an order of magnitude; this choice directly affects both the wall tension and the EDM loop factor and therefore bears on the central complementarity claim.

Authors: We agree that the cutoff scale Λ in the dimension-five operators affects both the domain-wall tension (through the effective potential) and the EDM loop factor, and that an explicit quantification strengthens the complementarity claim. In the original analysis we adopted Λ = 1 TeV as a representative benchmark. We have now performed additional scans for Λ = 0.5 TeV and Λ = 5 TeV. The qualitative features of the overlap region persist, although the precise boundaries shift by O(1) factors. We will revise §4.2 to include a short discussion of this dependence and add a supplementary panel (or figure) showing the GW and EDM reach for the three values of Λ. revision: yes
Referee: [Eq. (18)] Eq. (18) and the EDM loop expression: the claimed future sensitivity reach assumes a specific suppression from the dim-5 coefficient and the singlet vev; without an explicit error band or scan over the phase and coupling ranges, it is difficult to assess whether the overlap region survives reasonable variations in these inputs.

Authors: Eq. (18) does depend on the CP-violating phase and the combination of singlet vev and dim-5 coefficient. Our existing parameter scan already covers the ranges of phases and vevs that permit CP domain walls. To make the robustness explicit, we will add shaded bands to the relevant summary plots (around the discussion of Eq. (18) and in §4.2) that reflect the variation over the scanned phase interval and coupling strengths. A brief clarifying sentence will also be inserted near Eq. (18). revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper constructs a complex singlet extension with a CP-symmetric potential admitting degenerate vacua (leading to domain walls and GWs) and dimension-five Yukawa operators transmitting CP phases to the electron EDM via loops. Both signals are computed as functions of shared parameters (singlet VEV, couplings, cutoff) and compared via parameter scans. No step reduces a prediction to a fitted input by construction, no self-citation is load-bearing for the central claim, and no ansatz or uniqueness is smuggled in. The complementarity between GW and EDM regions follows directly from the explicit calculations without circular reduction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Central claim rests on existence of CP-related degenerate vacua in the scalar potential and generation of EDMs via dimension-five operators. No independent evidence beyond model construction.

free parameters (2)

Singlet potential parameters
Scanned to produce both detectable GW signals and EDM values; not derived from first principles.
Dimension-five Yukawa couplings and phases
Chosen to generate observable electron EDM while satisfying constraints.

axioms (2)

domain assumption The scalar potential admits CP-related degenerate vacua
Invoked to guarantee domain wall formation.
domain assumption Dimension-five Yukawa interactions generate CP-violating phases observable in EDMs
Assumed when coupling the singlet to SM fermions.

pith-pipeline@v0.9.0 · 7769 in / 1252 out tokens · 59594 ms · 2026-05-09T15:06:52.391273+00:00 · methodology

discussion (0)

Reference graph

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