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arxiv: 2511.21488 · v3 · pith:GLR254X2new · submitted 2025-11-26 · ✦ hep-ph · astro-ph.HE· gr-qc

Bayesian analysis of the complex singlet model with phase transition gravitational waves

Qingyuan Liang , Ligong Bian , Huai-Ke Guo , Yongcheng Wu This is my paper

Pith reviewed 2026-05-21 17:48 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.HEgr-qc
keywords complex singlet modelelectroweak phase transitiongravitational wavesBayesian analysisTaiji detectorHiggs self-couplingsstochastic background
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The pith

Taiji gravitational wave data can constrain Higgs self-couplings in the complex singlet model.

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

The authors examine the possibility of using gravitational waves generated during the electroweak phase transition in the complex singlet extension of the Standard Model to test this theory. They develop a likelihood function in the frequency domain that includes the expected signal along with astrophysical and instrumental noise for the Taiji detector. Through both approximate Fisher matrix calculations and full Bayesian nested sampling, they demonstrate that the detector's data would allow accurate recovery of the underlying parameters. These constraints on the wave spectrum are then mapped back to limits on the self-couplings of the Higgs boson in the model.

Core claim

The paper shows that Bayesian analysis of simulated Taiji observations, incorporating the stochastic gravitational wave background from the electroweak phase transition in the CxSM along with noise sources, leads to consistent parameter estimation and yields meaningful bounds on the Higgs self-couplings.

What carries the argument

A frequency-domain likelihood that combines the phase transition gravitational wave spectrum with astrophysical foregrounds and instrumental noise, analyzed via Bayesian nested sampling to infer CxSM parameters.

If this is right

  • Taiji observations would provide direct access to the thermodynamic properties of the electroweak phase transition.
  • Derived limits on Higgs self-couplings would complement direct measurements at colliders.
  • The framework allows propagation of spectral constraints to the scalar potential parameters.
  • Millihertz sensitivity of Taiji matches the expected frequency range for such signals.

Where Pith is reading between the lines

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

  • Similar Bayesian methods could be applied to other beyond-Standard-Model scenarios with strong first-order phase transitions.
  • Non-detection would restrict the viable parameter space for models aiming to explain the baryon asymmetry via electroweak baryogenesis.
  • Future data analysis pipelines for space-based detectors should include phase transition templates as standard components.

Load-bearing premise

The gravitational wave signal from the electroweak phase transition can be separated from astrophysical foregrounds and instrumental noise in the Taiji frequency band.

What would settle it

Absence of the predicted excess in the gravitational wave power spectrum in actual Taiji observations at the frequencies and amplitudes expected from the model would indicate that the assumed phase transition signals are not present or not detectable.

read the original abstract

We explore the prospects of probing the complex singlet extension of the Standard Model (CxSM) with gravitational waves from the electroweak phase transition. The study establishes a connection of the scalar potential parameters, the thermodynamic properties of the phase transition, with the directly measured stochastic gravitational-wave background in the presence of astrophysical background and foreground. Considering the space-based gravitational-wave detector Taiji, we construct a frequency-domain likelihood that incorporates instrumental and astrophysical noises, and we perform both Fisher-matrix forecasts and Bayesian nested sampling analysis. The comparison of these two approaches demonstrates consistent parameter recovery and highlights the sensitivity of Taiji to millihertz gravitational-wave signals. We further propagate the inferred constraints on the gravitational-wave spectrum back to the underlying CxSM parameters, obtaining meaningful limits on the Higgs self-couplings. The results emphasize the complementarity between gravitational-wave observations and collider measurements, showing that future missions such as Taiji can serve as a powerful probe of electroweak-scale new physics and the dynamical origin of the Higgs sector.

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.

Referee Report

1 major / 2 minor

Summary. The paper explores prospects for probing the complex singlet extension of the Standard Model (CxSM) via gravitational waves from the electroweak phase transition at the Taiji detector. It connects scalar potential parameters and phase-transition thermodynamics to the stochastic GW background, constructs a frequency-domain likelihood that includes instrumental and astrophysical noise, compares Fisher-matrix forecasts with Bayesian nested sampling, and propagates recovered spectrum constraints back to CxSM parameters to derive limits on Higgs self-couplings.

Significance. If the signal-isolation step is robust, the work would demonstrate how future mHz GW observations can furnish independent constraints on electroweak-scale extensions that complement collider measurements of the Higgs sector.

major comments (1)
  1. [Likelihood construction and results sections] The central claim—that constraints on the GW spectrum can be mapped back to meaningful limits on CxSM Higgs self-couplings—requires that the frequency-domain likelihood successfully isolates the phase-transition contribution from astrophysical foregrounds and instrumental noise. The manuscript states that the likelihood incorporates these noise models but does not present explicit validation (e.g., injection-recovery tests with realistic galactic-binary foreground spectra at expected Taiji sensitivity). Without such tests, bias in the recovered spectrum parameters would propagate directly into the reported limits on the scalar potential.
minor comments (2)
  1. [Methods] Clarify the precise definition of the frequency-domain likelihood (e.g., the form of the noise power spectral densities and any assumptions about stationarity) so that the reader can assess the separation procedure.
  2. [Results] The abstract asserts 'consistent parameter recovery' between Fisher and Bayesian approaches; a quantitative comparison (e.g., posterior widths or bias metrics) in the main text would strengthen this statement.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comment on the validation of the likelihood. We address the point below and have revised the manuscript to incorporate additional tests that directly support the central claim.

read point-by-point responses

  1. Referee: [Likelihood construction and results sections] The central claim—that constraints on the GW spectrum can be mapped back to meaningful limits on CxSM Higgs self-couplings—requires that the frequency-domain likelihood successfully isolates the phase-transition contribution from astrophysical foregrounds and instrumental noise. The manuscript states that the likelihood incorporates these noise models but does not present explicit validation (e.g., injection-recovery tests with realistic galactic-binary foreground spectra at expected Taiji sensitivity). Without such tests, bias in the recovered spectrum parameters would propagate directly into the reported limits on the scalar potential.

    Authors: We agree that explicit validation strengthens the mapping from recovered spectrum parameters to CxSM Higgs self-couplings. The original analysis already shows consistency between Fisher-matrix forecasts and Bayesian nested sampling under the combined noise model, which provides indirect support for unbiased recovery. To address the referee's request directly, the revised manuscript now includes injection-recovery tests that inject realistic galactic-binary foreground spectra (modeled at the expected Taiji sensitivity) together with instrumental noise and simulated phase-transition signals. These tests confirm that the phase-transition parameters are recovered without significant bias, and the propagated limits on the scalar potential parameters remain stable. A new subsection and figure have been added to the results section to document the tests and their outcomes. revision: yes

Circularity Check

0 steps flagged

No circularity in the Bayesian inference and parameter propagation chain

full rationale

The paper constructs a frequency-domain likelihood that incorporates external instrumental and astrophysical noise models, performs Fisher-matrix forecasts and Bayesian nested sampling to infer GW spectrum parameters from Taiji data, and then maps the resulting constraints outward to CxSM scalar potential parameters including Higgs self-couplings. This is a standard forward-modeling pipeline with no self-definitional steps, no fitted inputs renamed as predictions, and no load-bearing self-citations that reduce the central claim to unverified prior work by the same authors. The derivation remains self-contained against external benchmarks and does not reduce any output to its inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review; specific numerical values and detailed assumptions are not provided, so the ledger reflects typical elements inferred from the high-level description of connecting scalar potential parameters to phase transition thermodynamics and gravitational wave signals.

free parameters (1)
  • CxSM scalar potential parameters
    Multiple couplings in the complex singlet potential are constrained or fitted via the gravitational wave likelihood.
axioms (1)
  • domain assumption The complex singlet model admits a strong first-order electroweak phase transition capable of producing a detectable stochastic gravitational wave background
    This premise underpins the connection between model parameters, thermodynamic quantities, and the observable signal in the Taiji band.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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

    hep-ph 2026-05 unverdicted novelty 4.0

    In a complex singlet model with dimension-five Yukawa couplings, current electron EDM bounds already restrict part of the parameter space where gravitational waves from CP domain wall collapse would be detectable.

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