Model Parameter Reconstruction of Electroweak Phase Transition with TianQin and LISA: Insights from the Dimension-Six Model

TL;DR

This work investigates how space-based GW detectors TianQin and LISA can constrain the SMEFT dimension-six EWPT parameter $\Lambda$ from a SGWB generated by a strong first-order electroweak phase transition. Using a sound-wave DBPL template to connect phase-transition thermodynamics to GW observables, and a two-step forward mapping $\Lambda \to (\Omega_2, f_1, f_2)$ followed by Bayesian and ML-based inference, the authors quantify reconstruction precision for three benchmark points. They find sub-percent reconstruction of $\Lambda$ for BP1 on both detectors, with LISA extending reach to weaker signals and BP2–BP3, while TianQin is more limited by its frequency band. The results highlight detector complementarity and foreground-limited regimes, and underscore the potential of joint GW observations to probe BSM EWPT physics encoded in the $|H|^6$ SMEFT operator.

Abstract

We investigate the capability of TianQin and LISA to reconstruct the model parameters in the Lagrangian of new physics scenarios that can generate a strong first-order electroweak phase transition. Taking the dimension-six Higgs operator extension of the Standard Model as a representative scenario for a broad class of new physics models, we establish the mapping between the model parameter $Λ$ and the observable spectral features of the stochastic gravitational wave background. We begin by generating simulated data incorporating Time Delay Interferometry channel noise, astrophysical foregrounds, and signals from the dimensional-six model. The data are then compressed and optimized, followed by geometric parameter inference using both Fisher matrix analysis and Bayesian nested sampling with PolyChord, which efficiently handles high-dimensional, multimodal posterior distributions. Finally, machine learning techniques are employed to achieve precise reconstruction of the model parameter $Λ$. For benchmark points producing strong signals, parameter reconstruction with both TianQin and LISA yields relative uncertainties of approximately $20$--$30\%$ in the signal amplitude and sub-percent precision in the model parameter $Λ$. TianQin's sensitivity is limited to stronger signals within its optimal frequency band, whereas LISA can reconstruct parameters across a broader range of signal strengths. Our results demonstrate that reconstruction precision depends on signal strength, astrophysical foregrounds, and instrumental noise characteristics.

Figures (13)

• Figure 1: Schematic overview of the parameter reconstruction pipeline used to extract the model parameter $\Lambda$ with TianQin and LISA.
• Figure 2: Noise PSD of the AET channels in the TianQin detector. These orthogonal TDI channels are constructed to suppress laser frequency noise across the mission's frequency band.
• Figure 3: Equal-arm Michelson channels of the regular triangle detector.
• Figure 4: Response Functions of AET channels in TianQin.
• Figure 5: Sensitivity curves of the AET channels for the TianQin detector.