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

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.