Gravitational waves from patterns of electroweak symmetry breaking: an effective perspective

The future space-borne gravitational wave (GW) detectors would provide a promising probe for the new physics beyond the standard model that admits the first-order phase transitions. The predictions for the GW background vary sensitively among different concrete particle physics models but also share a large degeneracy in the model buildings, which motivates an effective model description on the phase transition based on different patterns of the electroweak symmetry breaking (EWSB). In this paper, using the scalar $N$-plet model as a demonstration, we propose an effective classification for three different patterns of EWSB: (1) radiative symmetry breaking with classical scale invariance, (2) Higgs mechanism in generic scalar extension, and (3) higher dimensional operators. We conclude that a strong first-order phase transition could be realized for (1) and (2) with a small quartic coupling and a small isospin of an additional $N$-plet field for the light scalar field model with and without the classical scale invariance, and (3) with a large mixing coupling between scalar fields and a large isospin of the $N$-plet field for the heavy scalar field model.