Electroweak phase transitions in a $U(1)_D$ extension of the standard model with dimension-six operators: Gravitational waves and LHC signatures

Abstract

We investigate the possibility of realizing strong first-order electroweak phase transition (SFOEWPT) in an effective field theory framework where the Standard Model is extended with a complex scalar singlet ($\phi$) charged under a local $U(1)_D$ gauge group. The tree-level scalar potential contains a dimension-six term of the form $|H|^2|\phi|^4$. We show that this higher-dimensional operator plays a crucial role in the phase transition dynamics by weakening the correlation between the Higgs-singlet portal coupling and the scalar mixing angle that typically constrains singlet-extended models. Consequently, SFOEWPT can be achieved over a significantly extended region of parameter space. The strength of the phase transition is primarily driven by the vacuum expectation value (VEV) of the singlet scalar which plays a central role in this analysis. We analyze the phase transition in this model and identify regions of parameter space consistent with SFOEWPT. The resulting phase transition can generate stochastic gravitational-wave signals potentially observable at future interferometers. The extended scalar sector in presence of the dimension-six operator also leads to distinctive multi-scalar production signatures at the LHC, intimately correlated with the singlet scalar VEV.