Abstract
We examine $CP$-violating effects on electroweak phase transition (EWPT) in the standard model with a complex singlet scalar focusing particularly on a scenario where additional scalars have masses close to 125 GeV. Such a high mass degeneracy makes collider signatures in the scenario standard model like, and current experimental data cannot distinguish them from the standard model predictions. We utilize a simplified scalar potential to understand impacts of $CP$ violation on EWPT qualitatively. Then, one-loop effective potential with a thermal resummation is employed for full numerical evaluations. As a phenomenological consequence, gravitational waves from the first-order EWPT are also evaluated. We find that the strength of the first-order EWPT would get weaker as the $CP$-violating effect becomes larger. As a result, gravitational wave amplitudes are diminished by the size of the $CP$ violation. Future gravitational wave experiments may shed light on $CP$ violation in the singlet scalar sector as well as the experimental blind spot due to the high mass degeneracy.
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