Effective field theory for a singlet scalar extension of the standard model and electroweak phase transition

In this paper, we study an effective field theory (EFT) for a singlet scalar extension of the standard model (SM). The tree- and one-loop level effective actions are derived by integrating out the heavy singlet scalar in the Lagrangian for the UV theory and by applying to the functional method, respectively. In the UV model, the light scalar field identified with the SM Higgs is assumed to be massless in the symmetric phase. When the heavy singlet scalar acquires a vacuum expectation value, the [Formula: see text] symmetry is broken and a mass term of the light scalar is induced. In light of EFT we derive, the electroweak vacuum resulting in 126[Formula: see text]GeV Higgs mass can be attained when the induced squared-mass term of the light scalar in the scalar potential becomes negative. This condition can occur when the constant of the scalar coupling between the two different scalars is allowed to be negative. We investigate how the EFT can be constrained by theory and experiments. We also examine whether or not electroweak phase transition (EWPT) in this scenario can be a first order. Some numerical results leading to the first-order EWPT while satisfying the constraints studied are presented.