Scale and electroweak first-order phase transitions

We consider phase transitions in the standard model (SM) without the Higgs mass term, which is coupled through a Higgs portal term to an SM singlet, classically scale-invariant gauge sector with SM singlet scalar fields. At lower energies the gauge-invariant scalar bilinear in the hidden sector forms a condensate, dynamically creating a robust energy scale, which is transmitted through the Higgs portal term to the SM sector. A scale phase transition is a transition between phases with zero and nonzero condensates. An interplay between the EW and scale phase transitions is therefore expected. We find that in a certain parameter space both the electroweak (EW) and scale phase transitions can be a strong first-order phase transition. The result is obtained by means of an effective theory for the condensation of scalar bilinear in the mean field approximation.