Real effective potentials for phase transitions in models with extended scalar sectors

Abstract: The effective potential obtained by loop expansion is usually not real in the range of field values explored by its minima during a phase transition. We apply the optimized perturbation theory in a fixed gauge to singlet scalar extensions of the Standard Model in order to calculate a one-loop effective potential that is real by construction. We test this computational scheme by comparing such a potential obtained in Landau gauge to that derived based on the Higgs pole mass. We carry out the latter construction by imposing physical renormalization conditions, which yields a potential without residual regularization scale dependence. We use our effective potential to study the parameter dependence of the critical temperatures in a two-step phase transition of the form $(0,0)\to (0,w')\to (v,w)$ that occurs for decreasing temperature in scalar extensions of the SM with two vacuum expectation values $v$ and $w$.