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

TL;DR

This paper introduces a method to compute a real, one-loop effective potential for scalar extensions of the Standard Model, enabling more accurate analysis of phase transitions with multiple vacuum expectation values.

Contribution

It applies optimized perturbation theory in a fixed gauge to produce a real effective potential, improving upon traditional loop expansion methods for phase transition studies.

Findings

The method yields a real effective potential with no residual scale dependence.

It accurately predicts critical temperatures in two-step phase transitions.

The approach is validated against potentials derived from physical renormalization conditions.

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 $w$.