# Thermal phase transition with full 2-loop effective potential

## TL;DR

This paper develops a resummed 2-loop effective potential calculation for extended Higgs models, avoiding high-temperature expansion, and assesses its impact on phase transition strength, relevant for cosmological phenomena.

## Contribution

It introduces a method to compute the 2-loop effective potential without high-T expansion and evaluates its effects on phase transition properties in extended Higgs models.

## Key findings

- 2-loop corrections weaken the phase transition but remain moderate
- High-T expansion performs well except for critical temperature Tc
- Strong phase transitions are still possible with large couplings

## Abstract

Theories with extended Higgs sectors constructed in view of cosmological ramifications (gravitational wave signal, baryogenesis, dark matter) are often faced with conflicting requirements for their couplings; in particular those influencing the strength of a phase transition may be large. Large couplings compromise perturbative studies, as well as the high-temperature expansion that is invoked in dimensionally reduced lattice investigations. With the example of the inert doublet extension of the Standard Model (IDM), we show how a resummed 2-loop effective potential can be computed without a high-T expansion, and use the result to scrutinize its accuracy. With the exception of Tc, which is sensitive to contributions from heavy modes, the high-T expansion is found to perform well. 2-loop corrections weaken the transition in IDM, but they are moderate, whereby a strong transition remains an option.