Gauge-independent treatment of the R2HDM effective potential

Develop a gauge-independent approach for calculating the finite-temperature effective potential and electroweak phase-transition observables in the real two-Higgs-doublet model, including within the on-shell-like renormalisation scheme used for the vacuum analysis.

Background

The paper calculates the thermal vacuum evolution and gravitational-wave spectra of the real, CP-conserving two-Higgs-doublet model using a four-dimensional effective potential. The strength parameter used to classify phase transitions is gauge dependent, so it is treated only as a proxy for the gauge-independent sphaleron energy.

The authors note that existing treatments do not provide a gauge-independent formulation for the R2HDM, either specifically or in a model-independent way, and that the issue also remains unresolved in the on-shell-like renormalisation scheme employed in the analysis. A successful solution would make predictions for phase-transition strength and related gravitational-wave signals more physically robust.

References

Nevertheless, the shape of the Higgs potential has not yet been fully determined experimentally, and the nature of the electroweak phase transition therefore remains one of the major open questions in particle physics.

— Interplay between decoupling and non-decoupling effective field theories in electroweak phase transitions  (2609.28171 - Hashino et al., 23 Sep 2026) in Section 1, Introduction

We are not aware, however, of a gauge-independent approach in the 2HDM nor in a model-independent way, and also not in the OS-like renormalisation scheme which we employ in our calculation.

— A Comprehensive Analysis of the R2HDM Vacuum Evolution and the Induced GW and Collider Phenomenology  (2608.25636 - Biermann et al., 26 Aug 2026) in Section 5, “Gravitational-Wave Signals and Uncertainties,” subsection preceding “Gravitational Wave Spectra”