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

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”