Perturbative aspects of the electroweak phase transition with a complex singlet and implications for gravitational wave predictions
4 affiliations
- 1Instituto de Física Teórica UAM/CSIC
- 2Deutsches Elektronen-Synchrotron DESY
- 3Universidad de Granada
- 4Universität Hamburg
Abstract
A bstract : We present a detailed analysis of strong first-order electroweak phase transitions within the extension of the Standard Model by a complex scalar singlet (cxSM). Focusing on the impact of renormalization scale and gauge dependence, we systematically compare commonly used perturbative frameworks for predicting thermodynamic observables that characterize the phase transition and the associated gravitational-wave (GW) spectrum. These include both the four-dimensional (4 D ) formalism and the dimensionally reduced three-dimensional effective field theory (3 D EFT) approach in different renormalization schemes. Within the 3 D EFT, we compute the effective potential up to two-loop order in a general R ξ gauge, and demonstrate that applying the ℏ-expansion yields gauge-independent results in excellent agreement with those obtained from a direct minimization of the loop-corrected potential. In contrast, large discrepancies between the two methods persist in the 4 D approaches. We find that, across most of the parameter space, the 3 D EFT approach provides predictions for phase-transition parameters and GW spectra with theoretical uncertainties in the GW peak amplitude that are reduced by more than an order of magnitude compared to the 4 D calculations. We point out, however, that the 3 D EFT approach is subject to an additional theory uncertainty from truncating the EFT at finite operator dimension and show that higher-dimensional operators within the 3 D EFT approach can substantially modify the predicted transition strength and GW signals. This indicates a potential breakdown of the high-temperature expansion precisely in the region with the lowest transition temperatures, where the strongest GW signals are expected and the detection prospects with LISA are most promising.
Related
- Towards accurate gravitational wave predictions: gauge-invariant nucleation in the electroweak phase transition
- QCD and electroweak phase transitions with hidden scale invariance: implications for primordial black holes, quark-lepton nuggets and gravitational waves
- Connecting Vector-like Muons, pNGB Dark Matter and Electroweak Phase Transition through Collider and Gravitational Wave
- Strong First-Order Electroweak Phase Transition and Gravitational Waves in a ℤ4 Fermion-Scalar Dark Matter Model
- Non-Perturbative Approach to Gravitational Particle Production in the Inflation-Kination Transition: Surveying a Wide Range of the Parameter Space
BibTeX
@article{biekotter2026perturbative,
title = {{Perturbative aspects of the electroweak phase transition with a complex singlet and implications for gravitational wave predictions}},
author = {Thomas Biekötter and Andrii Dashko and Maximilian Löschner and Georg Weiglein},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)060},
url = {https://link.springer.com/10.1007/JHEP10(2026)060},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Perturbative aspects of the electroweak phase transition with a complex singlet and implications for gravitational wave predictions
AU - Thomas Biekötter
AU - Andrii Dashko
AU - Maximilian Löschner
AU - Georg Weiglein
PY - 2026
DA - 2026/10/05
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)060
UR - https://link.springer.com/10.1007/JHEP10(2026)060
AB - A bstract : We present a detailed analysis of strong first-order electroweak phase transitions within the extension of the Standard Model by a complex scalar singlet (cxSM). Focusing on the impact of renormalization scale and gauge dependence, we systematically compare commonly used perturbative frameworks for predicting thermodynamic observables that characterize the phase transition and the associated gravitational-wave (GW) spectrum. These include both the four-dimensional (4 D ) formalism and the dimensionally reduced three-dimensional effective field theory (3 D EFT) approach in different renormalization schemes. Within the 3 D EFT, we compute the effective potential up to two-loop order in a general R ξ gauge, and demonstrate that applying the ℏ-expansion yields gauge-independent results in excellent agreement with those obtained from a direct minimization of the loop-corrected potential. In contrast, large discrepancies between the two methods persist in the 4 D approaches. We find that, across most of the parameter space, the 3 D EFT approach provides predictions for phase-transition parameters and GW spectra with theoretical uncertainties in the GW peak amplitude that are reduced by more than an order of magnitude compared to the 4 D calculations. We point out, however, that the 3 D EFT approach is subject to an additional theory uncertainty from truncating the EFT at finite operator dimension and show that higher-dimensional operators within the 3 D EFT approach can substantially modify the predicted transition strength and GW signals. This indicates a potential breakdown of the high-temperature expansion precisely in the region with the lowest transition temperatures, where the strongest GW signals are expected and the detection prospects with LISA are most promising.
SN - 1029-8479
ER -