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A Catalog of First-Order Electroweak Phase Transitions in the Standard Model Effective Field Theory

Eliel Camargo-Molina, Rikard Enberg, Johan Löfgren

TL;DR

This work develops a dimensionally reduced, gauge-invariant framework to catalog first-order electroweak phase transitions in the SMEFT truncated at dimension six. By mapping SMEFT Higgs-sector operators onto a 3D effective potential with a phi^6 term, the authors classify barrier formation into tree-level, radiative, and Coleman–Weinberg–type mechanisms, including supercooled variants, and organize these into a comprehensive catalog based on perturbative scale hierarchies. They then perform a global likelihood scan over the Higgs-sector Wilson coefficients using a genetic algorithm, enforcing the observed Higgs mass and experimental constraints, to identify regions capable of supporting a first-order transition. The paper discusses implications for electroweak baryogenesis, estimates gravitational-wave observability, and outlines a roadmap for refining predictions with higher-order perturbation theory and lattice studies, highlighting the SQTLB scenario as particularly promising for detectable gravitational waves.

Abstract

We use modern dimensionally-reduced effective field theory methods, with careful attention to scale hierarchies, to analyze and catalog the types of first-order electroweak phase transitions that are possible in the Standard Model Effective Field Theory (SMEFT). Our calculations lay the necessary groundwork to perform gauge invariant, properly resummed perturbative expansions, and therefore address many of the theoretical problems with phase transition calculations. We find three types of configurations of the scalar potential that allow for a first-order phase transition, namely tree-level barriers, radiative barriers, or radiative symmetry breaking through the Coleman-Weinberg mechanism. We also find versions of these with significant supercooling. We perform a global likelihood scan over the Wilson coefficients of SMEFT operators involving only the Higgs field, to identify parameter regions that exhibit these first-order phase transitions and are consistent with experimental and theoretical constraints. We comment on the possibilities for electroweak baryogenesis within the SMEFT, and roughly estimate if the gravitational wave spectra generated by the phase transitions are detectable.

A Catalog of First-Order Electroweak Phase Transitions in the Standard Model Effective Field Theory

TL;DR

This work develops a dimensionally reduced, gauge-invariant framework to catalog first-order electroweak phase transitions in the SMEFT truncated at dimension six. By mapping SMEFT Higgs-sector operators onto a 3D effective potential with a phi^6 term, the authors classify barrier formation into tree-level, radiative, and Coleman–Weinberg–type mechanisms, including supercooled variants, and organize these into a comprehensive catalog based on perturbative scale hierarchies. They then perform a global likelihood scan over the Higgs-sector Wilson coefficients using a genetic algorithm, enforcing the observed Higgs mass and experimental constraints, to identify regions capable of supporting a first-order transition. The paper discusses implications for electroweak baryogenesis, estimates gravitational-wave observability, and outlines a roadmap for refining predictions with higher-order perturbation theory and lattice studies, highlighting the SQTLB scenario as particularly promising for detectable gravitational waves.

Abstract

We use modern dimensionally-reduced effective field theory methods, with careful attention to scale hierarchies, to analyze and catalog the types of first-order electroweak phase transitions that are possible in the Standard Model Effective Field Theory (SMEFT). Our calculations lay the necessary groundwork to perform gauge invariant, properly resummed perturbative expansions, and therefore address many of the theoretical problems with phase transition calculations. We find three types of configurations of the scalar potential that allow for a first-order phase transition, namely tree-level barriers, radiative barriers, or radiative symmetry breaking through the Coleman-Weinberg mechanism. We also find versions of these with significant supercooling. We perform a global likelihood scan over the Wilson coefficients of SMEFT operators involving only the Higgs field, to identify parameter regions that exhibit these first-order phase transitions and are consistent with experimental and theoretical constraints. We comment on the possibilities for electroweak baryogenesis within the SMEFT, and roughly estimate if the gravitational wave spectra generated by the phase transitions are detectable.

Paper Structure

This paper contains 23 sections, 96 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theoretical framework
  3. The Catalog
  4. Overview of the catalog
  5. Details of the catalog
  6. Mapping the parameter space of the SMEFT
  7. The setup
  8. Viable parameter space
  9. Mapping 4D to 3D
  10. Identifying first-order phase transitions
  11. Phenomenology
  12. Electroweak baryogenesis and sphaleron transitions
  13. Gravitational wave signal
  14. Higgs pair production
  15. Discussion
  16. ...and 8 more sections

Figures (2)

  • Figure 1: An overview of how the 3D parameter space can be sliced into different power-counting regions. Each region matches an entry in the catalog, in table \ref{['tab:catalog']}. The white stars denote power-countings for which the SMEFT is estimated to predict the correct Higgs mass and vev, see subsection \ref{['ssec:param-mapping']}. The black dot indicating the SM is based on lattice studies Kajantie:1996mn together with the DR matching relations. On the axes, note the "logarithmic" scale, and the hatch marks which emphasize that the axes have been cut. Finally, note that these regions are a projection which might lose some information, as the values of $m_3^2$ are not included, and that certain supercooled countings have been excluded as they overlap with other regions. As such, the figure should only be taken as a guiding sketch.
  • Figure 2: The points found by our scan, with better likelihood points on top. The points are colored according to whether they fall within the $1\sigma$, $2\sigma$, or $3\sigma$ confidence regions compared to the SM null hypothesis. The black line is the simplified prediction for which parameters get the correct Higgs mass and vev, based on the analysis in \ref{['eq:CphiPrediction']}. The shaded regions reflect which power countings from table \ref{['tab:catalog']} will be relevant for studying the phase transition in those regions, according to the analysis in sections \ref{['ssec:param-mapping']} and \ref{['ssec:first-order']}. The boundaries demarcating these regions are leading-order estimates based on the analysis in Sec. \ref{['ssec:first-order']}; they are expected to shift and theoretical uncertainties upon the inclusion of higher-order corrections.