Strong Electroweak Phase Transitions in the Standard Model with a Singlet

Abstract: It is well known that the electroweak phase transition (EWPhT) in extensions of the Standard Model with one real scalar singlet can be first-order for realistic values of the Higgs mass. We revisit this scenario with the most general renormalizable scalar potential systematically identifying all regions in parameter space that develop, due to tree-level dynamics, a potential barrier at the critical temperature that is strong enough to avoid sphaleron wash-out of the baryon asymmetry. Such strong EWPhTs allow for a simple mean-field approximation and an analytic treatment of the free-energy that leads to very good theoretical control and understanding of the different mechanisms that can make the transition strong. We identify a new realization of such mechanism, based on a flat direction developing at the critical temperature, which could operate in other models. Finally, we discuss in detail some special cases of the model performing a numerical calculation of the one-loop free-energy that improves over the mean-field approximation and confirms the analytical expectations.

• The paper demonstrates that a singlet extension creates a tree-level barrier essential for strong first-order electroweak phase transitions.
• It identifies flat directions at the critical temperature, offering an analytically tractable framework to enhance thermal effects.
• Comprehensive parameter space analysis and numerical verification confirm viable regions for electroweak baryogenesis in singlet-extended models.

Overview of Strong Electroweak Phase Transitions in the Standard Model with a Singlet

The paper "Strong Electroweak Phase Transitions in the Standard Model with a Singlet" offers a comprehensive study of the conditions under which an extended Standard Model (SM) augmented by a scalar singlet can exhibit strong first-order electroweak phase transitions (EWPhTs). Previous investigations have suggested that such extensions can sustain first-order transitions; however, this work delves deeper into the specific mechanisms and parameter spaces involved, utilizing the most general form of the renormalizable scalar potential for a single real singlet.

The authors systematically analyze the conditions necessary for a strong EWPhT by focusing on the formation of a tree-level barrier, which separates broken and symmetric vacua at finite temperature. This barrier is crucial to prevent sphaleron-induced washout of the baryon asymmetry. Importantly, the paper identifies novel mechanisms that could enhance the strength of the EWPhT, including the existence of flat directions in the scalar field space at the critical temperature. Such flat directions allow a simple mean-field approximation and analytically tractable descriptions of the free energy, yielding robust theoretical insights.

Key Findings and Analysis

The paper highlights several important results and insights:

1. Tree-level Barriers: Central to a strong EWPhT is the existence of a tree-level barrier, distinct from the typical loop-induced cubic corrections that appear in thermal field theory. By examining several parameterizations and constraints on the scalar potentials, the authors determine the necessary conditions for these barriers to appear.
2. Flat Directions: Crucially, the paper identifies scenarios where flat directions arise at the critical temperature. These flat directions are significant because they enhance the impact of thermal effects, potentially leading to very strong first-order transitions, a key requirement for electroweak baryogenesis.
3. Parameter Space Exploration: Through analytical and numerical methods, diverse regions of parameter space are mapped out where strong transitions occur. The authors provide a systematic methodology for identifying such regions within the context of renormalizable extensions of the SM with a singlet.
4. Analytical Control and Numerical Verification: The study balances theoretical rigor with practical numerical approaches. A novel parametrization of the scalar potential parameters is introduced, enabling a stable description of the ewphic process. These analytical insights align well with results from precise numerical simulations that include one-loop corrections and thermal effects beyond the high-temperature approximation.
5. Special Cases and Model Extensions: Several specific cases and realistic extensions are discussed, including models with discrete symmetries (e.g., a $\mathbf{Z}_2$ symmetry), those relevant for the Next to Minimal Supersymmetric Standard Model (nMSSM), and models containing very light scalars. Each is analyzed to understand the rich spectrum of possible phase transitions.

Implications and Future Perspectives

The findings of this investigation have profound implications for theoretical physics and cosmology, particularly in understanding the nature of the electroweak symmetry-breaking process and its role in the early Universe. The enhanced transitions suggested by the presence of singlets or equivalent scalar fields open up new avenues for electroweak baryogenesis, offering ways to generate the observed matter-antimatter asymmetry without conflicting with current baryon number washout constraints.

Future studies could delve further into the implications of these findings, particularly concerning gravitational wave signals from the early Universe, which could serve as indirect evidence for such phase transitions. Moreover, as collider experiments continue to probe the Higgs sector and possible extensions beyond the SM, the theoretical frameworks and predictions outlined in this paper could guide experimental searches for singlet scalars and related phenomena. Exploring the interplay between these extensions and dark matter models also offers an intriguing avenue for further research. The insights gained from this study enrich the understanding of symmetry-breaking transitions and provide a solid foundation for developing models that meet theoretical and experimental challenges.