[Paper Review] Vacuum structure and electroweak phase transition in singlet scalar model

Parsa Ghorbani|arXiv (Cornell University)|Oct 29, 2020

Cosmology and Gravitation Theories15 references4 citations

TL;DR

This paper investigates the vacuum structure and electroweak phase transition in an extended Standard Model with an additional real singlet scalar field under $\mathbb{Z}_2$ symmetry. It systematically analyzes one-step and two-step phase transitions, deriving precise parameter constraints for a first-order transition, including the possibility of a first-order transition within an intermediate temperature window in two-step scenarios.

ABSTRACT

In the presence of a real singlet scalar field with $\mathbb{Z}_2$ symmetry in addition to the Higgs field in the Standard Model, we study all possible one-step and two-step electroweak phase transitions. For each scenario we provide with the necessary conditions on the parameters of the model to guarantee a first-order phase transition if ever possible. In particular, we examine the possibility of a first-order phase transition in an intermediate temperature interval in two-step phase transitions.

Motivation & Objective

• To understand the vacuum structure of the Standard Model extended by a real singlet scalar field with $\mathbb{Z}_2$ symmetry.
• To determine the conditions under which a first-order electroweak phase transition occurs, including one-step and two-step scenarios.
• To investigate the existence and parameter requirements for a first-order transition in an intermediate temperature interval during a two-step phase transition.
• To provide a comprehensive parameter space analysis for viable first-order phase transitions in the singlet scalar model.

Proposed method

• Constructing the scalar potential of the extended model including the Higgs and singlet scalar fields with $\mathbb{Z}_2$ symmetry.
• Analyzing the vacuum structure by minimizing the effective potential at finite temperature.
• Deriving necessary conditions on model parameters (e.g., quartic couplings, mass terms) for a first-order phase transition using the condition that the barrier between vacua must be sufficiently high.
• Examining two-step transitions by identifying intermediate metastable vacua and evaluating the temperature dependence of the potential.
• Applying the criterion that a first-order transition occurs if the true vacuum is reached via a nucleation barrier, requiring a positive barrier height at the critical temperature.
• Using numerical and analytical techniques to map regions in parameter space where first-order transitions are possible, including intermediate temperature intervals in two-step scenarios.

Experimental results

Research questions

• RQ1 What are the necessary conditions on the model parameters for a first-order electroweak phase transition in the singlet scalar model?
• RQ2 Can a first-order phase transition occur in an intermediate temperature range during a two-step electroweak phase transition?
• RQ3 How does the presence of a $\mathbb{Z}_2$-symmetric singlet scalar field alter the vacuum structure and phase transition dynamics?
• RQ4 What are the constraints on the scalar couplings and masses that allow for a strong first-order transition in both one-step and two-step scenarios?
• RQ5 Is there a viable parameter region where a two-step transition includes a first-order transition in an intermediate temperature window?

Key findings

• The model allows for both one-step and two-step electroweak phase transitions depending on the parameter values, particularly the singlet-Higgs mixing and quartic couplings.
• A first-order phase transition is possible in a two-step scenario if the intermediate vacuum is metastable and the barrier between the symmetric and broken phases remains sufficiently high at intermediate temperatures.
• The paper derives explicit conditions on the scalar potential parameters—such as the quartic coupling between the Higgs and singlet fields and the singlet mass—that ensure a first-order transition.
• For two-step transitions, a first-order transition can occur in a finite temperature interval between the two critical temperatures, provided the potential has a local maximum separating the intermediate and true vacua.
• The analysis shows that viable first-order transitions require fine-tuned but physically consistent parameter regions, especially in the singlet sector.
• The results demonstrate that the $\mathbb{Z}_2$-symmetric singlet scalar model can support strong first-order phase transitions, which are relevant for baryogenesis and gravitational wave production.