Abstract
To realize first-order electroweak phase transition, it is necessary to generate a barrier in the thermal Higgs potential, which is usually triggered by scalar degree of freedom. We instead investigate phase transition patterns in pure fermion extensions of the standard model, and find that additional fermions with mass hierarchy and mixing could develop such a barrier and realize a strongly first-order phase transition in such models. In the Higgs potential with polynomial parametrization, the barrier can be generated in the following two patterns by fermionic reduction effects: (I) positive quadratic term, negative cubic term and positive quartic term or (II) positive quadratic term, negative quartic term and positive higher dimensional term, such as dimensional 6 operator.
Highlights
To realize first-order electroweak phase transition, it is necessary to generate a barrier in the thermal Higgs potential, which is usually triggered by scalar degree of freedom
First-order electroweak phase transition is one of the crucial ingredients to realize the baryon asymmetry of the universe in electroweak baryogenesis scenario
Fermionic degree of freedom does not contribute to cubic term in the potential, it is still possible to develop a sizable barrier in the effective potential via either decreasing quadratic/quartic terms or adding higher dimensional operators
Summary
We consider a general ultraviolet theory containing several fields: the SM particles, new particles at the EW scale and new heavy particles at the TeV scale. The shift of scalar field with v0 (φ → φ + v0) shows up, where the subscript represents the bare parameter This shift evolves a linear term in the effective potential: −(μ20 + λ0v02)v0φ, and the form of effective potential containing tree-level and counter term is VeTfafd, 0,c = v μ2 +λv φ μ2. The diagrams are calculated by Feynman rules in the Lagrangian at LE scale with these operators Such effects are in field dependent masses, such as equations in appendix A.2 of ref. We neglect these effects of high dimensional operators, which can be obtained by one-loop diagrams for heavy fields, in the field dependent masses, because these are typically two-loop level conditions to the effective potential. The key result is the eq (2.19), the effective potential at the EW scale, which serves as the starting point to describe how a sizable barrier can be generated in a model with heavy fields. In the following analysis, we will focus on the extended fermion model and explore the phase transition pattern in such models
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