Electroweak baryogenesis between broken phases in multi-step phase transition

Hiroto Shibuya; Mayumi Aoki

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Electroweak baryogenesis between broken phases in multi-step phase transition

Mayumi Aoki, Hiroto Shibuya

High Energy Physics - Phenomenology · Submitted 22 Feb 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the second step PTs where the sphaleron rate is possible to be un-suppressed before the PTs, which can reproduce the sufficient baryon number asymmetry.

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Possibility of electroweak baryogenesis (EWBG) via multi-step phase transition (PT) is considered. We investigate the EWBG between $SU(2)$ broken phases in the second step PT of the two-step PT. The produced baryon number asymmetry is evaluated using a prototypical model with a $SU(2)$ charged CP-odd scalar field. We show that the second step PTs where the sphaleron rate is possible to be un-suppressed before the PTs, which can reproduce the sufficient baryon number asymmetry. Our studies can be adapted to models with extra $SU(2)$ scalar fields. We discuss specific models suitable for our scenario.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Possibility of electroweak baryogenesis (EWBG) via multi-step phase transition (PT) is considered.	background 0.73	0.34	0.05	hedged possibility 0.94
s1	We investigate the EWBG between $SU(2)$ broken phases in the second step PT of the two-step PT.	contribution 0.99	0.89	0.06	asserted 0.83
s2	The produced baryon number asymmetry is evaluated using a prototypical model with a $SU(2)$ charged CP-odd scalar field.	method 0.99	0.90	0.04	asserted 0.98
s3	We show that the second step PTs where the sphaleron rate is possible to be un-suppressed before the PTs, which can reproduce the sufficient baryon number asymmetry.	result 0.98	0.89	0.80	asserted 0.94
s4	Our studies can be adapted to models with extra $SU(2)$ scalar fields.	future work 0.75	0.45	0.04	hedged possibility 0.63
s5	We discuss specific models suitable for our scenario.	contribution 0.90	0.72	0.04	asserted 0.62

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Original abstract

Possibility of electroweak baryogenesis (EWBG) via multi-step phase transition (PT) is considered. We investigate the EWBG between $SU(2)$ broken phases in the second step PT of the two-step PT. The produced baryon number asymmetry is evaluated using a prototypical model with a $SU(2)$ charged CP-odd scalar field. We show that the second step PTs where the sphaleron rate is possible to be un-suppressed before the PTs, which can reproduce the sufficient baryon number asymmetry. Our studies can be adapted to models with extra $SU(2)$ scalar fields. We discuss specific models suitable for our scenario.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Stable Electroweak Strings and Nambu Monopoles Nested at Inert-Higgs Interfaces
hep-ph 2026-10 accept novelty 7.0 of 10

An interface between degenerate inert and inert-like Higgs vacua supports locally stable Z strings, fractional strings, and topologically protected Nambu monopoles that stay confined or deconfined depending on wall couplings.
Super-critical primordial black hole formation via delayed first-order electroweak phase transition
hep-ph 2025-01 conditional novelty 4.0 of 10

Delayed first-order electroweak phase transitions can form super-critical primordial black holes, and a timescale ratio t_H/t_V captures the threshold better than the standard density contrast.

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7 arXiv papers cite this in 8 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Cites it as background 5 papers

The two Higgs doublet model (2HDM) is one of the most straightforward extensions of the Higgs sector, in which EWBG has been studied for a long time [ref] .

Electroweak baryogenesis in 2HDM without EDM cancellation · Introduction · 0.93
In the past few years, multi-step phase transitions were studied in many papers within the loop-corrected effective potential, with a focus on baryogenesis and generation of non-standard spectra of gravitational waves, see for example [ref] and references therein.

Charge-breaking domain walls separating neutral vacua in multi-Higgs models · Phase transitions in multi-Higgs models · 0.80
The simplest extensions introduce additional scalar fields, such as the real/complex singlet extension [ref] , the two-Higgs-doublet model (2HDM) [ref] , or the $SU(2)$ dark sector [ref] .

Electroweak First-Order Phase Transition Triggered by Non-Gaussian Fluctuations of a $\mathbb{Z}_2$-Symmetric Spectator Scalar · Introduction · 0.96

What it cites · 67 sentences without a confident label

Contests 8 papers

In contrast to Ref. [ref] , using CosmoTransitions [ref] , we find the PTs where the sphaleron rates before the second step PT would be hardly suppressed.

CosmoTransitions: Computing Cosmological Phase Transition Temperatures and Bubble Profiles with Multiple Fields · Discussions and conclusion · contest 0.75
In contrast to Ref. [ref] , using CosmoTransitions [ref] , we find the PTs where the sphaleron rates before the second step PT would be hardly suppressed.

Baryon Asymmetry from a Two Stage Electroweak Phase Transition ? · Discussions and conclusion · contest 0.75
However, Ref. [ref] shows the inaccuracy of the method.] To obtain enough BAU in one-step PT in 2HDMs, a cancellation mechanism for suppressing the electron EDM is necessary [ref] .

Aligned CP-violating Higgs sector canceling the electric dipole moment · Discussions and conclusion · contest 0.77

Builds on 1 paper

Although Ref. [ref] used the simplified model and PT calculation, we investigate two-step PT in a more general model called the inert doublet model, including loop contributions for the scalar potential.

Baryon Asymmetry from a Two Stage Electroweak Phase Transition ? · Introduction · 0.93

Uses the method or tool of 3 papers

In order to treat a region where the calculation of $Γ_sph^br$ is not reliable, Ref. [ref] suggested treating the overall sphaleron by introducing the suppression factor $f_sph$ as $Γ_sph^sym f_sph$, where the factor is given by [equation] In this letter, we call the method the CKT prescription.

Electroweak Baryogenesis in Two Higgs Doublet Models and B meson anomalies · Sphaleron rates and baryon asymmetry · 0.99
The transport equations for the chemical potentials of the top quarks $μ_t$ and $μ_t^c$, left-handed bottom quarks $μ_b$, Higgs doublets $μ_h$, and the relevant plasma velocities $u_k$ ($k=t,b,t^c,h$) in the CK scheme are [ref] [equation]

Electroweak baryogenesis at high wall velocities · Transport equations · 0.94
The transport equations for the chemical potentials of the top quarks $μ_t$ and $μ_t^c$, left-handed bottom quarks $μ_b$, Higgs doublets $μ_h$, and the relevant plasma velocities $u_k$ ($k=t,b,t^c,h$) in the CK scheme are [ref] [equation]

New benchmark scenarios of electroweak baryogenesis in aligned two Higgs double models · Transport equations · 0.94

Uses data or values from 2 papers

The sphaleron energy $E_sph$ is given by [ref] [equation] where the constant $B$ is evaluated as the function of $x=m_h/m__W$, [equation] In the SM, the value of $B$ is $B≃1.96$.

Finite temperature field theory and phase transitions · Sphaleron rates and baryon asymmetry · 0.89
The value of the BAU $η_B≡(n_B-n_B̅)/s$ is observed by the Planck satellite as [ref] [equation] where $n_B (n_B̅)$ is the number density of (anti-)baryon number $n_B (n_B̅)$ and $s$ is the entropy density.

Planck 2018 results. VI. Cosmological parameters · Introduction · 1.00

Compares with 1 paper

The differences between the schemes are consistent with Ref. [ref] . ] The colors in the plane indicate the produced baryon asymmetries when the second step PT occurs from the point $(w_h, w__CP)$ to the EW vacuum.

Electroweak baryogenesis at high wall velocities · Numerical results · 0.89

Cites as background 42 papers

Refs. [ref] consider the two-step PT where the second step occurs from the point on the $ϕ_2$ axis to that on the $ϕ_1$ axis.

Two Stage Phase Transition in Two Higgs Models · Discussions and conclusion · 0.87
Refs. [ref] consider the two-step PT where the second step occurs from the point on the $ϕ_2$ axis to that on the $ϕ_1$ axis.

Baryon Asymmetry from a Two Stage Electroweak Phase Transition ? · Discussions and conclusion · 0.87
The features of the multi-step PTs are investigated in Refs. [ref] .

Possibility of multi-step electroweak phase transition in the two Higgs doublet models · Introduction · 0.94

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