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On the criterion of perturbativity with the mass-dependent beta function in extended Higgs models
High Energy Physics - Phenomenology · Submitted 24 Oct 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that in our method, in which the threshold effect is automatically included, the energy scale where the perturbation calculation breaks down can be higher than the one using the mass-independent beta function, especially when the blow up scale is relatively low.
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The abstract, sentence by sentence
In order to realize electroweak first order phase transition, a category of extended Higgs models with relatively large self-coupling constants is often considered. In such a scenario, the running coupling constants can blow up at an energy scale much below the Planck scale. To clarify the allowed parameter space of the model, it is important to evaluate the scale where perturbation calculation breaks down. In the renormalization group equation analysis using the mass-independent renormalization scheme, we need the matching condition to connect the low energy theory and the high energy theory. Consequently, the analysis depends on the detail of the matching condition. On the other hand, the analysis with the mass-dependent beta function is performed in a simpler way, because the threshold effect is automatically included in the beta function. Therefore, in this paper, using the mass-dependent beta function at the one-loop level, we discuss the application limit of perturbation calculation. First, in a toy model with two complex scalar fields, we explain the essence of our method and compare our results with those based on the mass-independent beta function. We then apply our method to the more realistic model; i.e., the inert doublet model. We find that in our method, in which the threshold effect is automatically included, the energy scale where the perturbation calculation breaks down can be higher than the one using the mass-independent beta function, especially when the blow up scale is relatively low.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In order to realize electroweak first order phase transition, a category of extended Higgs models with relatively large self-coupling constants is often considered. | background 1.00 | 0.05 | 0.02 | asserted 0.88 |
| s1 | In such a scenario, the running coupling constants can blow up at an energy scale much below the Planck scale. | background 1.00 | 0.07 | 0.02 | asserted 0.53 |
| s2 | To clarify the allowed parameter space of the model, it is important to evaluate the scale where perturbation calculation breaks down. | background 0.84 | 0.08 | 0.02 | asserted 0.99 |
| s3 | In the renormalization group equation analysis using the mass-independent renormalization scheme, we need the matching condition to connect the low energy theory and the high energy theory. | background 0.95 | 0.11 | 0.02 | asserted 1.00 |
| s4 | Consequently, the analysis depends on the detail of the matching condition. | background 0.66 | 0.07 | 0.02 | asserted 1.00 |
| s5 | On the other hand, the analysis with the mass-dependent beta function is performed in a simpler way, because the threshold effect is automatically included in the beta function. | method 0.63 | 0.10 | 0.05 | asserted 1.00 |
| s6 | Therefore, in this paper, using the mass-dependent beta function at the one-loop level, we discuss the application limit of perturbation calculation. | contribution 0.87 | 0.89 | 0.08 | asserted 0.89 |
| s7 | First, in a toy model with two complex scalar fields, we explain the essence of our method and compare our results with those based on the mass-independent beta function. | method 0.81 | 0.90 | 0.03 | asserted 0.85 |
| s8 | We then apply our method to the more realistic model; i.e., the inert doublet model. | method 0.67 | 0.87 | 0.03 | asserted 0.85 |
| s9 | We find that in our method, in which the threshold effect is automatically included, the energy scale where the perturbation calculation breaks down can be higher than the one using the mass-independent beta function, especially when the blow up scale is relatively low. | result 1.00 | 0.96 | 0.90 | asserted 0.99 |
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The paper
Original abstract
In order to realize electroweak first order phase transition, a category of extended Higgs models with relatively large self-coupling constants is often considered. In such a scenario, the running coupling constants can blow up at an energy scale much below the Planck scale. To clarify the allowed parameter space of the model, it is important to evaluate the scale where perturbation calculation breaks down. In the renormalization group equation analysis using the mass-independent renormalization scheme, we need the matching condition to connect the low energy theory and the high energy theory. Consequently, the analysis depends on the detail of the matching condition. On the other hand, the analysis with the mass-dependent beta function is performed in a simpler way, because the threshold effect is automatically included in the beta function. Therefore, in this paper, using the mass-dependent beta function at the one-loop level, we discuss the application limit of perturbation calculation. First, in a toy model with two complex scalar fields, we explain the essence of our method and compare our results with those based on the mass-independent beta function. We then apply our method to the more realistic model; i.e., the inert doublet model. We find that in our method, in which the threshold effect is automatically included, the energy scale where the perturbation calculation breaks down can be higher than the one using the mass-independent beta function, especially when the blow up scale is relatively low.
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References
How the literature uses it
3 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Uses its method or tool 1 paper
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We take into account the constraint from the triviality bound by employing mass dependent beta functions [ref] .
Primordial black holes from slow phase transitions: a model-building perspective · The $_2$-symmetric singlet extension of the SM · 0.99
What it cites · 46 sentences without a confident label
Uses the method or tool of 9 papers
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In order to obtain analytic formulae for the vertex functions, we use [ref] , [ref] and [ref] .
Generating Feynman Diagrams and Amplitudes with FeynArts 3 · Simplest example of the non-decoupling case · 1.00
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In order to obtain analytic formulae for the vertex functions, we use [ref] , [ref] and [ref] .
FeynRules 2.0 - A complete toolbox for tree-level phenomenology · Simplest example of the non-decoupling case · 1.00
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In order to obtain analytic formulae for the vertex functions, we use [ref] , [ref] and [ref] .
New Developments in FeynCalc 9.0 · Simplest example of the non-decoupling case · 1.00
Cites as background 17 papers
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For example, in the scenario based on EW baryogenesis [ref] , extended Higgs sectors are introduced to realize Strongly First Order EW Phase Transition (SFOPT), while it is smooth crossover in the SM [ref] .
The Standard Model cross-over on the lattice · Introduction · 0.85
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For example, in the scenario based on EW baryogenesis [ref] , extended Higgs sectors are introduced to realize Strongly First Order EW Phase Transition (SFOPT), while it is smooth crossover in the SM [ref] .
Is There a Hot Electroweak Phase Transition at $m_H\gsim m_W$? · Introduction · 0.85
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In addition, EW running coupling constants [ref] and vacuum stability [ref] in the SM, the proton decay [ref] and unification of the coupling constants [ref] in the GUT, etc., also have been studied in this method.
Precision Corrections to Supersymmetric Unification · Introduction · 0.84
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