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Scalar excitation with Leggett frequency in $^3$ He-B and the $125$ GeV Higgs particle in top quark condensation models as Pseudo - Goldstone bosons
High Energy Physics - Phenomenology · Submitted 26 Oct 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim As a result the only CP - even Goldstone boson acquires a mass and may be considered as the candidate for the role of the $125$ GeV scalar boson.
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The abstract, sentence by sentence
We consider the scenario, in which the light Higgs scalar boson appears as the Pseudo - Goldstone boson. We discuss examples both in condensed matter and in relativistic field theory. In $^3$He-B the symmetry breaking gives rise to 4 Nambu-Goldstone modes and 14 Higgs modes. At lower energy one of the four NG modes becomes the Higgs boson with small mass. This is the mode measured in experiments with the longitudinal NMR, and the Higgs mass corresponds to the Leggett frequency $M_{\rm H}=\hbar \Omega_L$. The formation of the Higgs mass is the result of the violation of the hidden spin-orbit symmetry at low energy. In this scenario the symmetry breaking energy scale $\Delta$ (the gap in the fermionic spectrum) and the Higgs mass scale $M_{\rm H}$ are highly separated: $M_{\rm H}\ll \Delta$. On the particle physics side we consider the model inspired by the models of \cite{dobrescu,Yamawaki}. At high energies the $SU(3)$ symmetry is assumed that relates the left - handed top and bottom quarks to the additional fermion $\chi_L$. This symmetry is softly broken at low energies. As a result the only CP - even Goldstone boson acquires a mass and may be considered as the candidate for the role of the $125$ GeV scalar boson. We consider the condensation pattern different from the one typical for the top - seesaw models, where the condensate $< \bar{t}_L\chi_R >$ is off - diagonal. In our case the condensates are mostly diagonal. Unlike \cite{dobrescu,Yamawaki} the explicit mass terms are absent and the soft breaking of $SU(3)$ symmetry is given solely by the four - fermion terms. This reveals the complete analogy with $^3$He, where there is no explicit mass term and the spin - orbit interaction has the form of the four - fermion interaction.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider the scenario, in which the light Higgs scalar boson appears as the Pseudo - Goldstone boson. | contribution 0.74 | 0.25 | 0.44 | asserted 0.65 |
| s1 | We discuss examples both in condensed matter and in relativistic field theory. | contribution 0.81 | 0.75 | 0.04 | asserted 0.74 |
| s2 | In $^3$He-B the symmetry breaking gives rise to 4 Nambu-Goldstone modes and 14 Higgs modes. | background 0.55 | 0.23 | 0.06 | asserted 1.00 |
| s3 | At lower energy one of the four NG modes becomes the Higgs boson with small mass. | result 0.81 | 0.22 | 0.11 | asserted 1.00 |
| s4 | This is the mode measured in experiments with the longitudinal NMR, and the Higgs mass corresponds to the Leggett frequency $M_{\rm H}=\hbar \Omega_L$. | result 0.70 | 0.17 | 0.14 | asserted 1.00 |
| s5 | The formation of the Higgs mass is the result of the violation of the hidden spin-orbit symmetry at low energy. | interpretation 0.84 | 0.33 | 0.11 | asserted 1.00 |
| s6 | In this scenario the symmetry breaking energy scale $\Delta$ (the gap in the fermionic spectrum) and the Higgs mass scale $M_{\rm H}$ are highly separated: $M_{\rm H}\ll \Delta$. | result 0.79 | 0.37 | 0.10 | asserted 1.00 |
| s7 | On the particle physics side we consider the model inspired by the models of \cite{dobrescu,Yamawaki}. | method 0.42 | 0.34 | 0.04 | asserted 0.83 |
| s8 | At high energies the $SU(3)$ symmetry is assumed that relates the left - handed top and bottom quarks to the additional fermion $\chi_L$. | method 0.66 | 0.15 | 0.04 | asserted 0.88 |
| s9 | This symmetry is softly broken at low energies. | method 0.62 | 0.16 | 0.04 | asserted 1.00 |
| s10 | As a result the only CP - even Goldstone boson acquires a mass and may be considered as the candidate for the role of the $125$ GeV scalar boson. | result 0.63 | 0.41 | 0.33 | hedged possibility 1.00 |
| s11 | We consider the condensation pattern different from the one typical for the top - seesaw models, where the condensate $< \bar{t}_L\chi_R >$ is off - diagonal. | contribution 0.72 | 0.65 | 0.06 | asserted 0.98 |
| s12 | In our case the condensates are mostly diagonal. | contribution 0.67 | 0.75 | 0.05 | asserted 0.98 |
| s13 | Unlike \cite{dobrescu,Yamawaki} the explicit mass terms are absent and the soft breaking of $SU(3)$ symmetry is given solely by the four - fermion terms. | contribution 0.57 | 0.66 | 0.11 | asserted 1.00 |
| s14 | This reveals the complete analogy with $^3$He, where there is no explicit mass term and the spin - orbit interaction has the form of the four - fermion interaction. | interpretation 0.97 | 0.62 | 0.26 | asserted 1.00 |
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The paper
Original abstract
We consider the scenario, in which the light Higgs scalar boson appears as the Pseudo - Goldstone boson. We discuss examples both in condensed matter and in relativistic field theory. In $^3$He-B the symmetry breaking gives rise to 4 Nambu-Goldstone modes and 14 Higgs modes. At lower energy one of the four NG modes becomes the Higgs boson with small mass. This is the mode measured in experiments with the longitudinal NMR, and the Higgs mass corresponds to the Leggett frequency $M_{\rm H}=\hbar \Omega_L$. The formation of the Higgs mass is the result of the violation of the hidden spin-orbit symmetry at low energy. In this scenario the symmetry breaking energy scale $\Delta$ (the gap in the fermionic spectrum) and the Higgs mass scale $M_{\rm H}$ are highly separated: $M_{\rm H}\ll \Delta$. On the particle physics side we consider the model inspired by the models of \cite{dobrescu,Yamawaki}. At high energies the $SU(3)$ symmetry is assumed that relates the left - handed top and bottom quarks to the additional fermion $\chi_L$. This symmetry is softly broken at low energies. As a result the only CP - even Goldstone boson acquires a mass and may be considered as the candidate for the role of the $125$ GeV scalar boson. We consider the condensation pattern different from the one typical for the top - seesaw models, where the condensate $< \bar{t}_L\chi_R >$ is off - diagonal. In our case the condensates are mostly diagonal. Unlike \cite{dobrescu,Yamawaki} the explicit mass terms are absent and the soft breaking of $SU(3)$ symmetry is given solely by the four - fermion terms. This reveals the complete analogy with $^3$He, where there is no explicit mass term and the spin - orbit interaction has the form of the four - fermion interaction.
Human review
How the literature uses it
5 arXiv papers cite this in 31 sentences
Papers citing it · 28 sentences without a confident label
Uses its method or tool 1 paper
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The possibility to apply the mentioned shift of the integration variable is used when we calculate the one - loop effective action for the composite scalar boson [ref] .
Modified top quark condensation model with the extra heavy fermion, the $125$ GeV Pseudo - Goldstone boson, and the additional heavy scalar bosons · Gap equation and the basis of mass eigenstates · 0.95
Uses its data or values 1 paper
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The decay of $H^'$ to $bb̅$ goes through the exchange by the virtual charged scalar whose mass was denoted in [ref] by $M^ (2)_H^±_t, H^±_χ$.
Modified top quark condensation model with the extra heavy fermion, the $125$ GeV Pseudo - Goldstone boson, and the additional heavy scalar bosons · Partial widths · 0.85
Cites it as background 1 paper
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The extensive discussion of this issue may be found in [ref] , and in the references therein.
Modified top quark condensation model with the extra heavy fermion, the $125$ GeV Pseudo - Goldstone boson, and the additional heavy scalar bosons · Conclusion and discussions · 0.86
What it cites · 26 sentences without a confident label
Uses data or values from 2 papers
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The corresponding experimental data are presented in Fig. 25 of [ref] .
Observation of the diphoton decay of the Higgs boson and measurement of its properties · The Effective lagrangian for the decays of the CP - even Pseudo - Goldstone boson (neglecting the ratio $m_t/m_χ$) · 0.95
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In the SM we have $c_Z=c_W = 1$, while $c_g ≃1.03 , c_γ ≈-0.81$ (see [ref] ).
Higgs After the Discovery: A Status Report · The Effective lagrangian for the decays of the CP - even Pseudo - Goldstone boson (neglecting the ratio $m_t/m_χ$) · 0.94
Compares with 2 papers
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Our model (as well as the models of [ref] ) contains the CP - even light Higgs, whose mass appears as a result of the soft breakdown of $SU(3)_L$ symmetry.
Higgs mass from compositeness at a multi-TeV scale · Conclusion and discussions · 0.97
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Our model (as well as the models of [ref] ) contains the CP - even light Higgs, whose mass appears as a result of the soft breakdown of $SU(3)_L$ symmetry.
Higgs as a Top-Mode Pseudo · Conclusion and discussions · 0.97
Cites as background 3 papers
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For the further discussion of this issue see [ref] and references therein.
Strong dynamics behind the formation of the $125$ GeV Higgs boson · Introduction · 0.87
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In addition to the TC and the top – quark condensation models, models were developed [ref] (topcolor, topcolor assisted Technicolor, etc) that contain the elements of both mentioned approaches.
A Flavorful Top-Coloron Model · Introduction · 1.00
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The NJL model in dimensional regularization was considered, for example, in [ref] .
Regularization in the Gauged Nambu--Jona-Lasinio Model · Introduction · 0.90
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