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REVIEW 5 major objections 5 minor 35 references

A scale invariant extension of the Georgi Machacek model

T0 review · 5 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A classically scale-invariant Georgi-Machacek model with a singlet generates the electroweak scale radiatively, preserves custodial symmetry, and predicts a scalon below about 200 GeV.

desk verdict Novel scale-invariant GM+singlet model, but the printed mass matrix and the Higgs chi-square analysis do not support the claimed viable regions. read the letter →

arxiv 2504.19187 v1 pith:Q4XKHATS submitted 2025-04-27 hep-ph

Hamza Taibi This is my paper · ORCID
classification hep-ph
keywords classicalscaleinvarianceGeorgi-MachacekmodelColeman-WeinbergmechanismGildener-WeinbergflatdirectionscaloncustodialsymmetryelectroweakbreakingHiggssignalstrengths
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper constructs a version of the Georgi-Machacek triplet Higgs model in which no mass parameter appears at the classical level: a gauge-singlet scalar is added and every term in the potential is quartic. It argues that radiative corrections, treated through the Gildener-Weinberg flat-direction formalism, generate a vacuum expectation value, so the electroweak scale emerges by dimensional transmutation rather than by hand. The resulting spectrum keeps the quintet and triplet states of the original model and adds three CP-even singlets: a light pseudo-Goldstone scalon, the 125 GeV Higgs, and a heavier scalar. Vacuum stability, perturbative unitarity, the $S$ parameter, and Higgs signal-strength data are then imposed, and the scan finds viable regions with scalon mass below about 200 GeV and the heavier scalar below about 600 GeV. If the construction is right, it offers a fine-tuning-free route to electroweak symmetry breaking that remains testable through modified Higgs couplings and new scalar states.

What carries the argument

The load-bearing object is the Gildener-Weinberg flat-direction construction applied to a scale-invariant potential. The tree-level potential is reduced to a radial field $\varphi$ and unit direction components $N_h,N_\delta,N_s$; the minimization conditions together with $V_0=0$ define a flat direction when $\det A=0$, and dimensional transmutation is invoked to locate the scale $\mu_{\mathrm{GW}}$ at which that condition is met. The one-loop effective potential then supplies the scalon mass $$$M_s^{2}$=\frac{1}{8\pi v_\$varphi^{2}$}\left(5M_{H_5}^4+3M_{H_3}^4+$M_h^{4}$+$M_H^{4}$+$6M_W^{4}$+$3M_Z^{4}$-$12M_t^{4}$\right),$$ and the CP-even mass matrix in the $(S,\phi_R,H_1^0)$ basis, rotated by angles $\alpha,\beta,\gamma$, decides which linear combination is the 125 GeV Higgs. The positivity requirement on this formula is what forces the new scalar states to be heavy enough to appear in the scan's viable bands.

What would settle it

Take a claimed viable point from the scan, reconstruct the quartic couplings from the mass and minimization equations, and check that the flat-direction existence condition is satisfied; if a point that passes all published constraints fails that check, the advertised regions are not realizable. Experimentally, discovering a scalon with mass above about 200 GeV would fall outside the paper's claimed viable region.

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Extended reading notes

Core claim

The central claim is that a classically scale-invariant extension of the Georgi-Machacek model --- one doublet, two triplets, and one gauge singlet with only quartic couplings --- can break electroweak symmetry radiatively. Along a flat direction of the tree-level potential, parameterized by $\varphi$ and a unit direction $(n_s,n_h,\sqrt{3}n_\delta)$, the one-loop effective potential $V_1(\varphi)=A\varphi^4+B\varphi^4\ln(\varphi^2/\mu_{\mathrm{GW}}^2)$ lifts the vacuum degeneracy and fixes $\langle\varphi\rangle=v_\varphi$ through $\ln(v_\varphi/\mu_{\mathrm{GW}})=-1/4-A/(2B)$. The spectrum retains the $H_5$ quintet and $H_3$ triplet states, and the CP-even neutral sector contains three singlets: one identified with the observed 125 GeV Higgs, one heavier scalar $H$, and the pseudo-Goldstone scalon, which acquires mass only at one loop. After imposing vacuum stability, unitarity, electroweak precision, and Higgs data, the paper finds viable parameter regions with $m_s\lesssim200$ GeV and $m_H\lesssim600$ GeV, with $v_\Delta\gtrsim45$ GeV favored.

Load-bearing premise

The load-bearing premise is that every point in the paper's six-parameter scan can be realized by quartic couplings for which the tree-level potential has a flat direction; the paper does not show the explicit mapping from the scanned masses and angles back to those couplings.

Editorial extensions

If this is right

  • The electroweak scale is not an input: radiative corrections select $v_\varphi$, so the model has no fundamental scalar mass parameter to be destabilized by quantum corrections.
  • The model predicts a light pseudo-Goldstone scalon, typically below 200 GeV, and a heavier CP-even scalar $H$ under about 600 GeV, with a triplet VEV above about 45 GeV; these are concrete search targets.
  • Custodial symmetry is preserved with $\rho\approx1$ at tree level, and the $S$ parameter plus the coupling modifiers $\kappa_V,\kappa_f$ provide electroweak precision and Higgs-data tests of the scheme.
  • If the invisible decay $h\to ss$ is kinematically open, the Higgs total width and signal strengths shift relative to the Standard Model, giving another observable signature.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: a decisive cross-check is to invert the six scanned parameters back to the eight quartic couplings and verify that every advertised viable point satisfies the flat-direction existence condition; the paper leaves that mapping implicit.
  • Beyond the paper: the mechanism should transplant to other custodial triplet constructions, since the defining ingredients are a quartic-only potential and an RG-selected flat direction rather than the specifics of this field content.
  • Beyond the paper: if the scalon is as light as claimed, precision probes of $hh$ production or of transitions such as $H\to hh$ may be more sensitive than the oblique parameters used here, because the light state's couplings are set by the same mixing angles that control the modified Higgs couplings.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. This paper constructs a classically scale-invariant extension of the Georgi-Machacek model by adding a real gauge singlet, using the Gildener-Weinberg formalism to generate the electroweak scale radiatively. The scalar sector is analyzed, theoretical constraints from bounded-from-below and unitarity are imposed, and a numerical scan is performed under electroweak precision (S parameter) and Higgs signal-strength constraints. The authors claim viable regions with scalon mass below about 200 GeV and heavy scalar below about 600 GeV.

Significance. The idea of combining classical scale invariance with a custodial-symmetric triplet sector is interesting, and the paper is self-contained in proposing a specific scalar potential and deriving many constraint equations. However, the central numerical claims rely on a mass matrix that is not derived from the stated potential and on a statistical acceptance criterion that cannot certify compatibility with Higgs data. As it stands, the paper does not establish that the model has viable parameter regions; the flaws are at the level of the core derivation rather than presentation.

major comments (5)
  1. [2.3, Eq. (2.11)] The mass matrix in Eq. (2.11) cannot be the Hessian of the tree-level potential (2.5). The term 3λ8 s^2 δ^2 in (2.5) must produce an S–H_1^0 mixing entry proportional to λ8 n_s n_δ, yet the printed (1,3) entry is 4√3 n_s n_δ with no coupling. Likewise, the h^2δ^2 term in (2.5) carries the combination 3(λ4+λ5/2), whereas the (2,3) entry of (2.11) contains 4λ2+2λ5. No field redefinition or flat-direction identity is given that would eliminate these couplings. Since Eq. (2.11) feeds the eigenvalues (2.17), the rotation (2.12)–(2.16), the coupling modifiers (3.21)–(3.22), the scalon formula (2.24), and the entire scan of Section 4, the numerical results derived from it are not supported.
  2. [Section 4, parameter count and scan] The scan samples (m_H3, m_H5, m_H, sβ, vΔ, vφ) independently but never demonstrates that these points correspond to solutions of the flat-direction conditions (2.8)–(2.9). The existence of a flat direction requires det A = 0, an additional condition beyond the parameter count in the text. Moreover, the paper does not provide the mapping from the scanned mass and mixing parameters back to the quartic couplings λ1...λ8, so a reader cannot check whether the potential (2.2) with those couplings is stable and unitarity-bounded. As a result, the points plotted in Figs. 1 and 2 are not shown to be points of the scale-invariant model.
  3. [Section 4, Higgs signal-strength fit] The reported best-fit value χ2_fit,µ = 119.33 for five signal-strength measurements is enormous for a fit with three free parameters (χ2/dof ≈ 24). The acceptance criterion |χ² − χ²_fit| < 7.815 then admits only points with χ² between approximately 111.5 and 127.1, all of which are strongly excluded by the data. The black dots in Figs. 1–2 are therefore not 'compatible with all constraints'; the model as implemented cannot reproduce the measured Higgs rates. This invalidates the central phenomenological claim of viable regions.
  4. [Section 3.3, Eqs. (3.19)–(3.20)] The text acknowledges that the T parameter is quadratically divergent in the GM framework and that this undermines naturalness, but then sets T = 0 and constrains only S. This is an assumption, not a derivation; custodial symmetry at tree level does not protect T at one loop. Since one of the paper's goals is to address the hierarchy problem without fine-tuning, the neglect of T significantly weakens the electroweak precision test, and the quoted 95% region is not a full electroweak precision fit.
  5. [2.4, Eq. (2.25)] There is a factor-of-π error in the scalon mass formula. From the one-loop coefficient B in Eq. (2.20), B = 1/(64π² v_φ⁴) [Tr M_S⁴ + 3 Tr M_V⁴ − 4 Tr M_F⁴], and the second derivative of V_1 in Eq. (2.23) at φ = v_φ is 8B v_φ². This yields m_s² = 1/(8π² v_φ²)[...], not 1/(8π v_φ²)[...] as printed in Eq. (2.25). The quoted scalon masses below 200 GeV are therefore not computed with the stated formula.
minor comments (5)
  1. [Section 4] The relation "v2 = vh^2 + 8v∆ = 246 GeV" is dimensionally inconsistent; it should read v² = v_h² + 8 v_Δ² = (246 GeV)².
  2. [2.3, Eq. (2.17)] The notation "cos2β" and "sin2β" is ambiguous: if it denotes cos²β or sin²β, these should be written explicitly, and if it denotes cos(2β) or sin(2β), the formulas should be checked for consistency.
  3. [Abstract] The phrase "three CP-even singlets" is misleading because the three neutral CP-even mass eigenstates are mixtures of the singlet S, the doublet neutral, and the triplet neutral, not all custodial singlets; rewording would improve clarity.
  4. [Figures 1 and 2 captions] The captions contain typographical errors such as "Const aints", "Elect oweak P ecision", and "Compat ibility", which should be corrected.
  5. [Reference [35]] The author list "G. Group" appears to be a garbled placeholder; if this refers to the Gfitter Group, the citation should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the model's central quantities are computed from the potential and scan, not fitted from the quantities they are said to predict.

full rationale

Walking the claimed derivation chain, the tree-level potential (2.2) is the input, the flat-direction conditions (2.8)-(2.9) are imposed, and the CP-even mass matrix (2.11) together with the one-loop Gildener-Weinberg potential (2.18)-(2.23) yields the tree-level spectrum and the radiatively generated scalon mass (2.24)-(2.25). The scalon mass is not fitted to the statement ms < 200 GeV; it is computed from the boson/fermion mass spectrum via the trace formula, and the quoted viable regions are outputs of a parameter scan subject to independent experimental constraints (the S parameter and Higgs signal strengths). The identification h1 = 125 GeV is an input/assignment rather than a predicted value, so it does not make the derived masses circular. No load-bearing step invokes a self-citation or an ansatz smuggled in through citation; the cited unitarity and vacuum-stability conditions are external constraints. Even if the numerical scan omits an explicit check of det A = 0 or the printed mass matrix (2.11) has algebraic inconsistencies, those are correctness issues for independent scrutiny rather than a circular reduction of an output to an input.

Assumptions & free parameters 6 free parameters · 5 assumptions · 2 invented entities

The construction rests on standard GW techniques, but the numerical scan introduces six free parameters that are effectively fitted to the S parameter and Higgs rates. The flat-direction assumption and the neglect of the T parameter are significant untested inputs.

free parameters (6)
  • m_H3 (triplet mass) = 0-1000 GeV
    The triplet scalar mass is varied freely in the numerical scan and constrained by S parameter and Higgs data.
  • m_H5 (quintet mass) = 0-1000 GeV
    The quintet mass is scanned and effectively fitted to the same observables.
  • m_H (heavy singlet mass) = 0-3000 GeV
    Scanned freely; the allowed region is then reported as a prediction, but the value is selected by the constraints.
  • s_beta (mixing sine) = [-1, 1]
    The CP-even mixing parameter is scanned and fitted to Higgs signal strengths.
  • v_Delta (triplet VEV) = 0-86.97 GeV
    The triplet vacuum expectation value is a free input; the lower bound of 45 GeV is an output of the fit.
  • v_phi (overall VEV scale) = 0-5000 GeV
    The scale v_phi enters the scalar masses and the scalon formula; it is scanned.
assumptions (5)
  • domain assumption The tree-level potential has a Gildener-Weinberg flat direction where V0=0 and the gradient vanishes (det A = 0 at some scale mu_GW).
    The entire radiative symmetry-breaking mechanism (Section 2.2) requires this condition to hold; the paper does not derive the explicit coupling relation.
  • domain assumption The neutral VEV alignment preserves custodial symmetry with equal VEVs for the real and complex triplets.
    Equation (2.1) and the GM construction; this choice yields rho approximately 1 at tree level.
  • standard math The one-loop effective potential along the flat direction has the Gildener-Weinberg form V1 = A phi^4 + B phi^4 ln(phi^2/mu_GW^2), and the scalon mass is given by the standard trace formula (2.25).
    Standard GW formalism, but its validity here depends on the flat direction condition being satisfied.
  • ad hoc to paper The T parameter and U parameter can be neglected; only the S parameter is constrained.
    Section 3.3 states the T parameter has a quadratic divergence requiring fine-tuning, which undermines the naturalness claim; the paper proceeds with S only.
  • domain assumption The scanned parameter points satisfy the flat-direction conditions (2.8)-(2.9).
    Section 4 scans masses and angles as independent without demonstrating consistency; this is the weakest link in the numerical analysis.
invented entities (2)
  • Real gauge-singlet scalar S independent evidence
    purpose: Enforces classical scale invariance and provides the flat direction that generates the electroweak scale.
    S mixes with the SM-like Higgs, generates the scalon and the heavier scalar H, and yields observable coupling deviations and a possible h to ss invisible decay; collider searches can test these predictions.
  • Scalon (pseudo-Goldstone boson) independent evidence
    purpose: The massless tree-level mode along the flat direction that acquires mass at one loop; it is the physical manifestation of broken scale invariance.
    Its mass is predicted by the loop formula (2.25) and bounded below about 200 GeV in the scan; observable through modified Higgs decays and direct production.

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Pith. "Pith review of A scale invariant extension of the Georgi Machacek model." pith.science (2026). https://pith.science/paper/Q4XKHATS

@misc{pith2026250419187,
  author       = {Pith},
  title        = {Pith review of: A scale invariant extension of the Georgi Machacek model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q4XKHATS}},
  note         = {Machine review of arXiv:2504.19187}
}
abstract

We propose a classically scale-invariant extension of the Georgi--Machacek model by augmenting its custodial \(SU(2)_L \times SU(2)_R\)-symmetric Higgs sector -- originally composed of a doublet and two triplets -- with a gauge-singlet scalar. Employing the Gildener--Weinberg formalism, we demonstrate that radiative symmetry breaking via the Coleman--Weinberg mechanism dynamically generates the electroweak scale along a flat direction. The scalar spectrum retains the quintet (\(H_5\)) and triplet (\(H_3\)) states of the original model while introducing three CP-even singlets: a pseudo-Goldstone boson (the \emph{scalon}), which acquires mass at one loop, and two additional massive scalars. One of these massive states corresponds to the observed \(125\,\mathrm{GeV}\) Higgs boson. We rigorously derive theoretical constraints from vacuum stability and perturbative unitarity, and we incorporate experimental bounds from electroweak precision tests (notably the \(S\) parameter) and Higgs signal strength measurements. Our parameter space analysis identifies viable regions where the scalon mass is below approximately \(200\,\mathrm{GeV}\) and the heavier scalar remains under \(600\,\mathrm{GeV}\). This framework addresses the hierarchy problem without fine-tuning, preserves custodial symmetry (with \(\rho \approx 1\) at tree level), and predicts testable deviations in Higgs couplings. Together with the extended scalar sector, these signatures provide promising avenues for direct investigation at collider experiments.

Figures

Figures reproduced from arXiv: 2504.19187 by the authors.

Figure 1
Figure 1. Constraints on ms and mH, in the scale invariant GM model, derived from electroweak precision and Higgs boson data. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 2
Figure 2. Constraints on v∆ and mH , in the scale invariant GM model, derived from electroweak precision and Higgs boson data. Conclusion In this work, we have constructed a scale invariant extension of the Georgi–Machacek model, aiming to address the long-standing hierarchy problem while preserving the rich phenomenology associated with custodial symmetric triplet models. Our approach begins with the formulation of a scale-i… view at source ↗

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Works this paper leans on

35 extracted references · 23 canonical work pages

  1. [1]

    Observation of a New Particle in the Search for the Standard Model Higgs Boson with the ATLAS Detector at the LHC,

    G. Aad, T. Abajyan, B. Abbott, J. Abdallah, S. A. Khalek, A. A. Abdelalim, R. Aben, B. Abi, M. Abolins, O. AbouZeid, et al. , “Observation of a New Particle in the Search for the Standard Model Higgs Boson with the ATLAS Detector at the LHC,” Phys. Lett. B 716 (2012) 1–29, arXiv:1207.7214

    arXiv 2012

  2. [2]

    Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC,

    S. Chatrchyan, V. Khachatryan, A. M. Sirunyan, A. Tumasyan, W. Adam, E. Aguilo, T. Bergauer, M. Dragicevic, J. Er¨ o, C. Fabjan,et al. , “Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC,” Phys. Lett. B 716 (2012) 30–61, arXiv:1207.7235

    arXiv 2012

  3. [3]

    Dynamics of Spontaneous Symmetry Breaking in the Weinberg-Salam Theory,

    L. Susskind, “Dynamics of Spontaneous Symmetry Breaking in the Weinberg-Salam Theory,” Phys. Rev. D 20 (1979) 2619

    work page 1979

  4. [4]

    A Supersymmetry primer,

    S. P. Martin, “A Supersymmetry primer,” Adv. Ser. Direct. High Energy Phys. 18 (1998) 1–98, arXiv:hep-ph/9709356

    arXiv 1998

  5. [5]

    On Naturalness in the Standard Model,

    W. A. Bardeen, “On Naturalness in the Standard Model,” tech. rep., SCAN-9602063, 1995

    work page 1995

  6. [6]

    Conformal Symmetry and the Standard Model,

    K. A. Meissner and H. Nicolai, “Conformal Symmetry and the Standard Model,” Phys. Lett. B 648 (2007) 312–317, arXiv:hep-th/0612165

    arXiv 2007

  7. [7]

    Effective Action, Conformal Anomaly and the Issue of Quadratic Divergences,

    K. A. Meissner and H. Nicolai, “Effective Action, Conformal Anomaly and the Issue of Quadratic Divergences,” Phys. Lett. B 660 (2008) 260–266, arXiv:0710.2840

    arXiv 2008

  8. [8]

    Conformal invariance from non-conformal gravity

    K. A. Meissner and H. Nicolai, “Conformal Invariance from Nonconformal Gravity,” Phys. Rev. D 80 (2009) 086005, arXiv:0907.3298

    work page Pith review arXiv 2009

Show all 35 references
  1. [9]

    Radiative Corrections as the Origin of Spontaneous Symmetry Breaking,

    S. R. Coleman and E. J. Weinberg, “Radiative Corrections as the Origin of Spontaneous Symmetry Breaking,” Phys. Rev. D 7 (1973) 1888–1910

    1973

  2. [10]

    Implications of Triviality for the Standard Model,

    M. Lindner, “Implications of Triviality for the Standard Model,” Z. Phys. C 31 (1986) 295–300

    1986

  3. [11]

    Precise Vacuum Stability Bound in the Standard Model,

    M. Sher, “Precise Vacuum Stability Bound in the Standard Model,” Phys. Lett. B 317 (1993) 159–163. 19

    1993

  4. [12]

    Electroweak Higgs as a Pseudo-Goldstone Boson of Broken Scale Invariance,

    R. Foot, A. Kobakhidze, and R. R. Volkas, “Electroweak Higgs as a Pseudo-Goldstone Boson of Broken Scale Invariance,” Phys. Lett. B 655 (2007) 156–161, arXiv:0704.1165

    2007 arXiv

  5. [13]

    Novel Effects in Electroweak Breaking from a Hidden Sector,

    J. R. Espinosa and M. Quiros, “Novel Effects in Electroweak Breaking from a Hidden Sector,” Phys. Rev. D 76 (2007) 076004, arXiv:hep-ph/0701145

    2007 arXiv

  6. [14]

    Solution to the Hierarchy Problem from an Almost Decoupled Hidden Sector within a Classically Scale Invariant Theory,

    R. Foot, A. Kobakhidze, K. L. McDonald, and R. R. Volkas, “Solution to the Hierarchy Problem from an Almost Decoupled Hidden Sector within a Classically Scale Invariant Theory,” Phys. Rev. D 77 (2008) 035006, arXiv:0801.0872

    2008 arXiv

  7. [15]

    Classically Conformal B–L Extended Standard Model,

    S. Iso, N. Okada, and Y. Orikasa, “Classically Conformal B–L Extended Standard Model,” Phys. Lett. B 676 (2009) 81–87, arXiv:0902.4050

    2009 arXiv

  8. [16]

    Stable Mass Hierarchies and Dark Matter from Hidden Sectors in the Scale-Invariant Standard Model,

    R. Foot, A. Kobakhidze, and R. R. Volkas, “Stable Mass Hierarchies and Dark Matter from Hidden Sectors in the Scale-Invariant Standard Model,” Phys. Rev. D 82 (2010) 035005, arXiv:1004.2612

    2010 arXiv

  9. [17]

    The Minimal Scale Invariant Extension of the Standard Model,

    L. Alexander-Nunneley and A. Pilaftsis, “The Minimal Scale Invariant Extension of the Standard Model,” JHEP 2010 (2010) 021, arXiv:1004.0178

    2010 arXiv

  10. [18]

    Natural Electroweak Symmetry Breaking from Scale Invariant Higgs Mechanism,

    A. Farzinnia, H.-J. He, and J. Ren, “Natural Electroweak Symmetry Breaking from Scale Invariant Higgs Mechanism,” Phys. Lett. B 727 (2013) 141–150, arXiv:1301.1011

    2013 arXiv

  11. [19]

    Physical Naturalness and Dynamical Breaking of Classical Scale Invariance,

    M. Heikinheimo, A. Racioppi, C. Spethmann, M. Raidal, and K. Tuominen, “Physical Naturalness and Dynamical Breaking of Classical Scale Invariance,” Mod. Phys. Lett. A 29 (2014) 1450077, arXiv:1401.1465

    2014 arXiv

  12. [20]

    Dark Matter and Neutrino Masses from a Scale-Invariant Multi-Higgs Portal,

    A. Karam and K. Tamvakis, “Dark Matter and Neutrino Masses from a Scale-Invariant Multi-Higgs Portal,” Phys. Rev. D 92 (2015) 075010, arXiv:1506.02656

    2015 arXiv

  13. [21]

    Doubly Charged Higgs Bosons,

    H. Georgi and M. Machacek, “Doubly Charged Higgs Bosons,” Nucl. Phys. B 262 (1985) 463–477

    1985

  14. [22]

    Higgs Boson Triplets with MW =MZ cosθw,

    M. S. Chanowitz and M. Golden, “Higgs Boson Triplets with MW =MZ cosθw,” Phys. Lett. B 165 no. 1-3, (1985) 105–108

    1985

  15. [23]

    What if the Higgs Couplings to W and Z Bosons are Larger than in the Standard Model?,

    A. Falkowski, S. Rychkov, and A. Urbano, “What if the Higgs Couplings to W and Z Bosons are Larger than in the Standard Model?,” JHEP 2012 (2012) 073, arXiv:1202.1532

    2012 arXiv

  16. [24]

    Neutrino Masses, Mixings, and Oscillations in SU(2) × U(1) Models of Electroweak Interactions,

    T. Cheng and L.-F. Li, “Neutrino Masses, Mixings, and Oscillations in SU(2) × U(1) Models of Electroweak Interactions,” Phys. Rev. D 22 no. 11, (1980) 2860

    1980

  17. [25]

    Neutrino Masses in SU(2) ⊗ U(1) Theories,

    J. Schechter and J. W. Valle, “Neutrino Masses in SU(2) ⊗ U(1) Theories,” Phys. Rev. D 22 no. 9, (1980) 2227

    1980

  18. [26]

    Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation,

    R. N. Mohapatra and G. Senjanovi´ c, “Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation,” Phys. Rev. D 23 no. 1, (1981) 165

    1981

  19. [27]

    Symmetry Breaking and Scalar Bosons,

    E. Gildener and S. Weinberg, “Symmetry Breaking and Scalar Bosons,” Phys. Rev. D 13 no. 12, (1976) 3333

    1976

  20. [28]

    Higgs Potential in the Type II Seesaw Model,

    A. Arhrib, R. Benbrik, M. Chabab, G. Moultaka, M. Peyranere, L. Rahili, and J. Ramadan, “Higgs Potential in the Type II Seesaw Model,” Phys. Rev. D 84 (2011) 095005, arXiv:1106.4654

    2011 arXiv

  21. [29]

    The Decoupling Limit in the Georgi-Machacek Model,

    K. Hartling, K. Kumar, and H. E. Logan, “The Decoupling Limit in the Georgi-Machacek Model,” Phys. Rev. D 90 (2014) 015007, arXiv:1312.3321

    2014 arXiv

  22. [30]

    Real Singlet Scalar Dark Matter Extension of the Georgi-Machacek Model,

    R. Campbell, S. Godfrey, H. E. Logan, and A. Poulin, “Real Singlet Scalar Dark Matter Extension of the Georgi-Machacek Model,” Phys. Rev. D 95 (2017) 016005, arXiv:1610.09374

    2017 arXiv

  23. [31]

    Naturalness Problems for ρ = 1 and Other Large 20 One-Loop Effects for a Standard-Model Higgs Sector Containing Triplet Fields,

    J. Gunion, R. Vega, and J. Wudka, “Naturalness Problems for ρ = 1 and Other Large 20 One-Loop Effects for a Standard-Model Higgs Sector Containing Triplet Fields,” Phys. Rev. D 43 (1991) 2322

    1991

  24. [32]

    Triplet Higgs Boson Collider Phenomenology after the LHC,

    C. Englert, E. Re, and M. Spannowsky, “Triplet Higgs Boson Collider Phenomenology after the LHC,” Phys. Rev. D 87 (2013) 095014, arXiv:1304.7337

    2013 arXiv

  25. [33]

    The Oblique Parameters in Multi-Higgs-Doublet Models,

    W. Grimus, L. Lavoura, O. Ogreid, and P. Osland, “The Oblique Parameters in Multi-Higgs-Doublet Models,” Nucl. Phys. B 801 (2008) 81–96, arXiv:0802.4353

    2008 arXiv

  26. [34]

    Review of Particle Physics,

    P. D. Group, R. Workman, V. Burkert, V. Crede, E. Klempt, U. Thoma, L. Tiator, K. Agashe, G. Aielli, B. Allanach, et al. , “Review of Particle Physics,” PTEP 2022 (2022) 083C01, arXiv:2206.15301

    2022 arXiv

  27. [35]

    The global electroweak fit at NNLO and prospects for the LHC and ILC,

    G. Group, M. Baak, J. C´ uth, J. Haller, A. Hoecker, R. Kogler, K. M¨ onig, M. Schott, and J. Stelzer, “The global electroweak fit at NNLO and prospects for the LHC and ILC,” Eur. Phys. J. C 74 (2014) 1–14, arXiv:1407.3792. 21

    2014 arXiv

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