Scotogenic mechanism from an extended $\boldsymbol{SU(2)_1 \times SU(2)_2 \times U(1)_Y}$ electroweak symmetry

Avelino Vicente; Javier Perez-Soler; Julio Leite

REVIEW 3 major objections 5 minor 31 references

Scotogenic mechanism from an extended $\boldsymbol{SU(2)_1 \times SU(2)_2 \times U(1)_Y}$ electroweak symmetry

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Promoting the electroweak gauge group to $\mathrm{SU}(2)_1 \times \mathrm{SU}(2)_2 \times \mathrm{U}(1)_Y$ yields, after symmetry breaking, a Scotogenic model in which an accidental $Z_2$ stabilizes dark matter and a naturally small…

desk verdict A genuinely new UV completion of the Scotogenic mechanism with an accidental Z2 and naturally small lambda5, but the scalar vacuum is assumed rather than proven; worth refereeing with the vacuum as the central issue. read the letter →

arxiv 2507.21223 v1 pith:I6IDRETG submitted 2025-07-28 hep-ph

Julio Leite , Javier Perez-Soler , Avelino Vicente This is my paper

classification hep-ph PACS 12.60.-i14.60.Pq95.35.+d

keywords ScotogenicmechanismradiativeneutrinomassdarkmatterstabilityaccidentalZ2symmetryextendedelectroweakgaugegroupleptonnumberviolationmutoegammascalartriplet

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 proposes a single framework that accounts for two observed facts—tiny neutrino masses and dark matter—by promoting the Standard Model's $\mathrm{SU}(2)_L$ gauge group to $\mathrm{SU}(2)_1 \times \mathrm{SU}(2)_2 \times \mathrm{U}(1)_Y$. It claims that after spontaneous breaking to $\mathrm{SU}(2)_L \times \mathrm{U}(1)_Y$, the low-energy theory is a Scotogenic model in which an accidental $Z_2$ makes the lightest odd field a stable dark matter candidate. The small coupling $\lambda_5$ that controls lepton-number violation is not inserted by hand: it is generated as $v_\Omega \lambda_{H\Delta\Omega} \mu_2^*/(4 m_\Delta^2)$ once the heavy scalar triplet $\Delta$ is integrated out, so it is naturally small. Neutrino masses then arise at one loop in the form $m_\nu = Y^T \Lambda Y$, with new states near the TeV scale and both neutrino mass orderings possible. The sympathetic reader would care because this removes the two most criticized ad hoc inputs of the original Scotogenic model: the imposed $Z_2$ parity and the unexplained smallness of $\lambda_5$.

What carries the argument

The engine is the double gauge-group structure $\mathrm{SU}(2)_1 \times \mathrm{SU}(2)_2 \times \mathrm{U}(1)_Y$ together with four scalar multiplets—$H$, $\eta$, $\Delta$, $\Omega$—and two generations of fermion bidoublets $\chi$ (fields carrying one index of each $\mathrm{SU}(2)$). The bitriplet $\Omega$ develops the vacuum that breaks the product group diagonally to the standard $\mathrm{SU}(2)_L$, and its couplings generate the effective $\lambda_5$ vertex after the heavy $\mathrm{SU}(2)_2$ triplet $\Delta$ is integrated out. The accidental $Z_2$, under which only $\chi$ and $\eta$ are odd, stabilizes the lightest odd particle. The one-loop neutrino mass is computed with $\eta_R$/$\eta_I$ and the neutral $\chi$ states running in the loop, giving $m_\nu = Y^T \Lambda Y$ with the loop function suppressing the scale of neutrino masses.

What would settle it

Numerically minimize the full scalar potential of Eq. (9) over all field directions, especially $v_\Omega = v_\xi$, nonzero $\eta$ vacuum values, and large $v_\Delta$; if any configuration with a different set of vacuum values has lower energy, the assumed vacuum is not the minimum and the model's central claim fails. On the experimental side, precision electroweak data that require the $\rho$ parameter to remain near 1 while no $Z'$ or $W'$ appears at the predicted multi-TeV scale would also falsify the scenario.

Watch

Extended reading notes

Core claim

The central claim is that the extended electroweak gauge structure itself supplies every ingredient the Scotogenic mechanism normally assumes. With the field content of Table 1 and the assumed vacuum hierarchy $v_\Delta \ll v_H \ll v_\Omega, v_\xi$, the product gauge symmetry forces the fermion bidoublets $\chi$ and the second scalar doublet $\eta$ to appear only in pairs, so a $Z_2$ parity is an accidental exact symmetry rather than a symmetry imposed by hand. Integrating out the heavy $\mathrm{SU}(2)_2$ triplet $\Delta$ leaves an effective quartic $\tfrac{\lambda_5}{2}(H^\dagger \eta)^2$ whose coefficient is $v_\Omega \lambda_{H\Delta\Omega} \mu_2^*/(4 m_\Delta^2)$; because $m_\Delta$ is the largest scale, $\lambda_5$ is naturally small and all lepton-number-violating effects, including neutrino masses, are suppressed. The one-loop neutrino mass matrix has the form $m_\nu = Y^T \Lambda Y$, and with two generations of $\chi$ it yields two non-zero masses that can fit either normal or inverted ordering while leaving one neutrino massless. The same $Z_2$-odd sector provides a dark matter candidate, either the neutral scalar $\eta_R$ or $\eta_I$ or the lightest neutral fermion $\chi$.

Load-bearing premise

The entire model depends on an assumption the paper states openly: the complicated scalar potential really has its lowest-energy point at the field values of Eq. (10), with the triplet vacuum value much smaller than the Higgs value and both much smaller than the bitriplet values; if that point is not the true minimum, the symmetry-breaking chain and everything built on it—the small $\lambda_5$, the loop neutrino mass, and the dark matter candidate—collapses.

Editorial extensions

If this is right

Dark matter is automatically stable: the lightest $Z_2$-odd state cannot decay, with the scalar case behaving like the inert doublet model and the fermion case like a singlet or triplet fermion dark matter candidate.
Neutrino masses are radiative and proportional to $\lambda_5$, so two neutrinos become massive while one stays massless; both normal and inverted mass ordering can fit oscillation data.
Lepton flavor violation, in particular $\mu \to e \gamma$, is predicted at rates near the current experimental limit; the current bound already excludes $\lambda_5$ below about $3\times 10^{-9}$ in the benchmark scenarios.
Electroweak precision data, mainly the $\rho$ parameter, push the $\mathrm{SU}(2)_1 \times \mathrm{SU}(2)_2$ breaking scale above roughly 20 TeV (or down to a few TeV if one gauge coupling is strong), so indirect searches are the principal probe.
The heavy spectrum contains $Z'$, $W'$, a singly charged $H^+$, and a doubly charged $\Omega^{++}$; at a low enough breaking scale these could produce exotic multi-lepton signatures at colliders.

Reading between the lines

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

The paper's vacuum assumption is the fragile point: the same construction becomes a complete proof only after a full minimization of the scalar potential, or at least a demonstration that Eq. (10) is a local minimum.
The accidental-$Z_2$ mechanism is a general principle: any representation choice under the product gauge group that forbids bilinears in the odd fields will produce a stable sector, pointing to a broader class of gauge-born Scotogenic models.
Because two $\chi$ generations give only two massive neutrinos, a future determination that all three neutrino masses are nonzero—or a confirmed neutrinoless double-beta decay signal—would force the model to add generations.
The heavy $\Delta$ scale imprints on observables beyond neutrino mass, such as the Higgs-scalar spectrum and lepton flavor violation, so precision flavor data provide an indirect test of whether the smallness of $\lambda_5$ really has this gauge-origin explanation.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The paper is a genuine model-building contribution: a UV completion of the Scotogenic mechanism from SU(2)_1 x SU(2)_2 x U(1)_Y, where the Z2 is accidental and the small lambda5 comes from integrating out a heavy triplet. That is new relative to [8,9], and the paper is honest about what it has and hasn't shown. The field content is unusual (real fermion bidoublets chi, bitriplet Omega), the analytic mass spectra are worked out in detail, the one-loop neutrino mass formula is a real calculation, and the LFV analysis is sensible and correctly uses Casas-Ibarra as a way to scan parameters, not as a prediction.

The soft spot is exactly the one the authors flag: the scalar vacuum is assumed, not derived. The text says the detailed study of the potential is beyond scope and simply assumes the VEV pattern of Eq. (10) with the hierarchy (11). The tadpole equations are necessary but not sufficient; the Hessian is never checked. The stress-test note worries about Eq. (20) implying m_Delta^2 > 0 forces a sign correlation between lambda_HDeltaOmega and v_Delta, and that compatibility with the other tadpoles and with the 2e-4 bound on epsilon_Delta is not demonstrated. That concern is fair and on point. The paper is transparent about this, so it is not a flaw hidden from the reader, but it is a load-bearing unverified assumption: if the minimum is not there, the symmetry breaking chain, the effective lambda5, and the neutrino mass formula all rest on sand.

The other weaknesses are minor. CP conservation is imposed without justification. The DM analysis imports known results from inert doublet and singlet-triplet models rather than doing a dedicated study; that's acceptable for a first paper but leaves the DM section as a sketch. Higher-dimensional operators that could break the accidental Z2 are not discussed; in a UV completion the accidentality is a low-energy statement.

Is the central argument solid? As a construction, yes. As an established mechanism, no, but the authors never claim more than they show. The paper deserves a serious referee: the model is new, the calculations are mostly careful, and the gap is fixable in principle (a vacuum stability analysis of the potential, even if numerical). I'd send it to review, but with a referee asked specifically to check the scalar potential minima and the sign consistency around Eq. (20). Not desk-reject material.

Recommendation: send to peer review. I'd flag the vacuum as the major point to resolve.

Referee Report

3 major / 5 minor

Summary. The paper proposes a gauged extension of the Standard Model electroweak sector, SU(2)_1 × SU(2)_2 × U(1)_Y, with the SM doublets charged under SU(2)_1 and new fields (two generations of a real fermion bidoublet χ, a scalar doublet η under SU(2)_2, a scalar triplet Δ under SU(2)_2, and a real scalar bitriplet Ω). The authors assume a vacuum in which Ω breaks SU(2)_1 × SU(2)_2 to the diagonal SM SU(2)_L, with a small VEV for Δ. They integrate out Δ to obtain a low-energy effective potential containing a naturally suppressed effective λ_5 coupling, and show that an accidental Z_2 leaves χ and η odd, so the lightest odd particle is a dark matter candidate. The paper derives analytic expressions for gauge boson masses, scalar masses, fermion masses, and a one-loop neutrino mass matrix of Scotogenic form, and then uses ρ-parameter bounds and µ → eγ data to constrain v_Ω, m_Δ, and related parameters.

Significance. If the assumed vacuum is actually a minimum of the full scalar potential and the formalism is corrected, this is an attractive ultraviolet completion of the Scotogenic mechanism: the dark matter stabilizing Z_2 arises accidentally from the gauge structure and representation content, and the smallness of lepton number violation is tied to the heavy Δ mass rather than to an ad hoc small λ_5. The paper contains a genuine one-loop calculation of the neutrino mass matrix, explicit analytic spectra for gauge and scalar sectors, and a first pass at precision electroweak and lepton-flavor-violating constraints, including a comparison with the MEG II bound. These are concrete, falsifiable elements that give the model phenomenological traction. However, the central construction currently rests on an unverified vacuum assumption, and there is an index-structure inconsistency in the central neutrino-mass formula and its Casas-Ibarra parametrization; both issues must be fixed before the mechanism can be regarded as established.

major comments (3)

[Sec. 2, Eq. (10)-(11); Sec. 3.2] The assumed scalar vacuum is never demonstrated to be a minimum. The text explicitly states that the detailed structure of the potential is beyond the scope of the paper and simply assumes the VEV configuration of Eq. (10) with the hierarchy of Eq. (11). The tadpole equations (15)-(18) are necessary conditions for an extremum, but they do not establish a local or global minimum, and the paper does not check that the Hessian is positive definite at this point. In particular, the scalar mass matrices of Sec. 3.2 are evaluated at the assumed vacuum, but positivity of the eigenvalues of M_S^2, M_P^2, M_H±^2, M_Ω++^2, m_R^2, and m_I^2 is not required or demonstrated, and no bounded-from-below condition is given. Equation (20) also imposes a sign constraint (λ_HΔΩ v_Δ < 0) whose compatibility with the remaining tadpole equations and with the bound ϵ_Δ ≲ 2×10^-4 from Eq. (108) is not checked. Since the symmetry-breaking chain (12), the effective λ_5 of Eq. (26), and the one-loop neutrino mass formula of Eq. (102) all rely on this vacuum, a benchmark parameter point with all scalar masses squared positive should be provided, or the paper should be explicitly reframed as a conditional construction.
[Eq. (102) and Eq. (114)] The index structure of the neutrino mass formula is inconsistent. With Y a 3×2 matrix and Λ a 2×2 matrix, the expression 'Y^T Λ Y' is 2×2, while the left-hand side of Eq. (102) is the 3×3 neutrino mass matrix; the summation displayed above Eq. (102) actually yields (Y Λ Y^T)_{αβ}. Correspondingly, Eq. (114) as written produces a 2×3 matrix from the product V† bΛ^{-1/2} R (0 √m2 0; 0 0 √m3) P U†, but the Yukawa matrix Y in Eq. (8) is 3×2. This is more than a typographical issue, because the Casas-Ibarra parametrization of Sec. 4.2 is used to set the size of the Yukawa couplings and therefore directly feeds the numerical LFV results in Figs. 4 and 5. Please correct the transposition convention and verify that the numerical implementation uses the corrected form.
[Sec. 4.2, Eqs. (113)-(116)] The numerical LFV analysis fixes several parameters in a somewhat ad hoc manner (e.g., y_χ = 0.05 I_2, λ_Hη = 0.1, λ_ηΩ = 0.01, v_Ω - v_ξ = 4 GeV) and uses R = I_2 for the Casas-Ibarra matrix. This is acceptable for an illustrative study, but the paper should state explicitly that the neutrino mass fit is imposed by construction through the Casas-Ibarra parametrization and is not a prediction of the model. More importantly, the figures and limits would be more convincing if at least one explicit benchmark point were given for which the vacuum is shown to be a local minimum, all scalar masses are positive, and the ρ-parameter constraints are simultaneously satisfied.

minor comments (5)

[Sec. 2] The sentence 'The VEV configuration in Eq. (22) enforces four tadpole equations' refers to Eq. (10), since Eq. (22) is defined later for the effective theory.
[Sec. 2, after Eq. (18)] The phrase 'solving Eqs. (15)-(18) for the squared mass parameters m_H^2, m_Δ^2, m_Ω^2 and v_Δ' lists v_Δ together with squared mass parameters; v_Δ is a VEV, not a mass parameter, and the sentence should be reworded.
[Sec. 3.2] The assumption that CP is conserved in the scalar sector is introduced without a comment on whether the parameters in Eq. (9) can all be chosen real while preserving the vacuum (10); a brief remark on the needed reality conditions would help.
[Sec. 4.1] The lower bound v_Ω ≳ 20 TeV from the ρ parameter is presented as very conservative, and the text notes that v_Ω could be reduced to 1-2 TeV for g_2 in the perturbative regime. Since this strongly affects the phenomenology (including the LFV limits in Sec. 4.2), it would be useful to show a scan or explicit examples with g_2 large enough to quantify the reduction.
[Sec. 4.2, Fig. 4] The caption states three values of m_η^2 with line styles '(blue)', '(blue, dashed)', and '(blue, dotted)', but the first line style is not specified; please indicate it explicitly (e.g., solid).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the neutrino-mass and LFV calculations are derived, with Casas-Ibarra used only to fit Y; the assumed scalar vacuum is a limitation, not a circular step.

full rationale

No circular step is exhibited. The central derivation chain is self-contained: the accidental Z2 follows from gauge invariance and the chosen representations, the effective λ5 is obtained by explicit tree-level matching in Eqs. (21) and (26), and the one-loop neutrino mass matrix is computed in Eqs. (99)-(102) from the mass eigenstates of Sec. 3.2 rather than imported from a fit. The Casas-Ibarra parametrization in Eq. (114) is used to fix the Yukawa matrix Y so that the model reproduces neutrino oscillation data, but the paper does not present the neutrino masses themselves as a prediction; the LFV rates in Sec. 4.2 are independent observables evaluated after that fit, so the fitted-input-called-prediction pattern does not apply. Self-citations [6,7] are used only as general motivation for UV-completing the Scotogenic idea, and the λ5 ≪ 1 suppression is derived from the assumed hierarchy vΩ μ2 ≪ mΔ^2, not taken from those citations. The main caveat is a limitation rather than circularity: after Eq. (9) the authors state that the "detailed structure of the complicated scalar potential in Eq. (9) is beyond the scope of our work. Instead, we will simply assume that its minimum is characterized by" the VEVs of Eq. (10). All subsequent results are conditional on that assumed vacuum, but no derived quantity reduces to an input by construction. Therefore the derivation is self-contained conditional on the stated assumptions.

Assumptions & free parameters 8 free parameters · 8 assumptions · 5 invented entities

The model introduces a large set of new parameters and relies on several unproven assumptions. The most important are an assumed scalar vacuum, CP conservation, and the exactness of the accidental Z2 at all scales. The quantitative neutrino mass fit is imposed through Casas-Ibarra, so the paper's contribution is a new constructed model, not a parameter-free derivation.

free parameters (8)

vOmega (scale of SU(2)_1 x SU(2)_2 breaking) = set to 20 TeV in Figure 4; lower bound vOmega >= 20 TeV from rho, reducible to 1-2 TeV for g2 near sqrt(4*pi)
Sets the masses of Z', W', heavy scalars and the size of rho and LFV corrections; chosen by hand to satisfy precision constraints.
mDelta (mass of the heavy triplet Delta) = integrated-out scale; LFV gives upper bound mDelta <= 2*10^8 GeV, and internal consistency requires mDelta well above…
The smallness of the effective lambda5 derives from 1/mDelta^2, Eq. (26).
lambda5 (effective LNV quartic) = fixed to 10^-8 in Fig. 4; excluded below about 3*10^-9 by MEG II
Controls radiative neutrino masses and the rate of mu -> e gamma.
Y (3x2 Yukawa matrix of chi) = not printed; set via Casas-Ibarra, Eq. (114), to reproduce NH neutrino data
Input from oscillation data; determines LFV predictions.
ychi (Yukawa of chi-Omega) = 0.05 times the 2x2 identity in numerical scan
Sets chi fermion mass splittings, Eqs. (91)-(93).
lambdaHeta, lambdaetaOmega (scalar quartics) = 0.1 and 0.01 in numerical scan
Control eta masses and mixing; chosen for illustrative scan.
vOmega - vxi (VEV difference) = 4 GeV in scan; constraint vOmega - vxi <= 5 GeV from rho
Measures the explicit breaking of SU(2)_L conservation by the vacuum.
M (bare mass of chi) and mEta (mass parameter of eta) = M in 0.2-2 TeV range in Fig. 4; M11=1 TeV, M22=1.5 TeV and mEta=500 GeV in Fig. 5
Fix the masses of the Z2-odd fermions and scalars in the loop.

assumptions (8)

ad hoc to paper The scalar potential has a minimum at the VEV configuration of Eq. (10) with hierarchy vDelta << vH << vOmega, vxi.
Stated in Sec. 2: detailed study of the scalar potential is beyond the scope; the minimum is simply assumed. This underpins the entire symmetry breaking pattern.
ad hoc to paper CP is conserved in the scalar sector, so CP-even and CP-odd states do not mix.
Assumed in Sec. 3.2 before defining the S and P bases; not derived or tested.
domain assumption The heavy triplet Delta is integrated out at tree level using the method of Ref. [11], neglecting O(1/mDelta^4) terms.
Used in Sec. 2 to obtain Veff and the effective lambda5; standard effective-field-theory assumption.
domain assumption The accidental Z2 symmetry remains exact at all scales, including non-renormalizable and quantum-gravity-induced operators.
Claimed in Sec. 2 and Sec. 3; not proven. If Planck-suppressed operators break Z2, the DM candidate could decay.
domain assumption Gauge couplings remain perturbative, with g1 = g2 = sqrt(2) g in parts of the numerical analysis.
Used for LFV scans and rho bounds; no running or perturbativity check is given.
domain assumption Casas-Ibarra parametrization, with R = I2 and normal hierarchy, correctly captures the neutrino mass matrix in the numerical analysis.
Used in Eq. (114); the choice of NH and R = I2 is not exhaustive and affects LFV predictions.
standard math Standard one-loop quantum field theory and Passarino-Veltman functions are used for mnu and LFV amplitudes.
Standard QFT technique, Eqs. (99)-(104).
standard math The real bidoublet chi is a valid fermion representation with zero lepton number and no gauge anomalies.
Based on Appendix A conventions; needed for the model to be consistent.

invented entities (5)

chi: two generations of real fermion bidoublet (1,2,2)_0 independent evidence
purpose: Runs in the one-loop neutrino mass diagram and provides a fermion dark matter candidate.
The model predicts charged and neutral chi states with LFV couplings; the resulting BR(mu -> e gamma) is testable at MEG II.
eta: scalar doublet under SU(2)_2 with hypercharge 1/2 independent evidence
purpose: The Z2-odd scalar in the Scotogenic loop; its neutral components can be inert doublet dark matter.
Inert doublet dark matter and LFV loops give testable signals; stability follows if eta is the lightest odd state.
Delta: scalar triplet under SU(2)_2 with hypercharge 1 independent evidence
purpose: Heavy field whose integration out generates the small lambda5 and hence naturally small lepton number violation.
Improved LFV searches can falsify the model's parameter space via the upper bound on mDelta.
Omega: real scalar bitriplet (1,3,3)_0 independent evidence
purpose: Breaks SU(2)_1 x SU(2)_2 to the diagonal SU(2)_L and generates Z', W', heavy scalars, and chi mass splittings.
Predicted Z', W' and a doubly charged scalar Omega++ with multi-lepton signatures; direct production possible if the breaking scale is near 1-2 TeV.
Heavy gauge bosons Z' and W' independent evidence
purpose: Gauge bosons of the broken SU(2)_1 x SU(2)_2 symmetry, with masses set by vOmega.
Their masses and mixings are constrained by electroweak precision data and are searchable at colliders if the breaking scale is low.

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Cite this review

Pith. "Pith review of Scotogenic mechanism from an extended $\boldsymbol{SU(2)_1 \times SU(2)_2 \times U(1)_Y}$ electroweak symmetry." pith.science (2026). https://pith.science/paper/I6IDRETG

@misc{pith2026250721223,
  author       = {Pith},
  title        = {Pith review of: Scotogenic mechanism from an extended $\boldsymbolSU(2)_1 \times SU(2)_2 \times U(1)_Y$ electroweak symmetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I6IDRETG}},
  note         = {Machine review of arXiv:2507.21223}
}

abstract

We propose an extension of the electroweak sector of the Standard Model in which the gauge group $SU(2)_L$ is promoted to $SU(2)_1 \times SU(2)_2$. This framework naturally includes a viable dark matter candidate and generates neutrino masses radiatively \`a la Scotogenic. Our scenario can be viewed as an ultraviolet extension of the Scotogenic mechanism, addressing some of its shortcomings. The resulting phenomenology may be probed through a range of experimental signatures, from precision electroweak measurements to searches for lepton flavor violation.

Figures

Figures reproduced from arXiv: 2507.21223 by the authors.

**Figure 2.** Neutrino mass generation in the low-energy theory. The only 1-loop contribution to neutrino masses, in the gauge (left) and mass bases (right). The star vertex in the gauge diagram is the effective λ5 coupling, see Eq. (26). the physical mass eigenstates. Charged loop diagrams do not contribute to the neutrino mass matrix. The neutrino mass matrix is given by the amplitude of the mass basis diagram summed over all i… view at source ↗

**Figure 3.** 1-loop contributions to the µ → eγ rate in our model. The photon line is not drawn, but can be attached to all internal charged lines. Our model also leads to mass mixing in the gauge sector. The Z boson does not correspond exactly to the pure SU(2)L gauge boson Zl , but has a non-zero component in Zh. Similarly, the W boson is an admixture of Wl (the pure SU(2)L boson) and Wh. As a result of this, the Z and W coup… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: BR(µ → eγ) as a function of M for three values of m2 η : (200 GeV)2 (blue), (1 TeV)2 (blue, dashed) and (2 TeV)2 (blue, dotted). The region in gray is excluded by the MEG II bound on BR(µ → eγ), see Eq. (112). a permutation matrix. m2 and m3 are the active neutrino mas…

**Figure 5.** Figure 5: Contours of BR(µ → eγ) in the vΩ − λ5 (left) and vΩ − m∆ (right) planes. The red line corresponds to the current MEG II limit on BR(µ → eγ) given in Eq. (112). The regions in gray are excluded by this bound. model. In our model, λ5 is an effective parameter, obtained a…

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Works this paper leans on

31 extracted references · 12 canonical work pages

[1]

Dark matter as the source of neutrino mass: theory overview and experimental prospects,

I. M. ´Avila, A. Karan, S. Mandal, S. Sadhukhan, and J. W. F. Valle, “Dark matter as the source of neutrino mass: theory overview and experimental prospects,” arXiv:2506.24027 [hep-ph]

arXiv
[2]

Radiative seesaw mechanism at weak scale,

Z.-j. Tao, “Radiative seesaw mechanism at weak scale,” Phys. Rev. D 54 (1996) 5693–5697, arXiv:hep-ph/9603309. 29

arXiv 1996
[3]

Verifiable radiative seesaw mechanism of neutrino mass and dark matter,

E. Ma, “Verifiable radiative seesaw mechanism of neutrino mass and dark matter,” Phys. Rev. D 73 (2006) 077301, arXiv:hep-ph/0601225

arXiv 2006
[4]

From the trees to the forest: a review of radiative neutrino mass models,

Y. Cai, J. Herrero-Garc ´ ıa, M. A. Schmidt, A. Vicente, and R. R. Volkas, “From the trees to the forest: a review of radiative neutrino mass models,” Front. in Phys. 5 (2017) 63, arXiv:1706.08524 [hep-ph]

arXiv 2017
[5]

Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking,

G. ’t Hooft, “Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking,” NATO Sci. Ser. B 59 (1980) 135–157

work page 1980
[6]

An ultraviolet completion for the Scotogenic model

P. Escribano and A. Vicente, “An ultraviolet completion for the Scotogenic model,” Phys. Lett. B 823 (2021) 136717, arXiv:2107.10265 [hep-ph]

work page Pith review arXiv 2021
[7]

Ultraviolet extensions of the Scotogenic model

D. Portillo-S´ anchez, P. Escribano, and A. Vicente, “Ultraviolet extensions of the Scotogenic model,” JHEP 08 (2023) 023, arXiv:2301.05249 [hep-ph]

work page Pith review arXiv 2023
[8]

Scotogenic model from an extended electroweak symmetry

P. Van Dong and D. Van Loi, “Scotogenic model from an extended electroweak symmetry,” Phys. Rev. D 110 no. 3, (2024) 035003, arXiv:2309.12091 [hep-ph]

work page Pith review arXiv 2024

Show all 31 references

[9]

Strongly coupled inert scalar sector with radiative neutrino masses,

A. E. C´ arcamo Hern´ andez, J. E. Puentes, R. Pasechnik, and D. Salinas-Arizmendi, “Strongly coupled inert scalar sector with radiative neutrino masses,” arXiv:2504.07193 [hep-ph]
[10]

Phenomenology of left-right symmetric dark matter,

C. Garcia-Cely and J. Heeck, “Phenomenology of left-right symmetric dark matter,” JCAP 03 (2016) 021, arXiv:1512.03332 [hep-ph]

2016 arXiv
[11]

Observable effects of general new scalar particles,

J. de Blas, M. Chala, M. P´ erez-Victoria, and J. Santiago, “Observable effects of general new scalar particles,” Journal of High Energy Physics 2015 no. 4, (Apr., 2015) . http://dx.doi.org/10.1007/JHEP04(2015)078

2015 doi
[12]

Generalizing the Scotogenic model,

P. Escribano, M. Reig, and A. Vicente, “Generalizing the Scotogenic model,” JHEP 07 (2020) 097, arXiv:2004.05172 [hep-ph]

2020 arXiv
[13]

One Loop Corrections for e+e− Annihilation Into µ+µ− in the Weinberg Model,

G. Passarino and M. J. G. Veltman, “One Loop Corrections for e+e− Annihilation Into µ+µ− in the Weinberg Model,” Nucl. Phys. B160 (1979) 151–207

1979
[14]

WIMP dark matter as radiative neutrino mass messenger,

M. Hirsch, R. A. Lineros, S. Morisi, J. Palacio, N. Rojas, and J. W. F. Valle, “WIMP dark matter as radiative neutrino mass messenger,” JHEP 10 (2013) 149, arXiv:1307.8134 [hep-ph]

2013 arXiv
[15]

Lepton Flavor Violation in the singlet-triplet scotogenic model,

P. Rocha-Moran and A. Vicente, “Lepton Flavor Violation in the singlet-triplet scotogenic model,” JHEP 07 (2016) 078, arXiv:1605.01915 [hep-ph]

2016 arXiv
[16]

Review of particle physics,

Particle Data Group Collaboration, S. Navas et al., “Review of particle physics,” Phys. Rev. D 110 no. 3, (2024) 030001

2024
[17]

Non-abelian gauge extensions for B-decay anomalies,

S. M. Boucenna, A. Celis, J. Fuentes-Martin, A. Vicente, and J. Virto, “Non-abelian gauge extensions for B-decay anomalies,” Phys. Lett. B 760 (2016) 214–219, arXiv:1604.03088 [hep-ph]. 30

2016 arXiv
[18]

Phenomenology of an SU (2) × SU (2) × U (1) model with lepton-flavour non-universality,

S. M. Boucenna, A. Celis, J. Fuentes-Martin, A. Vicente, and J. Virto, “Phenomenology of an SU (2) × SU (2) × U (1) model with lepton-flavour non-universality,” JHEP 12 (2016) 059, arXiv:1608.01349 [hep-ph]

2016 arXiv
[19]

Probing neutrino and Higgs sectors in SU (2)1 × SU (2)2 × U (1)Y model with lepton-flavor non-universality,

L. T. Hue, A. B. Arbuzov, N. T. K. Ngan, and H. N. Long, “Probing neutrino and Higgs sectors in SU (2)1 × SU (2)2 × U (1)Y model with lepton-flavor non-universality,” Eur. Phys. J. C 77 no. 5, (2017) 346, arXiv:1611.06801 [hep-ph]

2017 arXiv
[20]

General formulae for f1 → f2γ,

L. Lavoura, “General formulae for f1 → f2γ,” Eur. Phys. J. C 29 (2003) 191–195, arXiv:hep-ph/0302221

2003 arXiv
[21]

Lepton Flavor Violation in the Scotogenic Model,

T. Toma and A. Vicente, “Lepton Flavor Violation in the Scotogenic Model,” JHEP 01 (2014) 160, arXiv:1312.2840 [hep-ph]

2014 arXiv
[22]

New limit on the µ+->e+γ decay with the MEG II experiment,

MEG II Collaboration, K. Afanaciev et al., “New limit on the µ+->e+γ decay with the MEG II experiment,” arXiv:2504.15711 [hep-ex]

arXiv
[23]

Oscillating neutrinos and µ → e, γ,

J. A. Casas and A. Ibarra, “Oscillating neutrinos and µ → e, γ,” Nucl. Phys. B 618 (2001) 171–204, arXiv:hep-ph/0103065

2001 arXiv
[24]

Master Majorana neutrino mass parametrization,

I. Cordero-Carri´ on, M. Hirsch, and A. Vicente, “Master Majorana neutrino mass parametrization,” Phys. Rev. D 99 no. 7, (2019) 075019, arXiv:1812.03896 [hep-ph]

2019 arXiv
[25]

General parametrization of Majorana neutrino mass models,

I. Cordero-Carri´ on, M. Hirsch, and A. Vicente, “General parametrization of Majorana neutrino mass models,” Phys. Rev. D 101 no. 7, (2020) 075032, arXiv:1912.08858 [hep-ph]

2020 arXiv
[26]

2020 global reassessment of the neutrino oscillation picture,

P. F. de Salas, D. V. Forero, S. Gariazzo, P. Mart ´ ınez-Mirav´ e, O. Mena, C. A. Ternes, M. T´ ortola, and J. W. F. Valle, “2020 global reassessment of the neutrino oscillation picture,” JHEP 02 (2021) 071, arXiv:2006.11237 [hep-ph]

2021 arXiv
[27]

Predestined Dark Matter in Gauge Extensions of the Standard Model,

E. Ma, “Predestined Dark Matter in Gauge Extensions of the Standard Model,” LHEP 1 no. 1, (2018) 1–4, arXiv:1803.03891 [hep-ph]

2018 arXiv
[28]

Pattern of Symmetry Breaking with Two Higgs Doublets,

N. G. Deshpande and E. Ma, “Pattern of Symmetry Breaking with Two Higgs Doublets,” Phys. Rev. D 18 (1978) 2574

1978
[29]

Anatomy of the Inert Two Higgs Doublet Model in the light of the LHC and non-LHC Dark Matter Searches,

A. Belyaev, G. Cacciapaglia, I. P. Ivanov, F. Rojas-Abatte, and M. Thomas, “Anatomy of the Inert Two Higgs Doublet Model in the light of the LHC and non-LHC Dark Matter Searches,” Phys. Rev. D 97 no. 3, (2018) 035011, arXiv:1612.00511 [hep-ph]

2018 arXiv
[30]

Phenomenological profile of scotogenic fermionic dark matter,

A. Karan, S. Sadhukhan, and J. W. F. Valle, “Phenomenological profile of scotogenic fermionic dark matter,” JHEP 12 (2023) 185, arXiv:2308.09135 [hep-ph]

2023 arXiv
[31]

Fermion Triplet Dark Matter and Radiative Neutrino Mass,

E. Ma and D. Suematsu, “Fermion Triplet Dark Matter and Radiative Neutrino Mass,” Mod. Phys. Lett. A 24 (2009) 583–589, arXiv:0809.0942 [hep-ph]. 31

2009 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Dark matter as the source of neutrino mass: theory overview and experimental prospects,

I. M. ´Avila, A. Karan, S. Mandal, S. Sadhukhan, and J. W. F. Valle, “Dark matter as the source of neutrino mass: theory overview and experimental prospects,” arXiv:2506.24027 [hep-ph]

arXiv

[2] [2]

Radiative seesaw mechanism at weak scale,

Z.-j. Tao, “Radiative seesaw mechanism at weak scale,” Phys. Rev. D 54 (1996) 5693–5697, arXiv:hep-ph/9603309. 29

arXiv 1996

[3] [3]

Verifiable radiative seesaw mechanism of neutrino mass and dark matter,

E. Ma, “Verifiable radiative seesaw mechanism of neutrino mass and dark matter,” Phys. Rev. D 73 (2006) 077301, arXiv:hep-ph/0601225

arXiv 2006

[4] [4]

From the trees to the forest: a review of radiative neutrino mass models,

Y. Cai, J. Herrero-Garc ´ ıa, M. A. Schmidt, A. Vicente, and R. R. Volkas, “From the trees to the forest: a review of radiative neutrino mass models,” Front. in Phys. 5 (2017) 63, arXiv:1706.08524 [hep-ph]

arXiv 2017

[5] [5]

Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking,

G. ’t Hooft, “Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking,” NATO Sci. Ser. B 59 (1980) 135–157

work page 1980

[6] [6]

An ultraviolet completion for the Scotogenic model

P. Escribano and A. Vicente, “An ultraviolet completion for the Scotogenic model,” Phys. Lett. B 823 (2021) 136717, arXiv:2107.10265 [hep-ph]

work page Pith review arXiv 2021

[7] [7]

Ultraviolet extensions of the Scotogenic model

D. Portillo-S´ anchez, P. Escribano, and A. Vicente, “Ultraviolet extensions of the Scotogenic model,” JHEP 08 (2023) 023, arXiv:2301.05249 [hep-ph]

work page Pith review arXiv 2023

[8] [8]

Scotogenic model from an extended electroweak symmetry

P. Van Dong and D. Van Loi, “Scotogenic model from an extended electroweak symmetry,” Phys. Rev. D 110 no. 3, (2024) 035003, arXiv:2309.12091 [hep-ph]

work page Pith review arXiv 2024