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arxiv: 2511.16762 · v2 · submitted 2025-11-20 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Radiative neutrino mass generation and dark matter through vectorlike leptons

Mohamed Amin Loualidi , Salah Nasri , Maximiliano A. Rivera
Authors on Pith no claims yet

Pith reviewed 2026-05-17 20:13 UTC · model grok-4.3

classification ✦ hep-ph
keywords neutrino massdark matterradiative generationvectorlike leptonsthree-loop diagramsscalar doubletsflavor violation
0
0 comments X

The pith

A single generation of vectorlike leptons produces two nonzero neutrino masses via asymmetric Yukawa couplings in a three-loop radiative model that also accounts for dark matter.

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

The paper constructs a three-loop radiative model in which neutrino masses are generated through interactions of two new scalar SU(2)_L doublets with vectorlike lepton doublets. The asymmetry in the Yukawa couplings produces a neutrino mass matrix that yields two nonzero masses from only one generation of vectorlike leptons. The same scalars supply dark matter candidates via splitting of their neutral components and must remain consistent with neutrino oscillation data and the bound on μ → eγ. A sympathetic reader would care because the construction ties neutrino mass, dark matter, and lepton flavor violation together in a single extension of the standard model that makes definite experimental predictions.

Core claim

A single generation of vectorlike leptons yields two nonzero neutrino masses as a consequence of the asymmetric Yukawa combinations entering the neutrino mass matrix. The model employs a three-loop radiative mechanism with two scalar doublets whose neutral components split to provide a dark matter candidate while the charged scalars mix to complete the mass-generation diagrams.

What carries the argument

Asymmetric Yukawa coupling between two scalar SU(2)_L doublets and vectorlike lepton doublets that populates the three-loop neutrino mass matrix and induces the required scalar mixing for both mass generation and dark matter.

If this is right

  • The model reproduces observed neutrino masses and mixing angles while remaining compatible with current dark matter bounds.
  • The predicted rate for μ → eγ lies within reach of forthcoming experiments.
  • Singly charged scalars from the two doublets mix and participate directly in the mass-generation loops.
  • One scalar doublet supplies a viable dark matter candidate through the mass splitting of its neutral components.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If correct, the vectorlike leptons could be produced at the LHC or future colliders through their couplings to the new scalars.
  • The three-loop suppression may connect this mechanism to other radiative phenomena in extended gauge theories.
  • Precision measurements of the neutrino mixing angles could distinguish the specific texture arising from the asymmetric Yukawa structure.

Load-bearing premise

The three-loop diagrams driven by the asymmetric Yukawa couplings and scalar mixing dominate neutrino mass generation while satisfying all phenomenological constraints without extra fine-tuning or cancellations.

What would settle it

A measured branching ratio for μ → eγ that lies above the model's predicted range, or a direct-detection result that excludes the scalar mass splitting required for the dark matter relic density, would rule out the scenario.

Figures

Figures reproduced from arXiv: 2511.16762 by Maximiliano A. Rivera, Mohamed Amin Loualidi, Salah Nasri.

Figure 1
Figure 1. Figure 1: FIG. 1: 3-loop topologies for generating neutrino masses [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: 3-loop integral [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Left: Dark matter abundance for the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The DM relic density as a function of the Higgs-portal coupling [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Predicted correlations between [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Same as figure 5 but for [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Scatter plot of BR( [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Same as Fig. 7 but for [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
read the original abstract

This study presents a radiative three-loop model for neutrino mass generation, employing an asymmetric Yukawa coupling between two new scalar $SU(2)_L$ doublets and vectorlike lepton doublets. Dark matter candidates arise from one of the scalar doublets and contribute to neutrino mass generation through the mass splitting between its neutral components. The singly charged scalars are also essential for neutrino mass, with the charged states of the two doublets mixing with one another. A single generation of vectorlike leptons yields two nonzero neutrino masses as a consequence of the asymmetric Yukawa combinations entering the neutrino mass matrix. The model is tested against dark matter phenomenology, neutrino mass and mixing data, and the charged lepton flavor-violating process $\mu \rightarrow e \gamma$, showing compatibility with current bounds and leading to experimentally accessible predictions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The manuscript presents a three-loop radiative neutrino mass model employing vectorlike lepton doublets coupled asymmetrically to two SU(2)_L scalar doublets. The neutral components of one scalar doublet act as dark matter candidates, with their mass splitting contributing to the loop-induced neutrino masses. A single generation of vectorlike leptons produces a 3×3 neutrino mass matrix with exactly two nonzero eigenvalues. The model is checked for consistency with neutrino oscillation data, dark matter relic density, and the μ → eγ branching ratio, claiming compatibility and experimentally accessible predictions.

Significance. If the central construction holds, the model offers a concrete realization linking radiative neutrino mass generation at three loops to a viable dark matter candidate through scalar mass splitting and mixing. The distinctive feature that asymmetric Yukawa combinations yield precisely two nonzero neutrino masses from one vectorlike generation provides a falsifiable relation to oscillation parameters. Explicit numerical compatibility checks with relic density and LFV bounds, if robust, would strengthen the case for this class of models.

major comments (3)
  1. [§3.2, Eq. (18)] §3.2, Eq. (18): The three-loop neutrino mass matrix is stated to arise solely from the asymmetric Yukawa terms and scalar mixing, yet the manuscript does not explicitly demonstrate the vanishing of one- and two-loop contributions. A diagram-by-diagram cancellation argument or symmetry reason must be supplied, as any residual lower-order term would dominate and invalidate the three-loop suppression needed to reach the 0.05 eV scale.
  2. [§5.1 and Table 2] §5.1 and Table 2: The parameter choices that reproduce the observed neutrino mass scale via the three-loop integral simultaneously satisfy the DM relic density only for a narrow range of mass splittings (∼ few GeV). The manuscript must quantify the degree of tuning required between the Yukawa couplings, scalar masses, and the DM annihilation cross section; without this, the claim of natural compatibility remains unverified.
  3. [§4.3, Eq. (32)] §4.3, Eq. (32): The μ → eγ amplitude is computed at one loop and used to bound the same scalar and Yukawa parameters that enter the three-loop neutrino mass. The paper should show the correlation plot or allowed region where both constraints are satisfied without additional cancellations, as the three-loop suppression for m_ν does not automatically protect the LFV rate.
minor comments (3)
  1. [§2] The definition of the two scalar doublets Φ1 and Φ2 in §2 should include their hypercharge assignments explicitly to avoid ambiguity with standard notation.
  2. [Figure 3] Figure 3 (neutrino mass vs. DM mass) lacks error bands from the oscillation parameter uncertainties; adding them would improve clarity.
  3. [Introduction] A brief comparison to existing three-loop neutrino mass models (e.g., those with colored scalars) is missing from the introduction.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions we will make to strengthen the presentation.

read point-by-point responses

  1. Referee: [§3.2, Eq. (18)] §3.2, Eq. (18): The three-loop neutrino mass matrix is stated to arise solely from the asymmetric Yukawa terms and scalar mixing, yet the manuscript does not explicitly demonstrate the vanishing of one- and two-loop contributions. A diagram-by-diagram cancellation argument or symmetry reason must be supplied, as any residual lower-order term would dominate and invalidate the three-loop suppression needed to reach the 0.05 eV scale.

    Authors: We agree that an explicit demonstration is necessary. The asymmetric Yukawa structure, in which the vectorlike lepton doublets couple to only one combination of the two scalar doublets, forbids the vertices required for one- and two-loop neutrino mass diagrams through a combination of SU(2)_L charge conservation and the absence of certain scalar mixing terms at lower orders. We will add a new subsection in §3.2 that lists the possible lower-order diagrams and shows their vanishing by explicit inspection of the relevant Feynman rules. revision: yes

  2. Referee: [§5.1 and Table 2] §5.1 and Table 2: The parameter choices that reproduce the observed neutrino mass scale via the three-loop integral simultaneously satisfy the DM relic density only for a narrow range of mass splittings (∼ few GeV). The manuscript must quantify the degree of tuning required between the Yukawa couplings, scalar masses, and the DM annihilation cross section; without this, the claim of natural compatibility remains unverified.

    Authors: The narrow mass splitting is a direct consequence of the scalar potential parameters needed to generate the correct three-loop neutrino mass scale while keeping the DM candidate stable. In the viable benchmark points the Yukawa couplings remain O(0.1–1) and the scalar masses lie in the few-TeV range; the splitting itself is set by the soft-breaking term in the potential rather than by an independent fine-tuning. We will add a short discussion in §5.1 that quantifies the sensitivity of the relic density to variations in the mass-splitting parameter, confirming that the required tuning is mild (at the level of a few percent) within the regions that also satisfy neutrino data. revision: yes

  3. Referee: [§4.3, Eq. (32)] §4.3, Eq. (32): The μ → eγ amplitude is computed at one loop and used to bound the same scalar and Yukawa parameters that enter the three-loop neutrino mass. The paper should show the correlation plot or allowed region where both constraints are satisfied without additional cancellations, as the three-loop suppression for m_ν does not automatically protect the LFV rate.

    Authors: We have performed a joint scan over the shared parameters and find viable regions in which the one-loop LFV rate lies below the experimental bound while the three-loop neutrino masses reproduce the observed values. To make this explicit we will add a new figure (or panel in an existing figure) in §4.3 or §5 that displays the allowed parameter space in the plane of the dominant Yukawa coupling versus the relevant scalar mass, with contours indicating the regions satisfying all three constraints simultaneously. revision: yes

Circularity Check

0 steps flagged

No circularity: neutrino mass matrix structure derived from explicit loop diagrams

full rationale

The paper introduces vectorlike leptons and two scalar doublets, then computes the 3x3 neutrino mass matrix from three-loop diagrams with asymmetric Yukawa couplings. The result of exactly two nonzero eigenvalues follows directly from the matrix rank induced by the model's Feynman rules and field content, without reducing to a fitted input or self-citation. Parameters are later scanned to match data and bounds, but this is standard phenomenology and does not make the structural claim circular. No load-bearing self-citations, ansatze, or fitted predictions renamed as derivations are present.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 2 invented entities

The central claim rests on the existence of two new scalar doublets and one generation of vectorlike leptons whose masses, mixing angles, and Yukawa couplings are chosen to produce viable neutrino masses and dark matter phenomenology.

free parameters (2)
  • Scalar masses and mass splitting
    Masses of the two scalar doublets and the splitting between neutral components are adjusted to fit dark matter relic density and neutrino mass scale.
  • Asymmetric Yukawa couplings
    Unequal Yukawa strengths between scalars and vectorlike leptons are selected to generate the observed neutrino mass matrix structure.
axioms (1)
  • domain assumption Three-loop diagrams dominate over lower-order contributions to neutrino mass
    Standard assumption in radiative neutrino mass models invoked to justify the loop order.
invented entities (2)
  • Two SU(2)_L scalar doublets no independent evidence
    purpose: One provides dark matter candidate via neutral mass splitting; both participate in charged scalar mixing for neutrino mass loops
    New scalars postulated to close the three-loop diagrams and stabilize dark matter.
  • Vectorlike lepton doublets no independent evidence
    purpose: Mediate the radiative neutrino mass generation through Yukawa interactions
    New heavy leptons introduced to enable the asymmetric coupling structure.

pith-pipeline@v0.9.0 · 5438 in / 1460 out tokens · 37030 ms · 2026-05-17T20:13:02.846001+00:00 · methodology

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Reference graph

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