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arxiv: 2605.22656 · v1 · pith:IFRYL3M6new · submitted 2026-05-21 · ✦ hep-ph

Emergent Neutrino Texture Geometry from Dark Matter and Lepton Flavor Violation in the Scotogenic Model

Avinanda Chaudhuri This is my paper

Pith reviewed 2026-05-22 04:43 UTC · model grok-4.3

classification ✦ hep-ph
keywords scotogenic modelneutrino textureslepton flavor violationdark matter relic densityradiative neutrino massCasas-Ibarra parametrizationflavor geometryneutrino mass hierarchies
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The pith

In the scotogenic model, constraints from dark matter relic density and lepton flavor violation dynamically induce approximate suppressions in the neutrino mass matrix elements.

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

The paper examines how the minimal scotogenic model, which generates neutrino masses radiatively via dark matter loops, produces structured patterns in the neutrino Yukawa couplings when parameters are scanned under experimental bounds. Extensive use of the Casas-Ibarra parametrization shows that consistency with observed relic density and limits on processes like muon-to-electron conversion naturally suppresses certain off-diagonal entries while preventing cancellations on the diagonal. This creates a nontrivial flavor geometry without any hand-imposed symmetry. The analysis contrasts normal and inverted neutrino mass orderings and extracts scaling relations between dark matter mass and flavor-violating rates.

Core claim

Approximate suppressions can dynamically emerge from phenomenological consistency conditions. The interplay between relic density requirements, radiative neutrino mass generation, and lepton flavor violating observables induces a nontrivial flavor geometry in parameter space, with particular suppressions in the (eμ) and (eτ) sectors arising naturally while diagonal entries strongly resist cancellation.

What carries the argument

The Casas-Ibarra parametrization of the scotogenic Yukawa matrix under simultaneous dark matter relic density and lepton flavor violation constraints.

If this is right

  • Normal and inverted neutrino mass hierarchies produce distinct patterns in the emergent flavor geometry.
  • Approximate scaling relations connect dark matter mass to lepton flavor violation rates.
  • Reduced Casas-Ibarra parametrizations yield similar texture structures to the full geometry.
  • Diagonal neutrino mass matrix entries remain robust against suppression across the viable parameter space.

Where Pith is reading between the lines

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

  • Emergent textures may arise in other radiative neutrino mass models whenever dark matter and flavor constraints are imposed together.
  • Precision measurements of lepton flavor violation at future facilities could directly probe the predicted sector-specific suppressions.
  • Model builders could explore whether similar dynamical geometries appear when additional observables such as the effective Majorana mass are included in the scans.

Load-bearing premise

The assumption that the Casas-Ibarra parametrization combined with the chosen scan ranges and constraint thresholds sufficiently covers the physically relevant parameter space without introducing artificial biases or missing viable regions.

What would settle it

A broader scan that uncovers viable regions satisfying all constraints yet lacking the reported suppressions in the electron-muon and electron-tau sectors would falsify the claimed emergence of this flavor geometry.

Figures

Figures reproduced from arXiv: 2605.22656 by Avinanda Chaudhuri.

Figure 1
Figure 1. Figure 1: Statistical distributions of emergent texture suppression parameters [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Correlation between the emergent suppression parameter [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between reduced and full Casas–Ibarra geometries. The dominant emer [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison between emergent texture suppression distributions for normal hierarchy [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Dark matter relic abundance versus BR(µ → eγ) in the minimal fermionic scotogenic model. The color coding represents the scalar mass splitting ∆m = mR − mI . LFV-safe regions generically tend toward dark matter overabundance, revealing a strong geometric tension between the two sectors. Several important features emerge from the figure. First, the relic density and LFV observables exhibit a pronounced anti… view at source ↗
Figure 6
Figure 6. Figure 6: Dark matter relic density as a function of the dark matter mass for representative [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Dark matter relic density versus BR(µ → eγ) colored by the suppression parameter ϵeµ. Approximate flavor suppressions mildly soften the LFV tension but do not generically restore simultaneous dark matter and LFV viability. The figure reveals that smaller values of ϵeµ tend to populate somewhat more LFV-favored regions. This confirms that emergent flavor suppressions partially reduce flavor-violating am￾pli… view at source ↗
Figure 8
Figure 8. Figure 8: Phase diagram in the (M1, ∆m) plane. Colored points satisfy LFV constraints and are shaded according to the relic-density ratio Ωh 2/0.12. The figure demonstrates that LFV-safe regions generically populate strongly overabundant dark matter regimes across wide regions of parameter space. A striking feature of the phase diagram is that LFV-safe points appear throughout a broad region of parameter space, indi… view at source ↗
Figure 9
Figure 9. Figure 9: Normalized distributions of the emergent hierarchy invariant [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Emergent flavor-geometry manifold in the space of the hierarchy invariant [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
read the original abstract

We investigate the emergence of approximate neutrino texture structures in the minimal scotogenic model through large-scale Casas--Ibarra parameter scans subject to lepton flavor violation and dark matter constraints. We demonstrate that approximate suppressions can dynamically emerge from phenomenological consistency conditions. The interplay between relic density requirements, radiative neutrino mass generation, and lepton flavor violating observables induces a nontrivial flavor geometry in parameter space. Particular suppressions in the $(e\mu)$ and $(e\tau)$ sectors arise naturally, while diagonal entries strongly resist cancellation. We further compare normal and inverted mass hierarchies, analyze reduced versus full Casas--Ibarra geometries, and identify approximate scaling relations linking dark matter and flavor observables. Our results suggest that emergent flavor structures may represent dynamical consequences of radiative neutrino mass generation rather than externally imposed flavor symmetries.

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 / 2 minor

Summary. The manuscript investigates the minimal scotogenic model via large-scale numerical scans in the Casas-Ibarra parametrization, subject to dark-matter relic-density and lepton-flavor-violation constraints. It claims that approximate suppressions in the (eμ) and (eτ) entries of the neutrino Yukawa matrix emerge dynamically from the interplay of these phenomenological requirements together with radiative neutrino-mass generation, producing a nontrivial flavor geometry in parameter space; the work further contrasts normal versus inverted hierarchies, reduced versus full Casas-Ibarra geometries, and reports approximate scaling relations between dark-matter and flavor observables.

Significance. If the reported geometry proves robust to scan-range and prior variations, the result would be of moderate significance: it would illustrate how consistency conditions alone can induce effective neutrino textures in a radiative model without additional flavor symmetries, thereby linking dark-matter phenomenology directly to lepton-flavor structure. The absence of quantitative scan diagnostics, however, currently limits the strength of this interpretation.

major comments (3)
  1. [Section 4 (parameter scan and results)] The central claim that the (eμ) and (eτ) suppressions arise dynamically from consistency conditions rather than scan artifacts requires explicit demonstration that the observed geometry survives changes in the bounds or priors on the complex angles of the Casas-Ibarra matrix R. The manuscript provides no such variation study, leaving open the possibility that the reported nontrivial structure is induced by the chosen scan ranges.
  2. [Section 4 and Figure 3] No information is given on the total number of sampled points, acceptance fraction after relic-density and LFV cuts, convergence diagnostics, or uncertainty on the reported suppression factors. Without these statistics it is impossible to judge whether the claimed flavor geometry is statistically stable or sensitive to threshold choices.
  3. [Section 5.2] The comparison of reduced versus full Casas-Ibarra geometries (Section 5.2) shows differences but does not test robustness against the skeptic’s concern: whether the log-uniform priors and angle bounds preferentially exclude unsuppressed regions that would still satisfy the relic-density and LFV constraints.
minor comments (2)
  1. [Section 3] Notation for the Casas-Ibarra angles and phases is introduced without a compact summary table; a single table collecting definitions, ranges, and priors would improve readability.
  2. [Figures 4–6] Several figures lack explicit labels for the color scale or contour levels corresponding to the suppression factors; this makes quantitative comparison between panels difficult.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help clarify the presentation of our numerical results. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Section 4 (parameter scan and results)] The central claim that the (eμ) and (eτ) suppressions arise dynamically from consistency conditions rather than scan artifacts requires explicit demonstration that the observed geometry survives changes in the bounds or priors on the complex angles of the Casas-Ibarra matrix R. The manuscript provides no such variation study, leaving open the possibility that the reported nontrivial structure is induced by the chosen scan ranges.

    Authors: We agree that a dedicated robustness study against variations in the Casas-Ibarra parameters is required to strengthen the claim that the observed suppressions emerge dynamically. In the revised manuscript we will add a new subsection in Section 4 presenting additional scans performed with expanded ranges for the complex angles of R and with alternative (flat and log-flat) priors. These results will demonstrate that the (eμ) and (eτ) suppressions persist under such changes. revision: yes

  2. Referee: [Section 4 and Figure 3] No information is given on the total number of sampled points, acceptance fraction after relic-density and LFV cuts, convergence diagnostics, or uncertainty on the reported suppression factors. Without these statistics it is impossible to judge whether the claimed flavor geometry is statistically stable or sensitive to threshold choices.

    Authors: We acknowledge that the current version lacks quantitative scan diagnostics. In the revision we will report the total number of sampled points, the acceptance fraction after the relic-density and LFV cuts, the convergence criteria employed, and estimated uncertainties on the quoted suppression factors. This information will be inserted in Section 4 and in the caption of Figure 3. revision: yes

  3. Referee: [Section 5.2] The comparison of reduced versus full Casas-Ibarra geometries (Section 5.2) shows differences but does not test robustness against the skeptic’s concern: whether the log-uniform priors and angle bounds preferentially exclude unsuppressed regions that would still satisfy the relic-density and LFV constraints.

    Authors: We agree that the skeptic’s concern about possible prior-induced bias should be addressed explicitly. In the revised Section 5.2 we will include a dedicated test using alternative prior choices and wider angle bounds, checking whether unsuppressed (eμ) and (eτ) entries remain compatible with the relic-density and LFV constraints. The outcome of this test will be reported together with the existing reduced-versus-full comparison. revision: yes

Circularity Check

1 steps flagged

Flavor geometry reported as emergent is shaped by imposed LFV/DM scan constraints

specific steps
  1. fitted input called prediction [Abstract]
    "We demonstrate that approximate suppressions can dynamically emerge from phenomenological consistency conditions. The interplay between relic density requirements, radiative neutrino mass generation, and lepton flavor violating observables induces a nontrivial flavor geometry in parameter space."

    The paper scans parameters subject to relic-density, LFV, and mass-generation constraints, then presents the resulting distribution of flavor entries as an emergent geometry induced by those same conditions. The reported suppressions are therefore the filtered output of the imposed thresholds and scan ranges rather than an independent model prediction.

full rationale

The paper's central result—that approximate (eμ) and (eτ) suppressions and nontrivial flavor geometry arise dynamically—is obtained by performing large-scale scans in the Casas-Ibarra parametrization while enforcing relic density, radiative neutrino mass, and LFV bounds. The observed structure is therefore the direct statistical consequence of the selection criteria applied to the scanned parameters. While the underlying scotogenic model equations are independent, the specific geometry highlighted as 'emergent' reduces to the output of the constrained sampling procedure rather than a parameter-free derivation. No load-bearing self-citation or ansatz smuggling is evident from the provided text, keeping the circularity partial rather than total.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard scotogenic model assumptions plus the completeness and unbiased nature of the Casas-Ibarra scans; many free parameters typical of the model (Yukawa couplings, scalar masses, mixing angles) are implicitly fitted or scanned to satisfy the constraints.

free parameters (2)
  • Casas-Ibarra complex angles and phases
    Used to parametrize the neutrino Yukawa matrix during scans; values are chosen to satisfy neutrino oscillation data while exploring flavor geometry.
  • Dark matter mass and coupling parameters
    Scanned to enforce correct relic density; directly linked to the flavor observables in the reported scaling relations.
axioms (2)
  • domain assumption Neutrino masses are generated radiatively via the scotogenic loop involving the inert doublet and right-handed neutrinos.
    Standard assumption of the minimal scotogenic model invoked throughout the parameter scans.
  • domain assumption Lepton flavor violation bounds and dark matter relic density are independent external constraints that can be applied simultaneously without internal inconsistency.
    The paper treats these as phenomenological requirements that induce the flavor geometry.

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