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arxiv: 2606.20119 · v1 · pith:ZL6AB2A4new · submitted 2026-06-18 · ✦ hep-ph

The Simplest Dirac Scoto-Seesaw Realization

Sin Kyu Kang , Ranjeet Kumar , Hemant Kumar Prajapati This is my paper

Pith reviewed 2026-06-26 16:55 UTC · model grok-4.3

classification ✦ hep-ph
keywords Dirac neutrinosscoto-seesawU(1) B-Ldark matterZ' bosonneutrino mass orderingresidual symmetry
0
0 comments X

The pith

Chiral U(1) B-L charges for right-handed neutrinos generate atmospheric mass at tree level and solar mass radiatively while stabilizing dark matter with residual Z6.

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

The paper constructs a minimal Dirac scoto-seesaw model using an anomaly-free U(1) B-L gauge symmetry with the chiral charge assignment (-4,-4,5) on the three right-handed neutrinos. This assignment produces the two observed neutrino mass-squared differences through a combination of tree-level Dirac seesaw mixing and one-loop radiative corrections involving the dark sector fields. Spontaneous breaking of the gauge symmetry leaves an unbroken Z6 discrete symmetry that forbids the decay of a scalar or fermionic singlet dark matter candidate. Two explicit realizations are studied, one permitting both normal and inverted neutrino mass orderings and the other only normal ordering, with the chiral charges also suppressing the Z' dilepton width and thereby relaxing collider mass limits. The Z' portal plus co-annihilation channels enlarge the viable dark matter parameter space for both candidate types.

Core claim

The central claim is that the anomaly-free chiral U(1) B-L charge assignment (-4,-4,5) for right-handed neutrinos enforces a Dirac scoto-seesaw structure in which the atmospheric mass-squared difference arises at tree level while the solar difference is generated radiatively, with the residual Z6 symmetry after U(1) B-L breaking automatically stabilizing a dark matter candidate.

What carries the argument

The anomaly-free U(1) B-L gauge symmetry with chiral charges (-4,-4,5) assigned to the three right-handed neutrinos, which restricts the allowed Yukawa interactions to produce the scoto-seesaw neutrino mass pattern and leaves a Z6 residual discrete symmetry after spontaneous breaking.

If this is right

  • One minimal realization allows both normal and inverted neutrino mass orderings while the other restricts to normal ordering only, each with distinct predictions for oscillation parameters.
  • Suppression of the Z' dilepton branching ratio weakens the ATLAS lower bound on the Z' mass relative to vector-like B-L models.
  • The Z' portal together with annihilation and co-annihilation channels opens substantial regions of parameter space for both singlet scalar and fermionic dark matter to match the observed relic density.
  • The two realizations yield testable differences in neutrino observables and dark matter direct-detection rates.

Where Pith is reading between the lines

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

  • The same charge pattern could be embedded in larger gauge groups to generate additional mass hierarchies or flavor structures without extra discrete symmetries.
  • Dijet or missing-energy searches at colliders may provide stronger constraints on the Z' than dilepton searches in this chiral setup.
  • The radiative solar-mass loop could be connected to other scotogenic models to predict relations between neutrino mixing angles and dark matter annihilation cross sections.

Load-bearing premise

The U(1) B-L symmetry breaks in such a way that a residual Z6 symmetry remains unbroken and is sufficient to stabilize the chosen dark matter candidate.

What would settle it

Observation of inverted neutrino mass ordering in the realization that permits only normal ordering, or discovery of a Z' boson with unsuppressed dilepton branching fraction at the LHC.

Figures

Figures reproduced from arXiv: 2606.20119 by Hemant Kumar Prajapati, Ranjeet Kumar, Sin Kyu Kang.

Figure 1
Figure 1. Figure 1: FIG. 1: Neutrino mass generation from Dirac scoto-seesaw mechanism, where [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Correlation between [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Predicted correlation between [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Correlation between neutrino masses obtained for case-I corresponding to the IO case. The [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Correlation between the mass-squared differences for case-II in the IO scenario. The [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Model predictions for case-II in the NO scenario. The left panel corresponds to the [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Correlations of mass-squared differences with [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Correlation of neutrino masses [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: In the left panel correlation of neutrino mass [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Production cross section of the [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Branching fractions of the [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Comparison of [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Relic density (left panels) and spin-independent WIMP-nucleon scattering cross section [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Left: DM relic density [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: DM [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: DM [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: DM [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p028_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p028_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20: Relic density (left) and spin-independent direct detection cross section (right) as functions [PITH_FULL_IMAGE:figures/full_fig_p029_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21: Relic density (left panels) and spin-independent WIMP-nucleon scattering cross section [PITH_FULL_IMAGE:figures/full_fig_p034_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22: Relic density (left panels) and spin-independent WIMP-nucleon scattering cross section [PITH_FULL_IMAGE:figures/full_fig_p035_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p035_23.png] view at source ↗
read the original abstract

We present a simple Dirac scoto-seesaw framework based on the anomaly-free $U(1)_{B-L}$ charge assignment $(-4,-4,5)$ for $\nu_R$. This chiral charge assignment naturally accounts for the observed neutrino mass-squared differences, with $\Delta m^2_{\rm atm}$ generated at tree level and $\Delta m^2_{\rm sol}$ arising radiatively. After the spontaneous breaking of gauged $U(1)_{B-L}$, a residual $Z_6$ symmetry stabilizes the dark matter candidate. We investigate two minimal realizations of the framework, finding that both normal and inverted orderings are viable in one case, whereas only normal ordering survives in the other, with distinctive features for neutrino observables. Moreover, the chiral nature of the $U(1)_{B-L}$ charges suppresses the dilepton branching fraction of $Z'$, resulting in weaker ATLAS mass bounds than in the conventional vector $B-L$ scenario, thereby easing constraints on the dark sector. We explore the dark matter phenomenology of the singlet scalar and fermionic dark matter candidates. While singlet scalar DM is often severely constrained, the presence of the $Z'$ portal together with annihilation and co-annihilation channels substantially broadens the allowed parameter space. Thus, the framework offers a predictive scenario for neutrino and dark matter phenomenology that can be probed in future experiments.

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

0 major / 3 minor

Summary. The manuscript constructs a Dirac scoto-seesaw model based on an anomaly-free gauged U(1)_{B-L} with chiral charges (-4,-4,5) assigned to the three right-handed neutrinos. This assignment is used to generate the atmospheric neutrino mass-squared splitting at tree level while the solar splitting arises only radiatively. Spontaneous breaking of U(1)_{B-L} leaves a residual Z_6 that stabilizes dark-matter candidates. Two minimal realizations are presented; one allows both normal and inverted orderings while the other permits only normal ordering, with associated predictions for neutrino observables. The chiral charges suppress the Z' dilepton branching ratio relative to vector-like B-L models, and the dark-matter phenomenology of singlet scalar and fermionic candidates is explored via the Z' portal together with annihilation and co-annihilation channels.

Significance. If the explicit constructions and mass-generation mechanisms hold, the work supplies a minimal, gauge-consistent framework that simultaneously explains the two neutrino mass-squared differences through distinct perturbative orders and stabilizes dark matter via a discrete remnant symmetry. The reduced ATLAS bounds on the Z' and the broadened viable parameter space for both scalar and fermionic dark matter constitute concrete, testable features that distinguish the scenario from conventional B-L extensions.

minor comments (3)
  1. The abstract states that the charge assignment is anomaly-free, but the explicit cancellation of all gauge anomalies (including mixed anomalies with gravity) should be shown in a dedicated subsection or appendix for completeness.
  2. A side-by-side comparison table of the two minimal realizations (field content, charge assignments, and resulting mass matrices) would clarify why one permits inverted ordering while the other does not.
  3. The statement that the Z_6 remnant 'stabilizes the dark matter candidate' is central; an explicit listing of the Z_6 charges of all fields and a brief proof that the lightest odd state cannot decay would strengthen the claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No major comments were listed in the report, so there are no specific points requiring detailed rebuttal or clarification at this stage.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper selects the anomaly-free chiral U(1)_{B-L} charges (-4,-4,5) on the right-handed neutrinos as an explicit input to enforce the scoto-seesaw operator structure, with tree-level atmospheric and radiative solar mass splittings following directly from the allowed Lagrangian terms after symmetry breaking. This is a standard charge-assignment mechanism in flavored gauge models rather than a derivation that reduces to its own fitted outputs or self-citations; the residual Z_6 for DM stabilization is the usual discrete remnant, and the viability checks for normal/inverted orderings plus DM phenomenology are independent of any renaming or self-referential fitting. No load-bearing self-citation, ansatz smuggling, or prediction that collapses to an internal parameter fit appears in the abstract or described structure, so the central claims remain self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 3 invented entities

The central claim rests on the anomaly cancellation of the chosen charges, the existence of a residual discrete symmetry after breaking, and the introduction of new scalar and fermion fields whose stability and couplings are not independently verified outside the model.

free parameters (2)
  • U(1)B-L breaking vev
    Scale at which the new symmetry is broken; must be chosen to produce correct neutrino mass splittings.
  • DM mass and portal couplings
    Parameters controlling singlet scalar and fermionic DM annihilation rates to match observed relic density.
axioms (2)
  • standard math Charge assignment (-4,-4,5) is anomaly free under U(1)B-L
    Invoked to justify the gauge symmetry extension.
  • domain assumption Spontaneous breaking leaves an exact residual Z6 that stabilizes DM
    Central to the dark-matter stability claim.
invented entities (3)
  • Z' gauge boson no independent evidence
    purpose: Mediator of the new U(1)B-L interaction
    New particle required by the gauge extension; no independent evidence supplied.
  • Singlet scalar DM candidate no independent evidence
    purpose: Stable dark matter particle protected by Z6
    Postulated new scalar whose stability is asserted by the residual symmetry.
  • Fermionic DM candidate no independent evidence
    purpose: Alternative stable dark matter particle
    Postulated new fermion whose stability is asserted by the residual symmetry.

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Reference graph

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