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This paper argues that the lightest sterile neutrino in a minimal Type-I Dirac seesaw, produced by freeze-in, can match the observed dark matter relic abundance at masses above roughly 10^-2 GeV, because the right-handed mixing angle θ_R dr

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2026-08-03 01:16 UTC pith:2YF45Z3Q

load-bearing objection θ_R is a genuinely clean way to decouple sterile-neutrino DM from X-ray searches, but the paper's main scan rests on a Boltzmann-equation backreaction term that is not detailed-balance consistent. the 2 major comments →

arxiv 2603.20145 v2 pith:2YF45Z3Q submitted 2026-03-20 hep-ph

Sterile neutrino Dark Matter in the minimal Dirac Seesaw

J. Adhikary , A. Batra , K. Deka , F. R. Joaquim This is my paper
classification hep-ph
keywords Dirac seesawsterile neutrino dark matterfreeze-inright-handed mixing angleX-ray constraintsZ6 symmetryDelta N_effneutrino mass generation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that sterile neutrino dark matter can survive in a minimal Type-I Dirac seesaw framework. It argues that the lightest sterile neutrino, produced non-thermally via freeze-in from decays of Standard Model particles and one additional scalar, can reproduce the observed dark matter relic density in two regimes: a low-mass one controlled by the usual left-handed mixing angle θ_L, and a higher-mass regime (above ~10^-2 GeV) opened by the right-handed mixing angle θ_R. The crucial point is that θ_R contributes to production but not to the radiative decay N→νγ that generates X-ray bounds, so the higher-mass region escapes the constraints that usually rule out sterile neutrino dark matter. If the argument holds, the model provides the simplest known construction in which Dirac neutrino masses are seeded by dark matter, and it predicts no observable X-ray line in the θ_R-dominated region.

Core claim

The central claim is that the right-handed mixing angle θ_R, present in Dirac seesaw constructions, decouples sterile-neutrino production from its main observational constraint. In this model the lightest sterile neutrino N1 is produced non-thermally through decays of W, Z, the Higgs h and an extra scalar H. When θ_L is very small (~10^-15), production in the mass range M_N1 ≈ 10^-2 to 10^-1 GeV yields Ωh² in the observed interval 0.1126–0.1246, with h/H→N1 ν̄/N̄1 ν channels controlled by θ_R. Because the radiative decay N1→νγ proceeds through a W loop and depends only on θ_L, the X-ray limits that normally exclude sterile neutrino dark matter do not apply in this regime. The paper also find

What carries the argument

The machinery is a Z6 symmetry broken spontaneously to a residual Z3 that forbids all Majorana mass operators, together with the 6×6 Dirac mass matrix whose seesaw limit yields M_ν ≈ (v_φ v_σ/2) Y_ν M_N^{-1} Y_σ (Eq. 3). The active–sterile rotation is parametrised per generation by two independent angles, θ_L and θ_R (Eq. 5); θ_R governs the coupling of the singlet scalar σ and the heavy right-handed states to the dark matter candidate N1. The freeze-in Boltzmann equation (Eq. 9) then converts the decay channels W→N1 e, Z→N1 ν̄, h/H→N1 ν̄ into the comoving yield, and the relic density follows via Eq. (11). θ_R's role is to provide a production handle that does not change the N1→νγ amplitude.

Load-bearing premise

The argument rests on the assumption that a one-generation diagonalization of the 6×6 mass matrix is sufficient, so the scanned θ_L1, θ_R1, M_N1 values remain compatible with the full three-flavor neutrino oscillation data and the sum of neutrino masses below 0.12 eV; a full fit that pushes the couplings outside the scanned range would close the viable region.

What would settle it

A full three-flavor diagonalization of the model's mass matrix that finds no Yukawa configuration consistent with the measured solar and atmospheric mass-squared differences and the sum of neutrino masses ≤ 0.12 eV within the scanned range (θ_L1 ~ 10^-9–10^-15, M_N1 ~ 10^-4–10^-1 GeV) would falsify the claim; alternatively, a higher-loop calculation showing θ_R feeds N1→νγ at a rate exceeding X-ray bounds would close the θ_R-dominated region.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Sterile neutrino dark matter can have mass around 0.01–0.1 GeV, above the usually-assumed keV scale, while still giving the observed relic abundance.
  • In the θ_R-dominated regime the model predicts no X-ray line from N1 decay, so future null searches in that mass window are expected.
  • The same right-handed states that generate Dirac neutrino masses are the dark matter, making this a tree-level 'DM-seeded' neutrino mass mechanism.
  • The freeze-in contribution to ΔN_eff is ~10^-17, automatically satisfying current CMB constraints on extra relativistic species.
  • Only the three-generation version works; a two-generation variant is excluded by X-ray bounds on θ_L1.

Where Pith is reading between the lines

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

  • The separation of production and decay angles is a design principle likely to reappear in other Dirac neutrino models: any construction in which the right-handed sector has its own mixing angle can decouple freeze-in production from radiative-decay limits.
  • A direct test would be collider searches for the extra scalar H in decays to right-handed neutrinos; the required Yukawa couplings may yield displaced-vertex or missing-energy signatures.
  • The one-generation scan may not represent the full parameter space; a complete three-flavor fit could sharpen or shift the viable mass window, and is an obvious next calculation.
  • If a future X-ray line is observed at a mass in the θ_L-dominated region, it would support a shared-coupling scenario and disfavor this Dirac construction, since θ_R production leaves no line.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper proposes a Z6-symmetric extension of the SM with three right-handed neutrinos ν_Ri, three Dirac pairs N_Li, N_Ri, and a singlet scalar σ. After σ acquires a VEV, the residual Z3 symmetry forbids Majorana mass operators, leaving Dirac neutrino masses generated at tree level through the Type-I Dirac seesaw relation (3). The lightest sterile state N1 is assumed to be produced by freeze-in from SM gauge-boson and h/H decays. Using one-generation mixing angles θ_L and θ_R, the authors scan parameter space and claim that θ_R opens a DM-viable region at M_N1 ≳ 10^−2 GeV, with a benchmark Ωh² = 0.1128 (Table II), while θ_L-dominated production is X-ray excluded. The paper also computes ΔN_eff from freeze-in ν_R production and finds a negligible contribution. The main quantitative results are Fig. 2 and Table II.

Significance. The mechanism studied is interesting and timely: in a Dirac seesaw, a right-handed mixing angle could evade the usual X-ray bound on sterile-neutrino DM. The paper's approach is standard in several respects — freeze-in from decays with widths taken from Ref. [47], a public solver for ΔN_eff, and explicit checks of perturbativity, non-thermality, and DM lifetime. However, the central quantitative claim depends on the Boltzmann equation (9), whose back-reaction term has a detailed-balance error, and the one-generation diagonalization used to connect neutrino masses to the DM couplings is not shown to be compatible with neutrino oscillation data. These two issues make the presented viable region (Fig. 2, right panel) not yet established.

major comments (2)
  1. [Sec. III.A, Eq. (9)] The back-reaction term is written as ⟨Γ_i⟩(Y_i^eq − Y_N1). For a two-body decay A_i → N1 + X with X in equilibrium, detailed balance gives a net collision term proportional to ⟨Γ_i⟩ Y_i^eq (1 − Y_N1/Y_N1^eq), not ⟨Γ_i⟩(Y_i^eq − Y_N1). As written, the equation drives Y_N1 toward Y_i^eq rather than toward its own equilibrium yield. Since M_N1 ≪ m_i, the ratio Y_i^eq/Y_N1^eq is generally much smaller than unity in the regime where inverse decays are invoked, so the printed loss term is too strong. The post-peak depletion in Fig. 3 and the θ_R-dominated benchmark Ωh² = 0.1128 in Table II are consequences of this spurious term. With the standard freeze-in equation (back-reaction neglected) or the correct detailed-balance term, the yield freezes in earlier and at a higher value; the viable band in the right panel of Fig. 2 must be re-derived and may shift or close.
  2. [Sec. II, Eqs. (3)–(5)] The scan is performed under 'neglect intergenerational mixing among active and sterile neutrinos', with diagonal Yukawa matrices. In this limit the effective active-neutrino mass matrix (3) is diagonal, so the model predicts vanishing PMNS mixing angles, incompatible with observed neutrino oscillations. The text discusses the two-generation case, but no full three-flavor fit is presented for the scanned parameter region; the only applied neutrino-mass constraint is Σ m_ν ≤ 0.12 eV. Because the one-generation extraction of Y_ν1, Y_σ1 via Eq. (5) and the resulting DM production can change once off-diagonal entries are included to fit Δm²_ij and θ_PMNS, the claim that the minimal model possesses the displayed viable region is not demonstrated. Please provide a full 3×3 fit, or justify why the diagonal limit is representative of a model that fits neutrino oscillation data.
minor comments (5)
  1. [Table II] The entry 'θ1 = 10−15' should read 'θ_L1 = 10−15'. Also specify the fixed values of m_H, α, v_σ, and the non-scanned angle in the caption.
  2. [Eq. (7)] The summation symbols are typeset as '6X'; the ranges of j, l, i, k and the meaning of the indices should be corrected and clarified.
  3. [Fig. 3 caption] The caption says the displayed trajectory corresponds to 'the parameter point with the largest drop from its peak value', but this selection is not reproducible without showing the distribution of peak drops. Give the coordinates of the point and the peak/final yields.
  4. [Eq. (11)] T_present is not defined. Specify that it is a temperature below all relevant masses so that the yield has frozen out.
  5. [Sec. III.B, Eq. (15)] The collision term as printed appears to omit the phase-space integral over the parent momentum p1; clarify the notation so the expression matches the Monte-Carlo solver being used.

Circularity Check

0 steps flagged

No significant circularity: relic abundance is computed from an externally parameterized Boltzmann equation; the θ_R scan is not a fitted prediction.

full rationale

The central derivation chain is self-contained and externally benchmarked. The paper scans (M_N1, θ_L1, θ_R1) and solves the Boltzmann equation (Eq. 9) with decay widths from [47]; the resulting yield is compared against the externally measured Planck interval Ωh²=0.1126–0.1246. The θ_R coupling entering the h/H decay vertices (Eq. B1) is obtained by inverting the mass-matrix diagonalization (Eqs. 2,5), not by fitting to the relic density; the X-ray constraint on the radiative decay N→νγ is an external bound. The benchmark points in Table II are deliberately chosen to land in the viable interval, so they demonstrate existence of allowed parameter space rather than a prediction extracted from fitted inputs. The one-generation diagonalization and the detailed-balance form of Eq. (9) are potential correctness issues, but neither makes any output equal to an input by construction. There are no load-bearing self-citations by the present authors; the cited decay-width and ΔN_eff results are independent external computations. Therefore no circularity step is present.

Axiom & Free-Parameter Ledger

7 free parameters · 5 axioms · 2 invented entities

Central claim rests on: a symmetry ansatz (Z_6→Z_3), a one-generation truncation of the 3-flavor neutrino sector, hand-picked scalar-sector benchmarks (m_H, α, v_σ), and two scanned mixing angles plus a scanned mass. The Yukawa couplings are then derived from Eq. (5), so the real input freedom lives in the scan parameters and the neglected off-diagonal structure. No new entity carries independent falsifiable evidence; the model is a proof-of-possibility scan rather than a parameter-free prediction.

free parameters (7)
  • m_H (heavy scalar mass) = 500 GeV
    Chosen by hand (Sec. III). Does not appear to be scanned in the figures; affects the H-mediated production channel and the scalar coupling values via Eq. (A6).
  • α (scalar mixing angle) = 0.1
    Chosen by hand (Sec. III). Controls h–H mixing and the couplings in Eq. (B1), hence the h/H production rates.
  • v_σ (singlet VEV) = 150 GeV
    Chosen by hand (Sec. III). Sets the scale of the σ-involving Yukawa terms and enters the mass matrix Eq. (2).
  • θ_L1 (left-handed mixing angle) = scanned 10^-15 to ~10^-8
    Scanned in Fig. 2; essentially a free input in the scan. When large it drives W/Z-mediated production and is X-ray constrained; with tiny θ_L = 10^-15 the θ_R regime is isolated.
  • θ_R1 (right-handed mixing angle) = scanned 10^-10 to ~10^-5
    Scanned in Fig. 2; the key knob that drives h/H-mediated production without affecting N→νγ. One of the main advertised results is that θ_R is not constrained by X-rays.
  • M_N1 (DM sterile mass) = scanned 10^-4 to 10^-1 GeV
    Scanned in Fig. 2. The relic density and decay channels both depend on it.
  • Y_ν11, Y_σ11 (Yukawa couplings) = derived from Eq. (5) given θ_L, θ_R, M_N, v_σ, v_φ
    Not independent inputs: extracted from the mixing relations. But the underlying 3×3 matrices Y_ν, Y_σ are free; their off-diagonal entries are set to zero by fiat ('neglect intergenerational mixing').
axioms (5)
  • domain assumption Type-I seesaw relation M_ν ≈ (v_φ v_σ/2) Y_ν M_N^{-1} Y_σ (Eq. 3) in the limit M_N >> v_φ, v_σ.
    Standard Dirac-seesaw result used to connect Yukawas, M_N and neutrino masses. Invoked before Eq. (3).
  • ad hoc to paper Z_6 → Z_3 symmetry breaking forbids all Majorana operators while allowing the dimension-5 Dirac operator (ℓ̄_L Φ̃ ν_R) σ.
    The model-defining symmetry assumption; it is what makes neutrinos Dirac and keeps N_1 stable (Z_3 residual). Not externally verified, but it is the model definition, not a hidden gap.
  • domain assumption Freeze-in dominance: at the parameter points of interest the DW contribution is negligible (Eq. 8 estimate) and annihilations are suppressed by 1/m^4 relative to decays.
    Used to justify solving only the decay Boltzmann equation (Eq. 9). Assumption is standard for tiny couplings.
  • domain assumption Scalar potential is bounded from below and the specific VEV v_σ = 150 GeV with m_H = 500 GeV, α = 0.1 yields a viable scalar spectrum.
    Appendix A gives the stability conditions but the chosen benchmark point's consistency with them is not explicitly shown.
  • ad hoc to paper One-generation diagonalization (Eq. 5) adequately captures the neutrino-mixing and mass structure relevant for the DM calculation.
    The authors state 'we neglect intergenerational mixing among active and sterile neutrinos'. This is a significant simplification given the model is supposed to reproduce observed three-flavor neutrino oscillations, and the impact of the neglected entries on the scan is not assessed.
invented entities (2)
  • Six new fermions (ν_Ri, N_Li, N_Ri) no independent evidence
    purpose: Generate Dirac neutrino masses via tree-level seesaw; the lightest N is the dark-matter candidate.
    These are new particles beyond the SM. The paper provides no direct experimental handle; the X-ray-decay weakening is the only testable consequence and it is an absence of signal, not a positive prediction of a new entity.
  • Real singlet scalar σ with Z_6-charge ω^3 no independent evidence
    purpose: Breaks Z_6 to Z_3, gives mass to the ν_R via its VEV, and mixes into the heavy scalar H that mediates DM production.
    New scalar, necessary for the symmetry structure and the θ_R-mediated production. As with most FIMP/singlet constructions, no direct detection signature is calculated; the H scalar could mix with the SM Higgs, but no mixing/signal constraints are explored.

pith-pipeline@v1.3.0-alltime-deepseek · 12075 in / 9742 out tokens · 81151 ms · 2026-08-03T01:16:30.101382+00:00 · methodology

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read the original abstract

We study sterile neutrino dark matter in a minimal Type-I Dirac seesaw framework where the states responsible for generating Dirac neutrino masses at tree level can be viable dark matter candidates. A $\mathcal{Z}_6$ symmetry, spontaneously broken to a residual $\mathcal{Z}_3$ by the vacuum expectation value of a singlet scalar, forbids Majorana mass operators and ensures neutrino Diracness. The lightest sterile neutrino is produced non-thermally via freeze-in from decays of Standard Model particles and an additional scalar state. We show that the presence of an additional right-handed mixing angle, $\theta_R$, opens up viable regions of parameter space where the observed dark matter relic abundance can be reproduced while maintaining cosmological stability. This mainly stems from the absence of X-ray astrophysical constraints in our scenario. We further find that the freeze-in production of right-handed neutrinos yields a negligible contribution to $\Delta N_{\rm eff}$, consistent with current cosmological bounds.

Figures

Figures reproduced from arXiv: 2603.20145 by A. Batra, F. R. Joaquim, J. Adhikary, K. Deka.

Figure 1
Figure 1. Figure 1: FIG. 1: Feynman diagram for tree-level Dirac neutrino mass generation with U(1) [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Left: Parameter space in the ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Left: The evolution of the relic abundance is shown as a function of z corresponding to [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. $Z^\prime$ Portal Dark Matter with Observable $\Delta N_{\rm eff}$

    hep-ph 2026-07 accept novelty 5.5

    Dirac right-handed neutrinos in a U(1)_{B-L} Z' portal model produce observable ΔN_eff that, together with direct/indirect detection and collider bounds, carves out testable WIMP and FIMP dark-matter regions.

Reference graph

Works this paper leans on

54 extracted references · 2 canonical work pages · cited by 1 Pith paper

  1. [1]

    Nobel Lecture: Discovery of atmospheric neutrino oscillations,

    T. Kajita, “Nobel Lecture: Discovery of atmospheric neutrino oscillations,”Rev. Mod. Phys.88no. 3, (2016) 030501

    2016

  2. [2]

    Nobel Lecture: The Sudbury Neutrino Observatory: Observation of flavor change for solar neutrinos,

    A. B. McDonald, “Nobel Lecture: The Sudbury Neutrino Observatory: Observation of flavor change for solar neutrinos,” Rev. Mod. Phys.88no. 3, (2016) 030502

    2016

  3. [3]

    Particle dark matter: Evidence, candidates and constraints,

    G. Bertone, D. Hooper, and J. Silk, “Particle dark matter: Evidence, candidates and constraints,”Phys. Rept.405 (2005) 279–390,arXiv:hep-ph/0404175. [4]PlanckCollaboration, N. Aghanimet al., “Planck 2018 results. VI. Cosmological parameters,”Astron. Astrophys.641 (2020) A6,arXiv:1807.06209 [astro-ph.CO]. [Erratum: Astron.Astrophys. 652, C4 (2021)]

    Pith/arXiv arXiv 2005

  4. [5]

    µ→eγat a Rate of One Out of 10 9 Muon Decays?,

    P. Minkowski, “µ→eγat a Rate of One Out of 10 9 Muon Decays?,”Phys. Lett. B67(1977) 421–428

    1977

  5. [6]

    Complex Spinors and Unified Theories,

    M. Gell-Mann, P. Ramond, and R. Slansky, “Complex Spinors and Unified Theories,”Conf. Proc. C790927(1979) 315–321,arXiv:1306.4669 [hep-th]

    Pith/arXiv arXiv 1979

  6. [7]

    Horizontal gauge symmetry and masses of neutrinos,

    T. Yanagida, “Horizontal gauge symmetry and masses of neutrinos,”Conf. Proc. C7902131(1979) 95–99

    1979

  7. [8]

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

    J. Schechter and J. W. F. Valle, “Neutrino Masses in SU(2) x U(1) Theories,”Phys. Rev. D22(1980) 2227

    1980

  8. [9]

    The Future of Elementary Particle Physics,

    S. L. Glashow, “The Future of Elementary Particle Physics,”NATO Sci. Ser. B61(1980) 687

    1980

  9. [10]

    Neutrino Mass and Spontaneous Parity Nonconservation,

    R. N. Mohapatra and G. Senjanovic, “Neutrino Mass and Spontaneous Parity Nonconservation,”Phys. Rev. Lett.44 (1980) 912

    1980

  10. [11]

    Sterile-neutrinos as dark matter,

    S. Dodelson and L. M. Widrow, “Sterile-neutrinos as dark matter,”Phys. Rev. Lett.72(1994) 17–20, arXiv:hep-ph/9303287

    Pith/arXiv arXiv 1994

  11. [12]

    Radiative Decays of Massive Neutrinos,

    P. B. Pal and L. Wolfenstein, “Radiative Decays of Massive Neutrinos,”Phys. Rev. D25(1982) 766

    1982

  12. [13]

    Constraining DM properties with SPI,

    A. Boyarsky, D. Malyshev, A. Neronov, and O. Ruchayskiy, “Constraining DM properties with SPI,”Mon. Not. Roy. Astron. Soc.387(2008) 1345,arXiv:0710.4922 [astro-ph]. 11

    Pith/arXiv arXiv 2008

  13. [14]

    Sterile neutrino dark matter bounds from galaxies of the Local Group,

    S. Horiuchi, P. J. Humphrey, J. Onorbe, K. N. Abazajian, M. Kaplinghat, and S. Garrison-Kimmel, “Sterile neutrino dark matter bounds from galaxies of the Local Group,”Phys. Rev. D89no. 2, (2014) 025017,arXiv:1311.0282 [astro-ph.CO]

    Pith/arXiv arXiv 2014

  14. [15]

    NuSTAR Tests of Sterile-Neutrino Dark Matter: New Galactic Bulge Observations and Combined Impact,

    B. M. Roach, K. C. Y. Ng, K. Perez, J. F. Beacom, S. Horiuchi, R. Krivonos, and D. R. Wik, “NuSTAR Tests of Sterile-Neutrino Dark Matter: New Galactic Bulge Observations and Combined Impact,”Phys. Rev. D101no. 10, (2020) 103011,arXiv:1908.09037 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  15. [16]

    Deep Search for Decaying Dark Matter with XMM-Newton Blank-Sky Observations,

    J. W. Foster, M. Kongsore, C. Dessert, Y. Park, N. L. Rodd, K. Cranmer, and B. R. Safdi, “Deep Search for Decaying Dark Matter with XMM-Newton Blank-Sky Observations,”Phys. Rev. Lett.127no. 5, (2021) 051101, arXiv:2102.02207 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  16. [17]

    eXT Pperspectives for theνMSM sterile neutrino dark matter model,

    D. Malyshev, C. Thorpe-Morgan, A. Santangelo, J. Jochum, and S.-N. Zhang, “eXT Pperspectives for theνMSM sterile neutrino dark matter model,”Phys. Rev. D101no. 12, (2020) 123009,arXiv:2001.07014 [astro-ph.HE]

    Pith/arXiv arXiv 2020

  17. [18]

    Searches for sterile neutrinos and axionlike particles from the Galactic halo with eROSITA,

    A. Dekker, E. Peerbooms, F. Zimmer, K. C. Y. Ng, and S. Ando, “Searches for sterile neutrinos and axionlike particles from the Galactic halo with eROSITA,”Phys. Rev. D104no. 2, (2021) 023021,arXiv:2103.13241 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  18. [19]

    Decaying dark matter in dwarf spheroidal galaxies: Prospects for x-ray and gamma-ray telescopes,

    S. Andoet al., “Decaying dark matter in dwarf spheroidal galaxies: Prospects for x-ray and gamma-ray telescopes,” Phys. Rev. D104no. 2, (2021) 023022,arXiv:2103.13242 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  19. [20]

    A New dark matter candidate: Nonthermal sterile neutrinos,

    X.-D. Shi and G. M. Fuller, “A New dark matter candidate: Nonthermal sterile neutrinos,”Phys. Rev. Lett.82(1999) 2832–2835,arXiv:astro-ph/9810076

    Pith/arXiv arXiv 1999

  20. [21]

    Dodelson-Widrow Mechanism in the Presence of Self-Interacting Neutrinos,

    A. De Gouvˆ ea, M. Sen, W. Tangarife, and Y. Zhang, “Dodelson-Widrow Mechanism in the Presence of Self-Interacting Neutrinos,”Phys. Rev. Lett.124no. 8, (2020) 081802,arXiv:1910.04901 [hep-ph]

    Pith/arXiv arXiv 2020

  21. [22]

    Neutrino self-interactions: A white paper,

    J. M. Berrymanet al., “Neutrino self-interactions: A white paper,”Phys. Dark Univ.42(2023) 101267, arXiv:2203.01955 [hep-ph]

    Pith/arXiv arXiv 2023

  22. [23]

    Boosting the production of sterile neutrino dark matter with self-interactions,

    M. D. Astros and S. Vogl, “Boosting the production of sterile neutrino dark matter with self-interactions,”JHEP03 (2024) 032,arXiv:2307.15565 [hep-ph]

    Pith/arXiv arXiv 2024

  23. [24]

    Dark-matter sterile neutrinos in models with a gauge singlet in the Higgs sector,

    K. Petraki and A. Kusenko, “Dark-matter sterile neutrinos in models with a gauge singlet in the Higgs sector,”Phys. Rev. D77(2008) 065014,arXiv:0711.4646 [hep-ph]

    Pith/arXiv arXiv 2008

  24. [25]

    New Production Mechanism for keV Sterile Neutrino Dark Matter by Decays of Frozen-In Scalars,

    A. Merle, V. Niro, and D. Schmidt, “New Production Mechanism for keV Sterile Neutrino Dark Matter by Decays of Frozen-In Scalars,”JCAP03(2014) 028,arXiv:1306.3996 [hep-ph]

    Pith/arXiv arXiv 2014

  25. [26]

    A Fresh Look at keV Sterile Neutrino Dark Matter from Frozen-In Scalars,

    A. Adulpravitchai and M. A. Schmidt, “A Fresh Look at keV Sterile Neutrino Dark Matter from Frozen-In Scalars,” JHEP01(2015) 006,arXiv:1409.4330 [hep-ph]

    Pith/arXiv arXiv 2015

  26. [27]

    keV Sterile Neutrino Dark Matter from Singlet Scalar Decays: Basic Concepts and Subtle Features,

    A. Merle and M. Totzauer, “keV Sterile Neutrino Dark Matter from Singlet Scalar Decays: Basic Concepts and Subtle Features,”JCAP06(2015) 011,arXiv:1502.01011 [hep-ph]

    Pith/arXiv arXiv 2015

  27. [28]

    Thermalizing sterile neutrino dark matter,

    R. S. L. Hansen and S. Vogl, “Thermalizing sterile neutrino dark matter,”Phys. Rev. Lett.119no. 25, (2017) 251305, arXiv:1706.02707 [hep-ph]

    Pith/arXiv arXiv 2017

  28. [29]

    Imprint of the Seesaw Mechanism on Feebly Interacting Dark Matter and the Baryon Asymmetry,

    A. Datta, R. Roshan, and A. Sil, “Imprint of the Seesaw Mechanism on Feebly Interacting Dark Matter and the Baryon Asymmetry,”Phys. Rev. Lett.127no. 23, (2021) 231801,arXiv:2104.02030 [hep-ph]

    Pith/arXiv arXiv 2021

  29. [30]

    The Physics of Neutrinoless Double Beta Decay: A Primer,

    B. J. P. Jones, “The Physics of Neutrinoless Double Beta Decay: A Primer,” inTheoretical Advanced Study Institute in Elementary Particle Physics: The Obscure Universe: Neutrinos and Other Dark Matters. 8, 2021.arXiv:2108.09364 [nucl-ex]

    Pith/arXiv arXiv 2021

  30. [31]

    Neutrinoless Double-Beta Decay: A Roadmap for Matching Theory to Experiment,

    V. Ciriglianoet al., “Neutrinoless Double-Beta Decay: A Roadmap for Matching Theory to Experiment,” arXiv:2203.12169 [hep-ph]

    Pith/arXiv arXiv

  31. [32]

    Neutrinoless Double-Beta Decay: Status and Prospects,

    M. J. Dolinski, A. W. P. Poon, and W. Rodejohann, “Neutrinoless Double-Beta Decay: Status and Prospects,”Ann. Rev. Nucl. Part. Sci.69(2019) 219–251,arXiv:1902.04097 [nucl-ex]

    Pith/arXiv arXiv 2019

  32. [33]

    Neutrinoless Double beta Decay in SU(2) x U(1) Theories,

    J. Schechter and J. W. F. Valle, “Neutrinoless Double beta Decay in SU(2) x U(1) Theories,”Phys. Rev. D25(1982) 2951

    1982

  33. [34]

    Dirac neutrinos from flavor symmetry,

    A. Arandaet al., “Dirac neutrinos from flavor symmetry,”Phys. Rev. D89no. 3, (2014) 033001,arXiv:1307.3553 [hep-ph]

    Pith/arXiv arXiv 2014

  34. [35]

    Dirac or inverse seesaw neutrino masses withB−Lgauge symmetry andS 3 flavor symmetry,

    E. Ma and R. Srivastava, “Dirac or inverse seesaw neutrino masses withB−Lgauge symmetry andS 3 flavor symmetry,”Phys. Lett. B741(2015) 217–222,arXiv:1411.5042 [hep-ph]

    Pith/arXiv arXiv 2015

  35. [36]

    String completion of an SU(3) c ⊗SU(3) L ⊗U(1) X electroweak model,

    A. Addazi, J. W. F. Valle, and C. A. Vaquera-Araujo, “String completion of an SU(3) c ⊗SU(3) L ⊗U(1) X electroweak model,”Phys. Lett. B759(2016) 471–478,arXiv:1604.02117 [hep-ph]. 12

    Pith/arXiv arXiv 2016

  36. [37]

    Dirac Neutrinos and Dark Matter Stability from Lepton Quarticity,

    S. Centelles Chuli´ a, E. Ma, R. Srivastava, and J. W. F. Valle, “Dirac Neutrinos and Dark Matter Stability from Lepton Quarticity,”Phys. Lett. B767(2017) 209–213,arXiv:1606.04543 [hep-ph]

    Pith/arXiv arXiv 2017

  37. [38]

    Flavour-symmetric type-II Dirac neutrino seesaw mechanism,

    C. Bonilla, J. M. Lamprea, E. Peinado, and J. W. F. Valle, “Flavour-symmetric type-II Dirac neutrino seesaw mechanism,”Phys. Lett. B779(2018) 257–261,arXiv:1710.06498 [hep-ph]

    Pith/arXiv arXiv 2018

  38. [39]

    Dynamical seesaw mechanism for Dirac neutrinos,

    J. W. F. Valle and C. A. Vaquera-Araujo, “Dynamical seesaw mechanism for Dirac neutrinos,”Phys. Lett. B755(2016) 363–366,arXiv:1601.05237 [hep-ph]

    Pith/arXiv arXiv 2016

  39. [40]

    Realistic SU(3) c ⊗SU(3) L ⊗U(1) X model with a type II Dirac neutrino seesaw mechanism,

    M. Reig, J. W. F. Valle, and C. A. Vaquera-Araujo, “Realistic SU(3) c ⊗SU(3) L ⊗U(1) X model with a type II Dirac neutrino seesaw mechanism,”Phys. Rev. D94no. 3, (2016) 033012,arXiv:1606.08499 [hep-ph]

    Pith/arXiv arXiv 2016

  40. [41]

    Naturally light neutrinos inDiraconmodel,

    C. Bonilla and J. W. F. Valle, “Naturally light neutrinos inDiraconmodel,”Phys. Lett. B762(2016) 162–165, arXiv:1605.08362 [hep-ph]

    Pith/arXiv arXiv 2016

  41. [42]

    Dark matter stability and Dirac neutrinos using only Standard Model symmetries,

    C. Bonilla, S. Centelles-Chuli´ a, R. Cepedello, E. Peinado, and R. Srivastava, “Dark matter stability and Dirac neutrinos using only Standard Model symmetries,”Phys. Rev. D101no. 3, (2020) 033011,arXiv:1812.01599 [hep-ph]

    Pith/arXiv arXiv 2020

  42. [43]

    Effective Gauge Theories,

    S. Weinberg, “Effective Gauge Theories,”Phys. Lett. B91(1980) 51–55

    1980

  43. [44]

    Neutrino Decay and Spontaneous Violation of Lepton Number,

    J. Schechter and J. W. F. Valle, “Neutrino Decay and Spontaneous Violation of Lepton Number,”Phys. Rev. D25 (1982) 774. [45]Particle Data GroupCollaboration, S. Navaset al., “Review of particle physics,”Phys. Rev. D110no. 3, (2024) 030001

    1982

  44. [46]

    Sterile neutrino hot, warm, and cold dark matter,

    K. Abazajian, G. M. Fuller, and M. Patel, “Sterile neutrino hot, warm, and cold dark matter,”Phys. Rev. D64(2001) 023501,arXiv:astro-ph/0101524

    Pith/arXiv arXiv 2001

  45. [47]

    Freeze-in Production of Sterile Neutrino Dark Matter in U(1) B−L Model,

    A. Biswas and A. Gupta, “Freeze-in Production of Sterile Neutrino Dark Matter in U(1) B−L Model,”JCAP09(2016) 044,arXiv:1607.01469 [hep-ph]. [Addendum: JCAP 05, A01 (2017)]

    Pith/arXiv arXiv 2016

  46. [48]

    Minimal Decaying Dark Matter and the LHC,

    G. Arcadi and L. Covi, “Minimal Decaying Dark Matter and the LHC,”JCAP08(2013) 005,arXiv:1305.6587 [hep-ph]

    Pith/arXiv arXiv 2013

  47. [49]

    Sterile neutrino Dark Matter,

    A. Boyarsky, M. Drewes, T. Lasserre, S. Mertens, and O. Ruchayskiy, “Sterile neutrino Dark Matter,”Prog. Part. Nucl. Phys.104(2019) 1–45,arXiv:1807.07938 [hep-ph]

    Pith/arXiv arXiv 2019

  48. [50]

    The Search for Heavy Majorana Neutrinos,

    A. Atre, T. Han, S. Pascoli, and B. Zhang, “The Search for Heavy Majorana Neutrinos,”JHEP05(2009) 030, arXiv:0901.3589 [hep-ph]. [51]DESICollaboration, A. G. Adameet al., “DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations,”JCAP02(2025) 021,arXiv:2404.03002 [astro-ph.CO]

    Pith/arXiv arXiv 2009

  49. [52]

    Dirac neutrinos and neff. part ii. the freeze-in case,

    X. Luo, W. Rodejohann, and X.-J. Xu, “Dirac neutrinos and neff. part ii. the freeze-in case,”Journal of Cosmology and Astroparticle Physics2021no. 03, (Mar., 2021) 082.http://dx.doi.org/10.1088/1475-7516/2021/03/082

    work page doi:10.1088/1475-7516/2021/03/082 2021

  50. [53]

    Dirac neutrinos and neff,

    X. Luo, W. Rodejohann, and X.-J. Xu, “Dirac neutrinos and neff,”Journal of Cosmology and Astroparticle Physics2020 no. 06, (June, 2020) 058–058.http://dx.doi.org/10.1088/1475-7516/2020/06/058

    work page doi:10.1088/1475-7516/2020/06/058 2020

  51. [54]

    Minimal Dirac seesaw dark matter,

    Z. A. Borboruah, D. Borah, L. Malhotra, and U. Patel, “Minimal Dirac seesaw dark matter,”Phys. Rev. D112no. 1, (2025) 015022,arXiv:2412.12267 [hep-ph]

    Pith/arXiv arXiv 2025

  52. [55]

    Dirac neutrinos and dark matter within a minimal discrete symmetry model,

    Y. Reyimuaji and M. Abdughani, “Dirac neutrinos and dark matter within a minimal discrete symmetry model,”Phys. Lett. B868(2025) 139766,arXiv:2408.14166 [hep-ph]

    Pith/arXiv arXiv 2025

  53. [56]

    Naturally small Dirac neutrino mass andB−Ldark matter,

    E. Ma, P. K. Paul, and N. Sahu, “Naturally small Dirac neutrino mass andB−Ldark matter,”arXiv:2601.05926 [hep-ph]

    arXiv

  54. [57]

    Algorithmic Boundedness-From-Below Conditions for Generic Scalar Potentials,

    I. P. Ivanov, M. K¨ opke, and M. M¨ uhlleitner, “Algorithmic Boundedness-From-Below Conditions for Generic Scalar Potentials,”Eur. Phys. J. C78no. 5, (2018) 413,arXiv:1802.07976 [hep-ph]

    Pith/arXiv arXiv 2018