Pith. sign in

REVIEW 4 major objections 6 minor 31 references

One extended gauge structure can generate charged-fermion hierarchies, tiny neutrino masses with large mixing, and stable dark matter.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-31 14:33 UTC pith:KFSNSACR

load-bearing objection Clean anomaly-safe packaging of tri-hypercharge plus dark Z2, with explicit matrices, but flavor is dialed by hand and the DM “viable TeV window” is asserted rather than shown. the 4 major comments →

arxiv 2607.24452 v1 pith:KFSNSACR submitted 2026-07-27 hep-ph

Generation-separated hypercharges and dark charges: origin of flavor, neutrino masses, and dark matter

Duong Van Loi This is my paper
classification hep-ph
keywords generation-separated hyperchargehyperonsflavor hierarchiesseesawscotoseesawdark U(1)residual Z2dark matter
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 Standard Model does not explain why charged fermions have hierarchical masses, why neutrinos are so light yet mix strongly, or what stabilizes dark matter. This paper argues that a single extension—generation-separated hypercharges plus a dark U(1)—can address all three at once. After the three hypercharge factors break to ordinary hypercharge, only the third generation couples renormalizably to the Higgs; lighter generations get masses from higher-dimensional operators involving hyperon singlets, automatically producing mass hierarchies and small quark mixing. Right-handed neutrinos charged under the dark symmetry generate small active neutrino masses through a seesaw or scotoseesaw, while the dark symmetry’s residual Z2 stabilizes either a fermionic or scalar dark-matter candidate at the TeV scale. A sympathetic reader cares because the same gauge pattern, rather than three unrelated add-ons, is claimed to organize flavor, neutrinos, and dark matter together.

Core claim

After U(1)Y1⊗U(1)Y2⊗U(1)Y3 breaks to SM U(1)Y and U(1)D breaks to a residual Z2, one common gauge structure can simultaneously generate hierarchical charged-fermion masses and small CKM mixing from hyperon-suppressed operators, produce tiny neutrino masses with large mixing via seesaw or scotoseesaw, and stabilize fermionic or scalar dark matter with viable TeV-scale relic and direct-detection windows.

What carries the argument

Generation-separated hypercharges plus dark U(1)D: each SM generation is charged under its own U(1)Yi, so only third-generation Yukawas are renormalizable; hyperon VEVs supply the missing charges and suppress lighter generations, while residual Z2 after U(1)D breaking stabilizes dark matter and enables neutrino mass terms.

Load-bearing premise

The hyperon vacuum expectation values can simply be dialed to specific powers of the Wolfenstein parameter with order-one couplings, without a deeper mechanism fixing those ratios.

What would settle it

A global fit of the four-hyperon textures with O(1) couplings that fails to reproduce charged-fermion masses and CKM angles simultaneously, or a direct-detection / collider null result that closes the claimed TeV-scale Z2-odd fermion and scalar windows while leaving the same residual symmetry.

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

If this is right

  • Charged-fermion mass matrices are forced into hierarchical textures with approximate flavor alignment, so small CKM angles are structural rather than accidental.
  • Neutrino masses arise with rank at most two at leading order, naturally leaving one light neutrino massless or radiatively lifted.
  • The lightest Z2-odd state—either a right-handed neutrino or an inert scalar—is cosmologically stable and can saturate the observed relic density near the TeV scale.
  • Dark-sector gauge and scalar portals set both annihilation rates and spin-independent scattering cross sections testable by current and near-future direct-detection experiments.

Where Pith is reading between the lines

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

  • Without a UV completion that dynamically generates the chosen hyperon VEV ratios, the flavor explanation remains a parametric illustration rather than a prediction.
  • The same residual Z2 that stabilizes dark matter also restricts which scotogenic loops are allowed, so neutrino and dark-matter sectors are more tightly linked than in generic scotogenic models.
  • If the dark gauge boson or the hyperons lie near the flavor-breaking scale, precision flavor and collider searches for Z′ or singlet scalars become correlated probes of the whole construction.

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

4 major / 6 minor

Summary. The paper proposes an extension of the SM gauge group to SU(3)_C x SU(2)_L x U(1)_Y1 x U(1)_Y2 x U(1)_Y3 x U(1)_D, with each fermion generation charged under its own hypercharge factor and right-handed neutrinos carrying generation-dependent dark charges (1,-1,0). Anomaly cancellation is checked explicitly (Sec. II, Eq. (2)). The Higgs carries only Y3 charge, so first- and second-generation masses arise from hyperon-suppressed higher-dimensional operators; three realizations with two, three, and four hyperons are presented (Sec. III, Eqs. (10)-(19)), with hyperon VEVs chosen as powers of the Wolfenstein parameter lambda so that the resulting textures exhibit the observed hierarchies. In the four-hyperon model, neutrino masses are generated via a multi-messenger seesaw or a scotoseesaw with inert scalars (Sec. IV, Eqs. (22)-(36)), with numerical benchmark mass matrices quoted. Finally, the residual Z_2 from U(1)_D breaking stabilizes either a fermionic (nu_1R) or scalar DM candidate, for which TeV-scale relic abundance and direct-detection cross sections of order 10^-46 cm^2 are quoted schematically (Sec. V). The claimed result is a common gauge origin of flavor hierarchies, neutrino masses, and dark matter.

Significance. If the construction holds up, it offers a single anomaly-free gauge structure linking three BSM problems, which is an appealing organizational principle and in line with recent interest in deconstructed/tri-hypercharge models [26-28]. The manuscript does provide explicit, checkable charge assignments with generation-by-generation anomaly cancellation, fully written-out effective Yukawa and seesaw matrices, and in principle falsifiable TeV-scale DM benchmarks. However, the quantitative demonstrations are presently thin: the flavor textures are input-driven, the neutrino benchmarks are non-reproducible as printed, and the DM viability claim is unverified and possibly in tension with the cited direct-detection limits. The significance would be substantially raised by an actual fit, a reproducible neutrino benchmark, and an honest DM parameter-space check against LZ/PandaX-4T.

major comments (4)
  1. [Sec. V (DM), Eqs. (37)-(38)] Sec. V: the DM leg of the headline claim is asserted rather than shown, and the one quantitative statement given appears inconsistent with the very bounds cited. The SI cross section is quoted as sigma_SI ~ 10^-46 cm^2 'for a TeV-scale nu_1R and a representative mixing angle of order 10^-2', citing Refs. [32-34] -- but those references are the XENONnT, PandaX-4T, and LZ limits themselves, and at m_DM ~ 1 TeV the LZ/PandaX-4T reach is a few x 10^-47 cm^2. The 'representative' point is therefore at or above the current bound. Likewise the relic-abundance statement rests on a schematic <sigma v> ~ M^2/(4M^2 - m_h'^2)^2 with no coupling dependence, no 1/(16pi), and no resonance discussion. The abstract and Sec. VI claim 'viable TeV-scale parameter regions consistent with... current direct detection constraints'; this must either be demonstrated here (a minimal scan or explicit benchmark agai
  2. [Sec. IV.A, Eqs. (24)-(26)] The claim that the seesaw yields a rank-2 light-neutrino mass matrix is not consistent with the displayed structure. M_D in Eq. (24) has three linearly independent rows (h1, h2, h3/h4 entries in distinct columns), and M_M in Eq. (25) is generically invertible; by the congruence rank identity, M_nu = -M_D M_M^{-1} M_D^T then has rank 3 for generic O(1) couplings. The determinant of the displayed matrix in Eq. (26) vanishes only to the quoted numerical precision, i.e. the third eigenvalue is small but nonzero. Either an exact symmetry/texture reason for rank 2 must be identified, or the statement (including 'predicts two nonzero neutrino masses') should be rephrased as an approximate hierarchy. Relatedly, Eqs. (26) and (30) quote five-significant-figure matrices while the Yukawas are only specified as 'O(1)'; the actual values used should be given so the benchmarks are reproducible.
  3. [Sec. III, Eqs. (11), (14), (18)] The flavor hierarchies are obtained by construction: the hyperon VEVs are set to hand-chosen powers of the Wolfenstein parameter (v12/Lambda ~ lambda^2, v'12/Lambda ~ lambda^2.5, v23/Lambda ~ lambda^4, v'23/Lambda ~ lambda^4.5) with O(1) coefficients assumed, so the lambda-counting textures of Eq. (19) reproduce the input pattern. This is a legitimate illustrative exercise, and Sec. III does hedge ('our goal here is to illustrate the qualitative origin'), but the abstract and conclusion repeatedly claim the hierarchy 'arises naturally'. The paper would be strengthened by (a) tempering those statements, and (b) at minimum a chi^2 check that the textures with random O(1) coefficients actually accommodate the measured masses/CKM within O(1) spread, plus a comment on what dynamics could fix the v/Lambda ratios.
  4. [Secs. II-III (missing FCNC discussion)] Generation-non-universal hypercharge gauge bosons generically mediate tree-level flavor-changing neutral currents once fermions are rotated to the mass basis, with Delta F = 2 constraints (K^0-Kbar^0, B_d, B_s mixing) typically forcing M_Z'/g to very high scales unless the flavor structure is aligned. This is a standard and potentially load-bearing constraint on tri-hypercharge-type models (it is analyzed in Refs. [26-28], which the paper cites), yet it is never mentioned here. Given the textures in Eqs. (12)-(19) and the hyperon VEVs of Eq. (18), the author should estimate the off-diagonal Z' couplings and check consistency with meson-mixing bounds; otherwise the viability of the flavor sector remains open.
minor comments (6)
  1. [Sec. V, Eqs. (37)-(38)] Annihilation channels are written as 'nu_1R nu_1R -> f fc' and 'X X -> f fc'; presumably 'f f-bar' is intended.
  2. [Sec. V.A] The h-h' mixing is said to be 'induced by phi', but phi is not defined in the dark sector; presumably the U(1)_D-breaking singlet chi of Eq. (5) is meant. Please clarify the notation.
  3. [Secs. II-III] No scalar potential is written for the hyperons and chi, so the assumed VEV hierarchy (v23 << v12, differing by lambda^2) and the stability of the alignment of VEV directions are not addressed. A brief comment on whether the desired VEV pattern is a natural minimum would help.
  4. [Sec. II] The matching of the three U(1)_Yi gauge couplings to the SM hypercharge coupling after symmetry breaking is not discussed; a one-line statement of the matching condition (and kinetic-mixing assumptions) would be useful.
  5. [Sec. IV.B, Eqs. (35)-(36)] In the scotoseesaw estimate of Eq. (36), the loop formula is quoted only schematically; please state the assumed mass ordering and define M_f, m_R, m_I explicitly in the model's field content.
  6. [Sec. IV.B, Eq. (30)] The claimed large leptonic mixing from Eq. (30) is asserted ('reproduces the observed large leptonic mixing angles') without extracting theta_12, theta_13, theta_23; quoting the implied angles or at least one mixing observable would substantiate this.

Circularity Check

3 steps flagged

Flavor hierarchies and DM viability are arranged by hand or outsourced to author self-citations; the gauge construction itself is not circular.

specific steps
  1. fitted input called prediction [Sec. III.A–C, Eqs. (11)–(19)]
    "For illustration, we take ⟨ϕ12⟩/Λ ≡ v12/Λ ≃ λ, ⟨ϕ23⟩/Λ ≡ v23/Λ ≃ λ1.5, with λ≃0.224 being the Wolfenstein parameter. The resulting fermion mass matrices take the schematic form Mu∼v[[λ7.5,λ5.5,λ2.5],[λ8.5,λ4.5,λ1.5],[λ10,λ6,1]], ... These textures ... qualitatively reproduce the observed fermion mass hierarchies and the CKM structure |Vus|∼λ, |Vcb|∼λ2, |Vub|∼λ3."

    The target hierarchy (powers of λ matching masses and CKM) is inserted by choosing the hyperon VEV/cutoff ratios equal to those same powers of λ. The mass-matrix exponents are then arithmetic consequences of the operator dimensions times the chosen VEV ratios, not an independent output. Model II/III repeat the same move with different λ powers (Eqs. 14, 18). The paper frames this as illustration, but the abstract still presents hierarchical masses as arising from the framework.

  2. fitted input called prediction [Sec. IV.A, Eqs. (24)–(26) and benchmark text]
    "For a numerical illustration, we take m12,13≃v12≃O(105) GeV, m23≃v23≃O(104) GeV, M≃M′≃M33≃O(1014) GeV, while all Yukawa couplings are assumed to be O(1). ... The resulting light neutrino mass matrix is then approximately given by Mν≃[[0.0103473,−0.0123593,−0.0640642],[...],[...,0.399516]] eV."

    Messenger and Majorana scales are dialed (together with O(1) Yukawas) until the seesaw formula yields ~0.01–0.4 eV entries near oscillation data. The numerical matrix is therefore a benchmark fit, not a prediction fixed by the gauge charges alone. The scotoseesaw benchmark in IV.B does the same.

  3. self citation load bearing [Sec. V.A–B (DM viability); abstract and Sec. VI claim]
    "The DM phenomenology of this scenario has been studied in detail in Refs. [29–31]. Assuming the h′ portal dominates ... ⟨σv⟩∼M2ν1R/(4M2ν1R−m2h′)2, up to couplings of order unity. The observed relic abundance Ων1Rh2≃0.12 is reproduced for the typical freeze-out value ⟨σv⟩∼3×10−26 cm3/s. For direct detection ... σSIν1R–N∼10−46 cm2, for a TeV-scale ν1R and a representative mixing angle of order 10−2 [32–34]. ... As shown in Refs. [31, 35, 36], a TeV-scale scalar X can reproduce the observed relic abundance..."

    The abstract and conclusion assert 'viable TeV-scale parameter regions consistent with the observed dark matter relic abundance and current direct detection constraints,' but Sec. V performs no scan or likelihood. Relic and SI estimates are schematic ('up to couplings of order unity,' 'representative mixing 10−2') and the detailed viability is load-bearing on the author's overlapping prior papers [29–31]. Experimental limits [32–34] are cited as consistency checks without showing the benchmark actually lies below them.

full rationale

The paper's core construction—anomaly-free generation-separated U(1)Yi plus U(1)D, residual Z2 after χ VEV, and the allowed higher-dimensional Yukawa operators—is self-contained and not circular. What is circular, in a limited sense, is the quantitative flavor claim: hyperon VEV ratios are freely set to specific powers of the Wolfenstein parameter λ (Eqs. 11, 14, 18) so that the resulting mass-matrix textures automatically carry the observed m1≪m2≪m3 and CKM hierarchy; that is input pattern written as output pattern, though the paper mostly labels it 'illustration' rather than a first-principles prediction. Neutrino numerics similarly dial messenger/Majorana scales and O(1) Yukawas to land near oscillation-scale entries (Eqs. 26, 30). The abstract/conclusion claim of 'viable TeV-scale' DM regions consistent with relic density and direct detection is not derived in this work; Sec. V gives only schematic ⟨σv⟩ and σSI estimates and load-bearing cites the author's own prior papers [29–31] for the actual phenomenology. These are real but partial circularities: the unified gauge story has independent content, so the score is 4 rather than 6+.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 6 invented entities

The load-bearing content is a postulated gauge group and field content plus many free scales and O(1) couplings chosen to illustrate hierarchies, neutrino masses, and DM. Almost nothing is fixed by a uniqueness theorem; success is existence of parameter choices. Invented scalars, messengers, and the dark U(1) are introduced to engineer the three target phenomena.

free parameters (6)
  • Hyperon VEV ratios v12/Λ, v23/Λ, v′12/Λ, v′23/Λ (and Model I/II analogues) = e.g. Model III: λ², λ⁴, λ²·⁵, λ⁴·⁵ with λ≃0.224
    Set by hand to powers of λ (Eqs. (11), (14), (18)) to manufacture hierarchical Yukawa textures.
  • Cutoff Λ and overall hyperon scales = Λ ~ O(10^7) GeV (illustrative)
    Chosen so benchmarks match (Λ~10⁷ GeV giving v12~10⁵ GeV, v23~10⁴ GeV).
  • Dimensionless Yukawas h^u,d,e_ij and neutrino h_i, κ31,32 = O(1)
    Assumed O(1) without fit; control all mass eigenvalues and mixings.
  • Messenger and Majorana masses m12, m13, m23, M, M′, M33 = m12,13~10^5 GeV; m23~10^4 GeV; M~10^14 GeV
    Hand-set to 10⁴–10¹⁴ GeV to obtain sub-eV light neutrinos in examples.
  • Dark-sector portal couplings and scalar mixing angles (h–h′, X–h, μ, μ′, λ′) = mixings/couplings ~ 10^{-2} (representative)
    Order-of-magnitude values (~10⁻² mixing/couplings) used to claim σSI~10⁻⁴⁶ cm² and correct relic.
  • U(1)D charge normalization and χ VEV (dark breaking scale)
    Charges fixed to (1,-1,0) w.l.o.g.; χ~ (1,1,0,0,0,2) VEV sets RHN Majorana masses and Z′/h′ spectrum, left parametric.
axioms (6)
  • ad hoc to paper Gauge group is SU(3)C×SU(2)L×U(1)Y1×U(1)Y2×U(1)Y3×U(1)D with generation-separated hypercharges and SM fermions neutral under U(1)D.
    Postulated in Sec. II Eq. (1); motivated by prior tri-hypercharge literature but not derived.
  • ad hoc to paper SM Higgs carries hypercharge only under U(1)Y3, so only third-generation renormalizable Yukawas are allowed.
    Eq. (4); this assignment is what forces light-family masses into higher-dimensional operators.
  • domain assumption Extended hypercharge breaking and dark breaking are spontaneous via hyperon and χ VEVs, leaving exact residual Z2 from even U(1)D charge of χ.
    Standard SSB logic (Eqs. (3)–(6)); residual discrete stability is a common domain tool.
  • domain assumption Higher-dimensional operators are captured by spurion hyperons with a common cutoff Λ and unsuppressed O(1) coefficients besides VEV/Λ powers.
    Froggatt–Nielsen-style effective-field-theory assumption used throughout Sec. III.
  • standard math Light-neutrino masses follow the type-I-like seesaw formula Mν≃−MD MM⁻¹ MD^T after integrating out heavy neutral fermions; loops estimated by standard scotogenic integrals.
    Secs. IV.A–B; standard seesaw/scotogenic approximations.
  • domain assumption Observed DM relic corresponds to thermal freeze-out ⟨σv⟩~3×10^{-26} cm³/s and current SI bounds are ~10^{-46} cm² scale for TeV WIMPs.
    Sec. V citing Planck and xenon-based experiments; used as external targets for viability claims.
invented entities (6)
  • Hyperons ϕ12, ϕ23, φ12, φ23 (and Model I/II subsets) no independent evidence
    purpose: Break generation-separated hypercharges and supply spurion powers for hierarchical Yukawas.
    New SM-singlet scalars with fractional generation hypercharges; VEVs are free inputs.
  • Dark gauge symmetry U(1)D and residual Z2 no independent evidence
    purpose: Distinguish RH neutrinos, allow controlled Majorana masses, stabilize DM.
    Extra Abelian factor with charges (1,-1,0) on νR; breaking via χ with charge 2.
  • Right-handed neutrinos ν1R, ν2R, ν3R (and optional ν′3R) no independent evidence
    purpose: Neutrino mass generation and possible fermionic DM (ν1R).
    Standard singlets but with generation-dependent dark charges.
  • Vector-like messenger neutrinos ν12, ν13, ν23 no independent evidence
    purpose: Mediate flavor-structured Dirac couplings in the multi-state seesaw of Model III.
    Introduced in Sec. IV with hypercharge assignments that match hyperon transitions.
  • Inert scalars η, ρ (doublet and/or singlet) odd under Z2 no independent evidence
    purpose: Generate loop-level scotoseesaw contribution and/or scalar DM candidate X.
    Sec. IV.B and V.B; standard scotogenic-style fields tied to residual Z2.
  • Dark scalars/gauge bosons χ, h′, Z′ no independent evidence
    purpose: Break U(1)D, supply Majorana masses, mediate DM annihilation and portals.
    Necessary companions of gauged U(1)D; phenomenology largely deferred to citations.

pith-pipeline@v1.2.0-grok45-kimik3 · 17661 in / 5072 out tokens · 97786 ms · 2026-07-31T14:33:56.416361+00:00 · methodology

0 comments
read the original abstract

We study a framework with generation-separated hypercharges and dark charges. After the extended hypercharge symmetry $U(1)_{Y1}\otimes U(1)_{Y2}\otimes U(1)_{Y3}$ is spontaneously broken to the Standard Model $U(1)_Y$, hierarchical masses of charged fermions and small quark mixing can arise from higher-dimensional operators involving hyperon fields. Several realizations with different hyperon sectors are presented to illustrate possible flavor structures. Focusing on the realization with four hyperons, we examine neutrino mass generation through either a seesaw or a scotoseesaw mechanism, which can accommodate tiny neutrino masses and large neutrino mixing. The breaking of the dark gauge symmetry $U(1)_D$ leaves a residual $\mathbb{Z}_2$ symmetry that stabilizes dark matter, allowing either fermionic or scalar candidates with viable TeV-scale parameter regions consistent with the observed dark matter relic abundance and current direct detection constraints.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

31 extracted references · 18 linked inside Pith

  1. [2]

    Kajita,Nobel Lecture: Discovery of atmospheric neutrino oscillations,Rev

    T. Kajita,Nobel Lecture: Discovery of atmospheric neutrino oscillations,Rev. Mod. Phys.88(2016) 030501

    2016

  2. [3]

    A. B. McDonald,Nobel Lecture: The Sudbury Neutrino Observatory: Observation of flavor change for solar neutrinos,Rev. Mod. Phys.88(2016) 030502. [4]Planckcollaboration,Planck 2018 results. VI. Cosmological parameters,Astron. Astrophys.641 (2020) A6 [1807.06209]

    Pith/arXiv arXiv 2016

  3. [5]

    C. D. Froggatt and H. B. Nielsen,Hierarchy of Quark Masses, Cabibbo Angles and CP Violation, Nucl. Phys. B147(1979) 277

    1979

  4. [6]

    Altarelli and F

    G. Altarelli and F. Feruglio,Discrete Flavor Symmetries and Models of Neutrino Mixing,Rev. Mod. Phys.82(2010) 2701 [1002.0211]

    Pith/arXiv arXiv 2010

  5. [7]

    Ishimori, T

    H. Ishimori, T. Kobayashi, H. Ohki, Y. Shimizu, H. Okada and M. Tanimoto,Non-Abelian Discrete Symmetries in Particle Physics,Prog. Theor. Phys. Suppl.183(2010) 1 [1003.3552]

    Pith/arXiv arXiv 2010

  6. [8]

    S. F. King and C. Luhn,Neutrino Mass and Mixing with Discrete Symmetry,Rept. Prog. Phys.76 (2013) 056201 [1301.1340]

    Pith/arXiv arXiv 2013

  7. [9]

    Langacker,The Physics of HeavyZ ′ Gauge Bosons,Rev

    P. Langacker,The Physics of HeavyZ ′ Gauge Bosons,Rev. Mod. Phys.81(2009) 1199 [0801.1345]

    Pith/arXiv arXiv 2009

  8. [10]

    X.-G. He, G. C. Joshi, H. Lew and R. R. Volkas,Simplest Z-prime model,Phys. Rev. D44(1991) 2118. 15

    1991

  9. [11]

    K. S. Babu, C. F. Kolda and J. March-Russell,Leptophobic U(1)sand the R(b) - R(c) crisis,Phys. Rev. D54(1996) 4635 [hep-ph/9603212]

    Pith/arXiv arXiv 1996

  10. [12]

    Appelquist, B

    T. Appelquist, B. A. Dobrescu and A. R. Hopper,Nonexotic Neutral Gauge Bosons,Phys. Rev. D68 (2003) 035012 [hep-ph/0212073]

    Pith/arXiv arXiv 2003

  11. [13]

    Grinstein, M

    B. Grinstein, M. Redi and G. Villadoro,Low Scale Flavor Gauge Symmetries,JHEP11(2010) 067 [1009.2049]

    Pith/arXiv arXiv 2010

  12. [14]

    Minkowski,µ→eγat a Rate of One Out of10 9 Muon Decays?,Phys

    P. Minkowski,µ→eγat a Rate of One Out of10 9 Muon Decays?,Phys. Lett. B67(1977) 421

    1977

  13. [15]

    Yanagida,Horizontal gauge symmetry and masses of neutrinos,Conf

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

    1979

  14. [16]

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

    1980

  15. [17]

    Schechter and J

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

    1980

  16. [18]

    Magg and C

    M. Magg and C. Wetterich,Neutrino Mass Problem and Gauge Hierarchy,Phys. Lett. B94(1980) 61

    1980

  17. [19]

    Lazarides, Q

    G. Lazarides, Q. Shafi and C. Wetterich,Proton Lifetime and Fermion Masses in an SO(10) Model, Nucl. Phys. B181(1981) 287

    1981

  18. [20]

    R. Foot, H. Lew, X. G. He and G. C. Joshi,Seesaw Neutrino Masses Induced by a Triplet of Leptons, Z. Phys. C44(1989) 441

    1989

  19. [21]

    Ma,Verifiable radiative seesaw mechanism of neutrino mass and dark matter,Phys

    E. Ma,Verifiable radiative seesaw mechanism of neutrino mass and dark matter,Phys. Rev. D73 (2006) 077301 [hep-ph/0601225]

    Pith/arXiv arXiv 2006

  20. [22]

    Bertone, D

    G. Bertone, D. Hooper and J. Silk,Particle dark matter: Evidence, candidates and constraints,Phys. Rept.405(2005) 279 [hep-ph/0404175]

    Pith/arXiv arXiv 2005

  21. [23]

    J. L. Feng,Dark Matter Candidates from Particle Physics and Methods of Detection,Ann. Rev. Astron. Astrophys.48(2010) 495 [1003.0904]

    Pith/arXiv arXiv 2010

  22. [24]

    Arcadi, M

    G. Arcadi, M. Dutra, P. Ghosh, M. Lindner, Y. Mambrini, M. Pierre et al.,The waning of the WIMP? A review of models, searches, and constraints,Eur. Phys. J. C78(2018) 203 [1703.07364]

    Pith/arXiv arXiv 2018

  23. [25]

    Hambye,Hidden vector dark matter,JHEP01(2009) 028 [0811.0172]

    T. Hambye,Hidden vector dark matter,JHEP01(2009) 028 [0811.0172]

    Pith/arXiv arXiv 2009

  24. [26]

    Davighi and B

    J. Davighi and B. A. Stefanek,Deconstructed hypercharge: a natural model of flavour,JHEP11 (2023) 100 [2305.16280]

    Pith/arXiv arXiv 2023

  25. [27]

    Fern´ andez Navarro and S

    M. Fern´ andez Navarro and S. F. King,Tri-hypercharge: a separate gauged weak hypercharge for each fermion family as the origin of flavour,JHEP08(2023) 020 [2305.07690]

    arXiv 2023

  26. [28]

    Fern´ andez Navarro, S

    M. Fern´ andez Navarro, S. F. King and A. Vicente,Minimal complete tri-hypercharge theories of flavour,JHEP07(2024) 147 [2404.12442]

    arXiv 2024

  27. [29]

    Van Loi, A

    D. Van Loi, A. E. C´ arcamo Hern´ andez, V. Q. Tran and N. T. Duy,Tri-hypercharge versus tri-darkcharge,Eur. Phys. J. C85(2025) 1160 [2506.12873]

    arXiv 2025

  28. [30]

    Van Dong and D

    P. Van Dong and D. Van Loi,Scotoseesaw model implied by dark right-handed neutrinos,Phys. Rev. D110(2024) 115022 [2311.09795]. 16

    Pith/arXiv arXiv 2024

  29. [31]

    Van Dong, D

    P. Van Dong, D. Van Loi, D. T. Huong, N. T. Duy and D. Van Soa,Dark symmetry implication for right-handed neutrinos,Phys. Rev. D111(2025) 035014 [2407.02324]. [32]XENONcollaboration,First Dark Matter Search with Nuclear Recoils from the XENONnT Experiment,Phys. Rev. Lett.131(2023) 041003 [2303.14729]. [33]PandaXcollaboration,Dark Matter Search Results fro...

    Pith/arXiv arXiv 2025

  30. [35]

    de Boer, R

    T. de Boer, R. Busse, A. Kappes, M. Klasen and S. Zeinstra,Indirect detection constraints on the scotogenic dark matter model,JCAP08(2021) 038 [2105.04899]

    Pith/arXiv arXiv 2021

  31. [36]

    Van Loi, A

    D. Van Loi, A. E. C´ arcamo Hern´ andez, N. T. Duy, D. T. Binh and C. H. Nam,Physical implications of a double right-handed gauge symmetry,2601.06457

    Pith/arXiv arXiv