Pathways to Naturally Small Neutrino Masses

Ernest Ma (UC Riverside)

REVIEW

Pathways to Naturally Small Neutrino Masses

Ernest Ma (UC Riverside)

High Energy Physics - Phenomenology · Submitted 4 May 1998 · 15 references

Pith's verdict: The taxonomy paper: the 'only three' tree-level claim is right and became the standard type-I/II/III language, though the exhaustiveness step is asserted rather than shown.

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arXiv IDhep-ph/9805219 (version 4)

Pith IDSQMULMW4, Pith's permanent record of this paper and its review

CitationErnest Ma (UC Riverside). "Pathways to Naturally Small Neutrino Masses." arXiv:hep-ph/9805219 (1998). https://pith.science/paper/SQMULMW4

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Editor's note

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This is the paper that gave the field its type-I/II/III vocabulary, and it holds up. The claim in [abstract:s0] — that Λ⁻¹φ⁰φ⁰νᵢνⱼ has exactly three tree-level realizations — is correct, and Eqs. (4)–(6) really are the same operator written three ways. The remark that the antisymmetric νᵢlⱼ − lᵢνⱼ singlet doesn't generate it is the kind of small check that shows the author actually worked through the list rather than gesturing at it. The one-loop section is the more useful half for me: Fig. 3 subsumes the Zee model and the R-parity-violating supersymmetric case as special choices of hypercharge and color, and Figs. 4 and 5 are the topologies people had been using piecemeal without naming. The paper is honest about provenance — refs. [2] and [3] are credited for the triplet mechanisms, and it says outright that Fig. 4 has rarely been used and Fig. 5 was known mainly for quark and lepton masses. That is the right way to write a synthesis Letter. On the stress-test note: its group-theoretic argument is the correct proof, and it lands. Partition L,L,H,H into pairs; (LL)(HH) forces the scalar triplet, (LH)(LH) gives the singlet and triplet fermion. Nothing else couples renormalizably. So the reader's weakest_assumption is a presentational gap, not a hole — 'it is clear that there are only three ways' is doing real work with no display behind it, and a referee would reasonably ask for the two-line partition argument. Two smaller things. The supersymmetric SU(5) example needs a discrete Z₂ and a second, vev-less 24 to stop ψᵢ coupling to N and Σ; the paper says so plainly, but it means the 'example' is a demonstration that the mechanism can be embedded, not a prediction of the framework. And the abstract's 'three generic one-loop realizations' is a topology count, not a completeness theorem — the text itself lists variations of Figs. 4 and 5, so don't read it as parallel to the tree-level 'only three'. Neither point changes the verdict. This is a short Letter that reorganized how a subfield thinks, and it deserves referee time on the strength of the classification alone. Send it out; ask for the partition argument and nothing more.

Referee report

Significance

The paper is short but its organizing value is high: it converts a scattered model literature into a classification and makes the substantive point that the scalar-triplet and fermion-triplet completions are conceptually as simple as the seesaw. Strengths worth naming explicitly: the three operator forms in Eqs. (4)–(6) are shown to be identical, and I verified by direct expansion that they agree term by term; the mass formulas are internally consistent; the SU(5) representation assignments are correct (the 15 contains a (1,3,1) and the 24 contains (1,1,0) and (1,3,0)); the numerical estimates reproduce v²/M ≈ 10⁻³ eV at 10¹⁶ GeV and 0.1 eV at 10¹⁴ GeV; and the one-loop discussion anticipates later systematic topology classifications. The closing guidance that new particles in the one-loop realizations may lie near 100 GeV is a falsifiable statement, which is a genuine virtue of the paper.

Major objections (1)

[Tree-level classification, text immediately preceding Eq. (4)] The exhaustiveness of the tree-level list is the paper's headline claim (abstract:s0), but the text supports it only with the sentence 'it is clear that there are only three ways' before listing (I)–(III). The three operator forms in Eqs. (4)–(6) demonstrate that each listed case works; they do not demonstrate that no fourth case exists. A short argument would close the gap and should be added: with one heavy mediator and renormalizable cubic vertices, the four external legs L, L, H, H must be partitioned into two pairs at the two vertices; the only partitions are (LL)(HH), which forces a scalar triplet because the symmetric LL and HH products are both triplets, and (LH)(LH), which forces a mediator in L⊗H = 1⊕3, i.e. the fermion singlet and the fermion triplet. The paper's own remark that the antisymmetric singlet combination νᵢlⱼ − lᵢνⱼ does not generate Eq. (3) is precisely the step that excludes the remaining candidate, and it deserves to be presented as part of the argument rather than as an aside. The assumptions (single mediator, renormalizable interactions, no additional light fields, and that chains of mediators reduce to these cases) should be stated explicitly, since the claim is otherwise open to the reading that multi-mediator or higher-multiplet completions were overlooked.

Minor objections (8)

[Text following Eq. (12)] The choice q₁ = 1 in the sentence 'if we choose q₃ = 1, q₁ = 1, and q₂ = q′₂ = 1, then ω ∼ (1,2,−1/2) ∼ l_L' is inconsistent with the hypercharge −1/2 that the same sentence assigns to ω; the intended value is q₁ = −1/2, as the quark example q₁ = 1/6 two sentences later confirms. This should be corrected.
[Eq. (7)] The factor of 2 in (Mν)ᵢⱼ = −2fᵢⱼμv²/M² depends on whether the Lagrangian coupling is written as fᵢⱼνᵢνⱼξ⁰ or as (1/2)fᵢⱼνᵢνⱼξ⁰. The later statement that the mass matrix equals 2fᵢⱼu fixes the convention implicitly, but it would help to state it at Eq. (7).
[Discussion of the three tree-level realizations, paragraph before the acknowledgements] The statement that the three tree-level realizations would produce 'no other observable effect except for nonzero neutrino masses and mixing' is stronger than the analysis supports: the three differ at dimension six, and the scalar triplet's Yukawa couplings fᵢⱼ can mediate lepton-flavor-violating processes such as μ → eee through the doubly charged component. The intended point, that the three are indistinguishable at leading order in v/Λ, would be clearer if stated that way.
[Supersymmetric SU(5) example, paragraph on the atmospheric mass] The atmospheric-neutrino example, an additional Z₂-odd 24 of mass 10¹⁴ GeV, needs a caveat: the (3,2,−5/6) and (3*,2,5/6) components of that 24 couple to quark-lepton pairs with gauge strength, so proton decay is enhanced by (10¹⁶/10¹⁴)² relative to the standard GUT estimate. Either the example should be checked against proton-decay limits or the mass should be raised and the atmospheric mass obtained another way.
[One-loop section, abstract and concluding paragraph] The abstract's phrase 'the three generic one-loop realizations' and the concluding 'There are also three one-loop realizations (plus variations)' read as a completeness claim, but the section constructs three examples and does not argue that no other one-loop topology exists. Either a sentence of justification should be added or the wording should be softened to 'three representative realizations'.
[Concluding paragraph] 'The detailed structures of this and the other two diagrams are systematically described here for the first time' is a priority claim that a reader cannot readily verify; it would be safer to say what is new relative to Refs. [9], [10], [11], and [14] rather than to assert firstness.
[Figs. 2–5] The couplings (fᵢⱼ, μ, and the Yukawa and quartic couplings of Eq. (15)) are not shown on the diagrams, and the hypercharges of the internal lines are not labelled. Adding them would let a reader check the gauge invariance of each diagram without reconstructing it from the text.
[Eq. (3)] The operator is written without the 1/2 that accompanies identical Majorana fields and without an explicit SU(2) contraction. Since the normalization matters for comparing with Eqs. (4)–(6) and with Eq. (7), it would be worth fixing once.

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The paper

The paper claims

The paper argues that every extension of the standard model which gives neutrinos mass at tree level reduces, at low energy, to one dimension-five operator, and that this operator can be completed in exactly three ways.

The reading

Neutrinos have mass, and in the minimal standard electroweak model the only renormalizable way to write that mass down is a single dimension-five operator, $Lambda^{-1}varphi^0varphi^0 u_i u_j$, suppressed by a large scale $Lambda$. Ernest Ma's claim is that this one operator is a complete organizing principle: every extension of the standard model that keeps the same light particles and generates neutrino mass at tree level must reduce to it, and there are exactly three ways to complete it with a heavy field. The payoff is a short list in place of a large catalogue: a heavy singlet fermion (the familiar seesaw), a heavy scalar triplet that acquires a naturally tiny vacuum expectation value, and a heavy Majorana fermion triplet. Choosing among the three is not a matter of taste but a statement about what lies beyond the standard model, and the paper argues that the second and third are conceptually just as simple as the first, which has dominated the literature. The same operator, taken at one loop, also absorbs almost every previously proposed radiative neutrino-mass model into three generic diagrams.

What carries the argument

The machinery is the dimension-five operator itself, used as a classification device rather than a model. Because it is the unique gauge-invariant operator of its dimension built from the standard model's light fields, any heavy physics that gives neutrinos Majorana mass must reproduce it at low energy, and the possible completions are sorted by which external legs the heavy mediator touches: $psiPhi$ (fermion singlet), $psi psi$ (scalar triplet), and $psiPhi$ again (fermion triplet). The triplet scalar case works through a small induced vacuum expectation value, $u = -mu v^2/M^2$, which reproduces the direct coupling $2 f_{ij} u$ to neutrinos, so no right-handed neutrino is needed. At one loop the same logic sorts diagrams by topology: Fig. 3 (two fermions and two scalars in the loop, the structure behind the Zee and R-parity-violating models), Fig. 4 (an invariant fermion mass in the loop, requiring exotic scalar charges such as $3/2$), and Fig. 5 (four fermion multiplets and one complex scalar).

Extended reading notes

Core claim

The central claim is that the effective operator $Lambda^{-1}varphi^0varphi^0 u_i u_j$ has only three tree-level realizations, obtained by asking which pair of external legs a single heavy field can attach to: a heavy fermion singlet $N$ coupling to $psi_i$ and $Phi$, a heavy scalar triplet $xi$ coupling to $psi_i psi_j$ and to $Phi Phi$, or a heavy Majorana fermion triplet $Sigma$ coupling to $psi_i$ and $Phi$. The paper backs each with the complete gauge-invariant form of the operator, Eqs. (4) to (6), and notes that the singlet combination of two lepton doublets, $ u_i l_j - l_i u_j$, does not generate the operator, which is why the scalar-triplet route needs $psi_i psi_j$ instead. The three are indistinguishable at low energy, so the choice is a statement about physics beyond the standard model: three right-handed neutrinos argue for SO(10), while the triplet routes fit inside SU(5) alone, since the 15 contains $xi$ and the 24 contains both $N$ and $Sigma$. As a worked example, a supersymmetric SU(5) model with an extra 24-plet that has no vacuum expectation value, made odd under a discrete $Z_2$ symmetry, gives one neutrino a seesaw mass of order $10^{-3}$ eV for $M sim 10^{16}$ GeV, in the range suggested by solar data; a second such multiplet at $10^{14}$ GeV would give about $0.1$ eV for atmospheric oscillations. The paper then classifies the one-loop realizations into three generic diagrams (Figs. 3 to 5), of which the first contains most existing radiative models as special cases.

Load-bearing premise

The exhaustiveness claim rests on the assertion that it is clear there are only three ways, an inspection of which pairs of external legs a single heavy field with renormalizable couplings can attach to, rather than on a systematic group-theoretic enumeration of all possible completions.

Editorial extensions

If this is right

If the classification holds, any tree-level model of Majorana neutrino mass is one of three completions, so building a model means choosing among them rather than inventing a new mechanism.
The singlet route needs three right-handed neutrinos and points toward SO(10), while the scalar-triplet and fermion-triplet routes fit inside SU(5) alone, since the 15 contains the triplet scalar and the 24 contains both the singlet and triplet fermions.
A heavy Higgs triplet with a tiny vacuum expectation value is not fine-tuned but follows from the operator, so it deserves the attention the singlet seesaw has received.
In supersymmetric SU(5), one extra 24-plet with no vacuum expectation value and odd under a discrete $Z_2$ gives a neutrino mass near $10^{-3}$ eV, and a second at $10^{14}$ GeV gives near $0.1$ eV, covering solar and atmospheric scales.
In the loop realizations, any new fermion doublet without an invariant mass must take its mass from the Higgs vacuum expectation value, so it should lie near 100 GeV and be reachable in the near future.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the classification turns only on the external-leg quantum numbers, the same three-way split should apply to dimension-five operators built from two Higgs doublets and two fermion doublets, so extended scalar sectors would inherit the same short list.
Since all three tree-level completions are identical at low energy, neutrino mass and mixing measurements alone can never select among them; only discovery or exclusion of the mediating particles can.
The discrete $Z_2$ symmetry in the SU(5) example is doing the work of suppressing the coupling of the standard $5^*$ to the singlet and triplet fermions, which invites the question of whether a continuous symmetry or a different multiplet assignment would give the same suppression with fewer new fields.
The one-loop realizations generically demand exotic charges, such as a scalar with charge $3/2$, which suggests searching for multiply charged scalars rather than for heavy neutral ones as the near-term test of these models.

Original abstract

In the minimal standard electroweak gauge model, there is an effective dimension-five operator which generates neutrino masses, and it has only three tree-level realizations. One is the canonical seesaw mechanism with a right-handed neutrino. Another is having a heavy Higgs triplet as recently proposed. The third is to have a heavy Majorana fermion triplet, an example of which is presented here in the context of supersymmetric SU(5) grand unification. The three generic one-loop realizations of this operator are also discussed.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,153 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.37 · compares with prior results 0.49 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

In the minimal standard electroweak gauge model, there is an effective dimension-five operator which generates neutrino masses, and it has only three tree-level realizations. One is the canonical seesaw mechanism with a right-handed neutrino. Another is having a heavy Higgs triplet as recently proposed. The third is to have a heavy Majorana fermion triplet, an example of which is presented here in the context of supersymmetric SU(5) grand unification. The three generic one-loop realizations of this operator are also discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In the minimal standard electroweak gauge model, there is an effective dimension-five operator which generates neutrino masses, and it has only three tree-level realizations.	background 0.92	0.12	0.16	asserted 1.00
s1	One is the canonical seesaw mechanism with a right-handed neutrino.	background 0.92	0.06	0.06	asserted 1.00
s2	Another is having a heavy Higgs triplet as recently proposed.	background 0.94	0.06	0.05	asserted 0.98
s3	The third is to have a heavy Majorana fermion triplet, an example of which is presented here in the context of supersymmetric SU(5) grand unification.	contribution 0.94	0.78	0.25	asserted 0.99
s4	The three generic one-loop realizations of this operator are also discussed.	contribution 0.95	0.61	0.06	asserted 0.90

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from argument 0.57.

What was examined, and what was not

sources read

arXiv listing abstract v4

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Call it N and let its mass be M and its coupling to νi be fi , then Λ−1 = fifj/2M. As φ 0 acquires a nonzero vev [vacuum expectation value hφ 0 i = v], we can identify fiv as a Dirac mass mi linking νi to N and the neutrino mass matrix is simply −mimj/M. This is of course just the well-known seesaw mechanism, with N identified as the right-handed neutrino with a large Majorana mass. Note that with one such singlet, only one linear combination of νi gets a tree-level mass. Hence the usual scenario requires three N’s. This mechanism of generating naturally small neutrino masses…

**Figure 2.** Tree-level realization of the effective operator (3) with heavy scalar triplet. νi χ ω φ 0 ω c νj η φ 0

**Figure 3.** First one-loop realization of the effective operator (3). 11

**Figure 4.** Second one-loop realization of the effective operator (3). νi ω σ c σ ω c νj φ 0 φ 0 ζ

**Figure 5.** Third one-loop realization of the effective operator (3). 12

Figures reproduced from arXiv:hep-ph/9805219 by the authors.

References

Works cited (15)

[2]

E. Ma and U. Sarkar, Univ. of Calif., Riverside Report No. UCRHEP-T209, hep- ph/9802445 (Phys. Rev. Lett., in press)

View on Pith
[3]

This mechanism was proposed by R. Foot, H. Lew, X.-G. He, a nd G. C. Joshi, Z. Phys. C44, 441 (1989), using a triplet of leptons with masses relevant to present phenomenol- ogy

View on Pith 1989
[1]

M. Gell-Mann, P. Ramond, and R. Slansky, in Supergravity (ed. P. van Nieuwenhuizen and D. Z. Freedman, North-Holland, Amsterdam, 1979), p. 315 ; T. Yanagida, in Pro- ceedings of the Workshop on the Uniﬁed Theory and the Baryon N umber in the Universe (ed. O. Sawada and A. Sugamoto, KEK Report No. 79-18, Tsukuba , Japan, 1979)

View on Pith 1979
[4]

S. Dimopoulos and H. Georgi, Nucl. Phys. B193, 150 (1981); N. Sakai, Z. Phys. C11, 153 (1981). 9

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[5]

R. Davis, Prog. Part. Nucl. Phys. 32, 13 (1994); Y. Fukuda et al. , Phys. Rev. Lett. 77, 1683 (1996); P. Anselmann et al. , Phys. Lett. B357, 237 (1995); B361, 235 (1996); J. N. Abdurashitov et al. , Phys. Lett. B328, 324 (1994)

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[6]

For a review, see for example H. E. Haber and G. Kane, Phys. Rep. 117, 75 (1985)

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[7]

Y. Fukuda et al. , Phys. Lett. B335, 237 (1994); hep-ex/9803006

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[8]

C. Athanassopolous et al. , Phys. Rev. Lett. 75, 2650 (1995); 77, 3082 (1996); hep- ex/9709006

View on Pith 1995
[9]

For a brief review of radiative quark and lepton masses, s ee K. S. Babu and E. Ma, Mod. Phys. Lett. A4, 1975 (1989)

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[10]

A. Zee, Phys. Lett. 93B, 389 (1980)

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[11]

L. Hall and M. Suzuki, Nucl. Phys. B231, 419 (1984)

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[12]

T. P. Cheng and L.-F. Li, Phys. Rev. D22, 2860 (1980)

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K. Kang, J. Kim, J. E. Kim, K. S. Soh, and H. S. Song, Phys. R ev. D22, 2869 (1980)

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[14]

G. C. Branco, W. Grimus, and L. Lavoura, Nucl. Phys. B312, 492 (1989)

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[15]

K. S. Babu and E. Ma, Phys. Rev. Lett. 61, 674 (1988); Phys. Lett. B228, 508 (1989). See also S. T. Petcov and S. T. Toshev, Phys. Lett. B143, 175 (1984). 10 νi φ0 N νj φ0 Fig. 1. Tree-level realization of the eﬀective operator (3) with he avy fermion singlet. νi νj ξ0 φ0 φ0 Fig. 2. Tree-level realization of the eﬀective operator (3) with he avy scalar tr...

View on Pith 1988

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Search for heavy Majorana neutrinos in same-sign dilepton channels in proton-proton collisions at $\sqrt{s} =$ 13 TeV
hep-ex 2018-06 accept novelty 5.0 of 10

No same-sign dilepton excess is observed in 35.9 fb^-1 of 13 TeV CMS data, yielding 95% CL upper limits on heavy Majorana neutrino mixing |VeN|^2 and |VmuN|^2 for masses from 20 to 1600 GeV.
Flavour Dependent Gauged Radiative Neutrino Mass Model
hep-ph 2015-01 conditional novelty 5.0 of 10

A gauged muon-minus-tau symmetry forces a two-zero texture in the neutrino mass matrix, allowing only inverted hierarchy and predicting CP phases, while a light Z' boson can account for the muon g-2 anomaly.
Systematic classification of two-loop realizations of the Weinberg operator
hep-ph 2014-11 conditional novelty 5.0 of 10

A complete diagrammatic classification shows that all genuine two-loop neutrino mass models are variations of three basic diagrams, and all finite non-genuine ones reduce to five basic types.
Looking for the minimal inverse seesaw realisation
hep-ph 2014-01 conditional novelty 5.0 of 10

The minimal inverse seesaw that fits three-flavour neutrino data needs two right-handed neutrinos and two sterile singlets, while a 3+1 scheme needs two right-handed neutrinos and three sterile singlets.
LHC bounds on Lepton Number Violation mediated by doubly and singly-charged scalars
hep-ph 2013-11 conditional novelty 5.0 of 10

Existing ATLAS and CMS doubly-charged scalar searches already constrain lepton-number-violating decays into same-sign dileptons plus W or Z bosons, with bounds that depend on which electroweak multiplet the scalar belongs to.
Dirac neutrinos from flavor symmetry
hep-ph 2013-07 conditional novelty 5.0 of 10

A Delta(27) flavor-symmetry model forbids Majorana neutrino masses, making neutrinos Dirac, and fits oscillation data with a correlation between the atmospheric octant and the lightest neutrino mass.
125 GeV Higgs Boson and the Type-II Seesaw Model
hep-ph 2013-01 conditional novelty 5.0 of 10

In the type-II seesaw model, a 125 GeV Higgs can coexist with a stable vacuum up to the Planck scale for a wide range of triplet couplings, and any diphoton enhancement implies an upper bound on the seesaw scale.
The mu - e Conversion in Nuclei, mu --> e gamma, mu --> 3e Decays and TeV Scale See-Saw Scenarios of Neutrino Mass Generation
hep-ph 2012-05 conditional novelty 5.0 of 10

In three TeV-scale see-saw models, the rates of mu to e gamma, mu to 3e, and mu-to-e conversion are computed as functions of neutrino oscillation parameters, with the ratios of rates shown to depend mainly on the new-...
Les Houches 2011: Physics at TeV Colliders New Physics Working Group Report
hep-ph 2012-03 conditional novelty 5.0 of 10

The report proposes a Dark Matter Les Houches Agreement file format, extends the Flavour and SUSY accords to dipole moments and see-saw models, and reports new tool modules for automated RGE derivation and model validation.
Multi-Lepton Collider Signatures of Heavy Dirac and Majorana Neutrinos
hep-ph 2011-12 conditional novelty 5.0 of 10

In a left-right symmetric model, same-sign di-lepton events at the LHC signal a Majorana heavy neutrino and tri-lepton events signal a Dirac one, allowing the two seesaw types to be distinguished.
Neutrinoless double beta decay in seesaw models
hep-ph 2010-05 accept novelty 5.0 of 10

Mass-dependent nuclear matrix elements for six double-beta emitters show that light sterile neutrinos can cancel the standard light-neutrino contribution, suppressing the decay rate by six or more orders of magnitude ...
Testability of Type I Seesaw at the CERN LHC: Revealing the Existence of the B-L Symmetry
hep-ph 2009-07 conditional novelty 5.0 of 10

Heavy Majorana neutrinos produced via a B-L Z' at the LHC yield same-sign dilepton plus four-jet signals whose lepton-flavor mix can, for simple choices of the unknown seesaw matrix, track the light neutrino mass hierarchy.
Neutrino Masses and the LHC: Testing Type II Seesaw
hep-ph 2008-05 accept novelty 5.0 of 10

The decay branching fractions of a doubly and singly charged Higgs triplet at the LHC are fixed by the light neutrino mass matrix, so measuring them can distinguish normal, inverted, and quasi-degenerate neutrino mass...
$\mu \to e \gamma$ and $\tau \to l \gamma$ decays in the fermion triplet seesaw model
hep-ph 2008-03 conditional novelty 5.0 of 10

In the type-III seesaw, the ratio of radiative to three-body lepton-flavor-violating decays is fixed near 10^-3, so a positive mu-to-e-gamma or tau-to-l-gamma signal would contradict existing mu-to-eee and tau-to-3l b...
Seesaw at LHC
hep-ph 2006-12 conditional novelty 5.0 of 10

A fermionic adjoint in non-supersymmetric SU(5) delivers type I plus type III seesaw, and unification plus proton decay push the weak triplet down to the electroweak scale where the LHC can reach it.
General parametrization of Majorana neutrino mass models
hep-ph 2019-12 accept novelty 4.5 of 10

A constructive proof and case-by-case catalogue showing that the Yukawa couplings of any Majorana neutrino mass model can be parametrized in terms of measured neutrino data plus free model parameters.
FIMP dark matter in the scotogenic model at low-reheating temperatures
hep-ph 2026-09 conditional novelty 4.0 of 10

Low reheating temperatures enlarge the freeze-in couplings of scotogenic fermion dark matter to order 0.1, bringing the region mN = 60-700 GeV, T_rh = 5-50 GeV within reach of current and next-generation direct detection.
New constraints on non-unitary neutrino mixing from 8 years of IceCube DeepCore atmospheric neutrino data
hep-ph 2026-07 unverdicted novelty 4.0 of 10

IceCube DeepCore data constrains non-unitary neutrino mixing with α33 > -0.027 at 90% CL and no evidence for deviation from unitarity.
Neutrino Mass Induced $n$-$\overline{n}$ Oscillation
hep-ph 2025-10 conditional novelty 4.0 of 10

In the Georgi-Glashow SU(5) theory, generating a Majorana neutrino mass necessarily produces neutron–antineutron oscillation from the same operator.
Searches for Long-Lived Particles at the Future FCC-ee
hep-ex 2022-03 conditional novelty 4.0 of 10

Preliminary FCC-ee simulations suggest a Tera-Z run could yield roughly one detectable displaced heavy-neutral-lepton decay at 50 GeV and mixing 6e-6, and that Dirac versus Majorana nature may be separable through lep...
Cosmological searches for the neutrino mass scale and mass ordering
astro-ph.CO 2019-07 unverdicted novelty 4.0 of 10

Thesis summarizing an upper limit of 0.12 eV on the neutrino mass sum, bias calibration via CMB lensing cross-correlations, and tighter limits plus stronger normal-ordering preference in non-phantom dynamical dark ene...
Probing right handed neutrinos at the LHeC and lepton colliders using fat jet signatures
hep-ph 2018-11 conditional novelty 4.0 of 10

Boosted fat-jet searches at a 1.3 to 1.8 TeV LHeC and at 1 and 3 TeV lepton colliders could probe electron-flavor heavy neutrino mixing down to about 10^-5 for neutrino masses up to roughly 2.9 TeV.
Seesaw roadmap to neutrino mass and dark matter
hep-ph 2018-02 conditional novelty 4.0 of 10

Generalized dimension-5 Weinberg operators with extra scalars open new seesaw contractions, and in the Dirac case the same discrete lepton-number symmetry that protects Diracness can also stabilize a scalar dark matte...
Dark Matter in the minimal Inverse Seesaw mechanism
hep-ph 2014-06 conditional novelty 4.0 of 10

In the (2,3) inverse seesaw a keV sterile neutrino supplies at most 43 percent of dark matter, and a new singlet scalar is required to reach the full abundance at low pseudo-Dirac masses.
Neutrinoless Double-Beta Decay: A Roadmap for Matching Theory to Experiment
hep-ph 2022-03 accept novelty 3.0 of 10

The paper lays out a multi-scale effective-field-theory, lattice-QCD, and ab initio nuclear program for turning a neutrinoless double-beta decay signal into an identified microscopic mechanism.
White Paper on Light Sterile Neutrino Searches and Related Phenomenology
hep-ex 2022-03 accept novelty 3.0 of 10

A comprehensive review of the four short-baseline neutrino anomalies, the beyond-Standard-Model interpretations proposed for them, and the experimental portfolio needed to resolve them.
The minimal seesaw and leptogenesis models
hep-ph 2020-08 accept novelty 3.0 of 10

A comprehensive review of the two-right-handed-neutrino seesaw and its leptogenesis, organizing parametrizations, texture zeros, flavor symmetries and CP-violation predictions against current neutrino oscillation data.
Phenomenological Study of Type II Seesaw with $\Delta(27)$ Symmetry
hep-ph 2019-09 reject novelty 3.0 of 10

A Δ(27) flavor-symmetric type-II seesaw model reproduces neutrino oscillation data only after an ad hoc diagonal perturbation is added, and its CP violation predictions reduce to parameter scans.
Neutrino Non-Standard Interactions: A Status Report
hep-ph 2019-07 accept novelty 3.0 of 10

The report compiles the 2019 status of neutrino non-standard interactions across model building, oscillation and scattering constraints, and future experimental sensitivity, without presenting a new result of its own.
Charged Lepton Flavour Violation: An Experimental and Theoretical Introduction
hep-ph 2017-08 accept novelty 3.0 of 10

No charged lepton flavour violation has been observed, but current muon limits already constrain new physics and planned experiments will improve sensitivity by orders of magnitude.
From the trees to the forest: a review of radiative neutrino mass models
hep-ph 2017-06 accept novelty 3.0 of 10

Radiative neutrino mass models are catalogued and ordered along three axes (effective operator, loop order, diagram topology), with the phenomenology of the best-studied examples summarized.
Neutrinos and Collider Physics
hep-ph 2015-02 conditional novelty 3.0 of 10

The paper reviews collider and low-energy probes of TeV-scale seesaw models, compiling current limits on heavy sterile neutrino mixing and projecting future LHC, beam-dump, and lepton-collider sensitivities.

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How the literature uses it

233 arXiv papers cite this in 273 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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This is the group-theoretical reason that the three types of seesaws reduce to the unique dimension-five Weinberg operator $$ in SM [ref] and that its higher-dimensional generalizations are also unique at each dimension [ref] .

Neutrino Mass Operators of Dimension up to Nine in Two-Higgs-doublet Model · Mass operators up to dimension nine · 0.97
A simple analysis based on gauge invariance shows that the tree level diagrams in seesaws, corresponding to the three seesaw Lagrangians above, are the only possible ones [ref] .

Lepton Flavour Symmetries · Tree-level origin of the Weinberg operator · 0.98

Cites it as background 155 papers

The origin of the neutrino mass is associated with the seesaw mechanism [ref] which in turn solely depends on the Majorana nature of the neutrinos.

Leptons and other forces of Nature · Introduction · 0.87
If neutrinos are Majorana particles, their mass at low energy is described by a unique dimension-5 operator [ref] [equation] Using only renormalizable interactions, there are only three tree-level realizations of this operator [ref] .

Supersymmetric seesaw type II: CERN LHC and lepton flavour violating phenomenology · Introduction · 0.89
The seesaw can be implemented at tree-level in exactly three realizations [ref] : exchange of a fermionic singlet, a.k.a. the right-handed neutrino (type-I) [ref] ; of a scalar triplet (type-II) [ref] ; or of a fermionic triplet (type-III) [ref] .

LHC and lepton flavour violation phenomenology of a left-right extension of the MSSM · Introduction · 0.86

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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