REVIEW
A Model for Neutrino Masses and Dark Matter
High Energy Physics - Phenomenology · Submitted 28 Oct 2002 · 13 references
Pith's verdict: An economical and legitimate model, but the dark-matter abundance in Eq. (14) does not follow from the calculation as written; worth referees, not a desk reject.
T0 · AI review
Why Pith says this
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Referee report
The paper
The paper claims
A single TeV-scale extension of the Standard Model is claimed to explain both the small masses of neutrinos and the dark matter, with the right-handed neutrino playing both roles.
The reading
What carries the argument
The carrying mechanism is the three-loop diagram that converts a lepton-number-violating Majorana mass for the right-handed neutrino into a left-handed Majorana neutrino mass, suppressed by three loops rather than by a superheavy scale. The $Z_2$ symmetry is what makes the diagram the leading contribution: it removes the tree-level Dirac mass and keeps $N_R$ from decaying, so the same symmetry that suppresses the neutrino mass also produces the stable relic. The freeze-out calculation — equating $n_{N_R} σ$ to $√{g_*} T_D^2/M_{pl}$ and solving for $M_R/T_D$ — is the second piece of machinery, turning the annihilation cross-section into a relic abundance.
Extended reading notes
Core claim
The claim is that a variant of the Zee model, with two charged scalar singlets $S_1$ and $S_2$ and one right-handed neutrino $N_R$, produces phenomenologically acceptable neutrino masses and a viable weakly interacting dark matter candidate near the electroweak scale. A $Z_2$ symmetry under which only $S_2$ and $N_R$ are odd forbids Dirac neutrino masses, while an explicit Majorana mass term for $N_R$ breaks lepton number. Neutrino mass then arises only through the three-loop diagram of the paper's Figure 1, giving the dimension-five operator $LLHH/Λ$ with $Λ$ of order $(4π^2)^3 M_{S_2}/(f^2 λ_s λ_l^2 g_α^2)$, which exceeds $10^9$ GeV for $M_{S_2}$ around a TeV and yields masses at the $0.1$ eV scale. Because $N_R$ is the lightest $Z_2$-odd state, it is stable, and its annihilation into right-handed charged leptons with $⟨σv⟩ ∼ g^4 M_R^2/(π M_{S_2}^4)$ gives $Ω_{N_R} ∼ 0.1$–$1$. The authors check that the resulting couplings survive bounds from muon decay, $μ → e + γ$, and neutrinoless double $\beta$ decay for $f_{eα} ∼ 0.1$ and $M_{S_1}$ of a few TeV.
Load-bearing premise
The load-bearing premise is that the same order-one Yukawa couplings and TeV-scale scalar masses that produce a $0.1$ eV neutrino mass also produce an annihilation rate whose relic abundance lands at the observed dark matter density.
Editorial extensions
If this is right
- Neutrino masses near $0.1$ eV follow from TeV-scale scalars and order-one Yukawa couplings, so no grand-unified desert is required to make neutrinos light.
- The right-handed neutrino has no direct neutral-current coupling to quarks, so existing nuclear-recoil dark matter detectors would see nothing, and a different detection technique would be needed.
- The dominant decay of $S_2$ is into a charged lepton plus the right-handed neutrino, giving a missing-energy signature at an $e^+e^-$ linear collider whose center-of-mass energy exceeds twice $M_{S_2}$.
- Flavor-violating bounds from $μ → e + γ$ and from muon decay are satisfied for $f_{eα} ∼ 0.1$ and $M_{S_1}$ of a few TeV, so the model sits within current limits while remaining within their reach.
- Because lepton number is broken explicitly, neutrinoless double beta decay remains a live test of the same couplings that generate the neutrino mass.
Reading between the lines
- The same Yukawa couplings $g_α$ and the same mass ratio $M_R/M_{S_2}$ set both the loop-induced neutrino mass and the annihilation rate, so the two observables are not independent; a combined fit would test whether a single parameter point can satisfy both at once.
- Stability of the dark matter candidate rests entirely on the unbroken $Z_2$. If that symmetry is broken even slightly, the right-handed neutrino decays, and the model then predicts a decaying dark matter component whose lifetime is set by the same small breaking term.
- The logic that higher loop order lowers the required new-physics scale suggests a family of models trading loop suppression for TeV-scale testability, of which this is one instance rather than a special case.
- Because the candidate is invisible to spin-independent nuclear recoil searches, the near-term test is more likely to come from collider searches for $S_2$ production with missing energy than from direct detection.
Original abstract
We propose a model for neutrino masses that simultaneously results in a new dark matter candidate, the right-handed neutrino. We derive the dark matter abundance in this model, show how the hierarchy of neutrino masses is obtained, and verify that the model is compatible with existing experimental results. The model provides an economical method of unifying two seemingly separate puzzles in contemporary particle physics and cosmology.
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.
The abstract, sentence by sentence
We propose a model for neutrino masses that simultaneously results in a new dark matter candidate, the right-handed neutrino. We derive the dark matter abundance in this model, show how the hierarchy of neutrino masses is obtained, and verify that the model is compatible with existing experimental results. The model provides an economical method of unifying two seemingly separate puzzles in contemporary particle physics and cosmology.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose a model for neutrino masses that simultaneously results in a new dark matter candidate, the right-handed neutrino. | contribution 1.00 | 0.85 | 0.52 | asserted 0.90 |
| s1 | We derive the dark matter abundance in this model, show how the hierarchy of neutrino masses is obtained, and verify that the model is compatible with existing experimental results. | contribution 0.90 | 0.95 | 0.24 | asserted 1.00 |
| s2 | The model provides an economical method of unifying two seemingly separate puzzles in contemporary particle physics and cosmology. | interpretation 0.98 | 0.45 | 0.40 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:hep-ph/0210389 by the authors.
References
How the literature uses it
116 arXiv papers cite this in 152 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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We present an economic model that establishes a link between neutrino masses and properties of the dark matter candidate.
A minimal model linking two great mysteries: neutrino mass and dark matter · 0.86
Papers citing it · 71 sentences without a confident label
Compares with it 3 papers
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This is in contrast to an early three-loop model proposed by Krauss, Nasri and Trodden (KNT) [ref] followed by similar recent attempts to explain small neutrino masses by adding to the SM content only additional weak singlets [ref] , or by substituting a real scalar triplet for a charged scalar singlet in the KNT model [ref] .
Scotogenic R\nuMDM at Three-Loop Level · Introduction · 0.97
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(iii) Since the models of Class 2 bear resemblance in particle content (when $S$ carries hypercharge $Y =1$) and neutrino mass matrix structure with the Krauss-Nasri-Trodden radiative neutrino mass model [ref] , the collider phenomenology and search strategies for the BSM states are also quite similar to those used to probe the Krauss-Nasri-Trodden model and related models [ref] , in particular regarding multi-leptons [ref] .
Lepton number violating operators with standard model gauge fields: A survey of neutrino masses from 3-loops and their link to dark matter · Class 2 · 0.91
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In addition, a scalar singlet with $𝖣 = -2δ$ is required to spontaneously break $U(1)_𝖭$ to a residual parity and to generate large Majorana masses for the right-handed neutrinos.[In contrast to this construction, in many existing DM models the stabilizing symmetry—typically a discrete $ℤ_2$ parity—is imposed by hand at the outset, rather than emerging as a residual symmetry of a spontaneously broken gauge symmetry [ref] .]
Physical implications of a double right-handed gauge symmetry · Introduction · 0.85
Cites it as background 73 papers
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Thus a vast literature has recently arisen along this idea [ref] .
An Extended Colored Zee-Babu Model · Introduction · 0.97
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As for the neutrino sector, two mechanisms of type-II seesaw [ref] and radiative seesaw with several loops[ As for the other radiative seesaw models, see Refs. [ref] .] are involved to induce the neutrino observables.
$T_7$ Flavor Model in Three Loop Seesaw and Higgs Phenomenology · Introduction · 0.96
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There is a class of models, the so-called radiative seesaw models, where right-handed neutrinos are introduced [ref] .
Lower bounds on lepton flavor violating branching ratios in a radiative seesaw model · Introduction · 0.94
Discussion
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