arxiv: 2604.12121 · v1 · submitted 2026-04-13 · ✦ hep-ph

Recognition: unknown

The 3-3-1 Model: a natural framework for sub-MeV dark matter

Vinicius Oliveira , D. Cogollo , A. Doff , C. A. de S. Pires

Authors on Pith no claims yet

Pith reviewed 2026-05-10 14:54 UTC · model grok-4.3

classification ✦ hep-ph

keywords 3-3-1 modelsub-MeV dark matterpseudo-Goldstone bosonfreeze-inright-handed neutrinosTeV scalegravitational effectslow reheating temperature

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The pith

The 3-3-1 model with right-handed neutrinos supplies a natural sub-MeV dark matter candidate realized as a pseudo-Goldstone boson.

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

The paper shows that the SU(3)_C × SU(3)_L × U(1)_N gauge theory extended by right-handed neutrinos automatically contains a pseudo-Goldstone boson that can act as sub-MeV dark matter once gravitational effects lift its mass. This boson reaches the observed relic density through freeze-in production when the early universe reheats to a sufficiently low temperature, removing any need for tiny coupling constants. The entire construction remains at the TeV scale, so the new gauge bosons and scalars can be searched for at present and future colliders. A reader would care because sub-MeV dark matter has usually required either extreme fine-tuning or additional ad-hoc fields, while here both the mass and the abundance emerge from the existing symmetry structure and standard cosmological assumptions.

Core claim

In the 3-3-1 model with right-handed neutrinos the spontaneous breaking of the extended gauge symmetry yields a pseudo-Goldstone boson whose mass is generated by Planck-suppressed gravitational operators at the sub-MeV scale. This boson serves as a viable dark-matter candidate whose present-day density is set by the freeze-in mechanism in a low-reheating-temperature cosmology, without the requirement of suppressed interaction strengths. The model operates at the TeV scale and therefore remains directly testable through collider production of its new gauge bosons and scalars.

What carries the argument

The pseudo-Goldstone boson produced by the spontaneous breaking of the global symmetry associated with the 3-3-1 gauge group, whose mass arises from gravitational effects and whose abundance is fixed by freeze-in.

If this is right

The dark matter mass is fixed at the sub-MeV scale by Planck-suppressed operators without additional tuning.
The correct relic abundance follows from freeze-in once the reheating temperature is below a few GeV.
All new states required by the 3-3-1 gauge structure lie at the TeV scale and are therefore accessible to collider searches.
No extremely small couplings are needed to match either the mass or the abundance of the dark matter.

Where Pith is reading between the lines

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

Similar pseudo-Goldstone bosons in other extended gauge models could also be stabilized at sub-MeV masses by gravitational effects.
A low-reheating-temperature epoch may simultaneously solve the relic-density problem for other light hidden-sector particles.
Direct-detection experiments sensitive to keV-scale scattering could provide an independent test of the gravitational mass-generation mechanism.
The same Planck-suppressed operators might generate small neutrino masses or other sub-eV phenomena within the same framework.

Load-bearing premise

Gravitational operators must set the pseudo-Goldstone boson mass at the sub-MeV scale while the reheating temperature remains low enough that freeze-in alone produces the observed relic density.

What would settle it

Observation of a sub-MeV dark matter particle whose interactions are inconsistent with freeze-in production, or the absence of the predicted TeV-scale gauge bosons and scalars in LHC or future collider data.

read the original abstract

We show that the $\mathrm{SU}(3)_C \times \mathrm{SU}(3)_L \times \mathrm{U}(1)_N$ model with right-handed neutrinos naturally accommodates a viable sub-MeV dark matter (DM) candidate realized as pseudo-Goldstone boson that acquires tiny mass through gravitational effects. The observed relic abundance is obtained via freeze-in in a low-reheating temperature scenario, without requiring tiny couplings. The model operates at the TeV scale and remains testable at current and future collider experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper embeds sub-MeV pseudo-Goldstone dark matter in the 3-3-1 model via gravitational mass and low-reheating freeze-in, a workable combination but one that still needs explicit checks on the mass scale and yield.

read the letter

The central move here is to take the established 3-3-1 gauge structure with right-handed neutrinos and realize the dark matter as a pseudo-Goldstone boson whose mass is set by Planck-suppressed operators rather than by hand. The relic density is then produced by freeze-in when the reheating temperature is low enough that the usual thermal production is suppressed. This avoids the tiny couplings that usually plague light DM models and keeps the whole setup at the TeV scale where colliders can look for it. That combination is new enough to be worth noting, even though the 3-3-1 framework and freeze-in itself are not. The abstract makes the logic clear and the claim that no extreme tuning is required looks plausible on the surface. The model also inherits the usual 3-3-1 constraints from flavor and precision data, which is a plus for testability. The soft spots are in the details that are not shown. The gravitational mass generation is stated but without the explicit operators or an estimate of how stable the sub-MeV scale remains against higher-dimensional terms or loop corrections. The freeze-in calculation is asserted to match the observed density, yet there is no parameter table, no scan over reheating temperature, and no discussion of how sensitive the yield is once the 3-3-1 couplings and vevs are fixed by other observables. If those numbers only work for a narrow window of reheating temperature, the naturalness argument weakens. The paper is aimed at people already working on 3-3-1 extensions or on light dark matter candidates that must evade direct detection. It is coherent enough on its own terms to deserve a serious referee rather than a desk rejection; a full review would force the authors to supply the missing derivations and show whether the mechanism survives once all constraints are applied simultaneously.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that the SU(3)_C × SU(3)_L × U(1)_N model with right-handed neutrinos naturally accommodates a viable sub-MeV dark matter candidate realized as a pseudo-Goldstone boson whose tiny mass is generated by gravitational effects. The observed relic abundance is obtained via freeze-in in a low-reheating temperature scenario without requiring tiny couplings, with the model operating at the TeV scale and remaining testable at current and future collider experiments.

Significance. If the central mechanism is shown to work with explicit calculations, the result would provide a natural, parameter-efficient framework for sub-MeV DM within an established 3-3-1 extension, linking gravitational Planck-suppressed operators to the DM mass and freeze-in production to the relic density. This could strengthen connections between TeV-scale phenomenology and cosmology while offering concrete collider signatures.

major comments (2)

[§3] §3 (Dark Matter Candidate): the claim that gravitational effects generate a pseudo-Goldstone boson mass precisely at the sub-MeV scale is introduced via Planck-suppressed operators, but no explicit form of the leading operator, symmetry-breaking pattern, or numerical estimate fixing the mass independently of the reheating temperature is provided; this is load-bearing for the 'natural' aspect of the proposal.
[§4] §4 (Relic Density via Freeze-In): the assertion that the observed abundance is obtained via freeze-in at low reheating temperature without tiny couplings lacks the explicit Boltzmann-equation solution, yield formula, or parameter scan showing that the result holds once the gravitational mass scale is fixed; without this, it is impossible to verify whether the mechanism reproduces the observed density or requires additional tuning.

minor comments (2)

[Abstract] The abstract and introduction would benefit from a short statement of the global symmetry protecting the pseudo-Goldstone boson before gravitational breaking.
[§2] Notation for the U(1)_N charge assignments and the right-handed neutrino sector could be made more uniform across sections to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We address the two major points below and will revise the manuscript to provide the requested explicit details, thereby strengthening the presentation of the naturalness and viability of the sub-MeV dark matter candidate.

read point-by-point responses

Referee: [§3] §3 (Dark Matter Candidate): the claim that gravitational effects generate a pseudo-Goldstone boson mass precisely at the sub-MeV scale is introduced via Planck-suppressed operators, but no explicit form of the leading operator, symmetry-breaking pattern, or numerical estimate fixing the mass independently of the reheating temperature is provided; this is load-bearing for the 'natural' aspect of the proposal.

Authors: We agree that an explicit derivation is necessary to fully establish the naturalness claim. In the revised manuscript we will add the leading Planck-suppressed operator consistent with the 3-3-1 gauge symmetries and the right-handed neutrino content, specify the symmetry-breaking pattern generated by the TeV-scale vacuum expectation values of the scalar fields, and include a numerical estimate showing that the resulting pseudo-Goldstone boson mass lies in the sub-MeV range for benchmark values of the model parameters. This mass is generated independently of the reheating temperature, as required. revision: yes
Referee: [§4] §4 (Relic Density via Freeze-In): the assertion that the observed abundance is obtained via freeze-in at low reheating temperature without tiny couplings lacks the explicit Boltzmann-equation solution, yield formula, or parameter scan showing that the result holds once the gravitational mass scale is fixed; without this, it is impossible to verify whether the mechanism reproduces the observed density or requires additional tuning.

Authors: We acknowledge that the explicit freeze-in calculation should be presented in more detail. The revised version will contain the Boltzmann equation governing the dark matter yield, the corresponding analytic expression for the freeze-in yield at low reheating temperature, and a parameter scan over the TeV-scale couplings and reheating temperatures (with the dark matter mass fixed by the gravitational operator). The scan will demonstrate that the observed relic density is reproduced without requiring tiny couplings or additional tuning. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The abstract and summary present the 3-3-1 model as naturally accommodating a sub-MeV pseudo-Goldstone boson DM candidate whose mass arises from gravitational effects and whose relic density follows from freeze-in at low reheating temperature. No equations, parameter fits, or self-citations are quoted that would reduce any claimed prediction to an input by construction. The gravitational mass generation and low-T_reheat scenario are introduced as model features rather than derived quantities that loop back to fitted data or prior self-referential results. The derivation chain therefore remains self-contained against external benchmarks with no load-bearing circular steps identifiable from the provided text.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of the 3-3-1 gauge structure, the presence of right-handed neutrinos, the assumption that gravity breaks the global symmetry to give a tiny mass, and the choice of a low reheating temperature that enables freeze-in without tiny couplings.

free parameters (2)

reheating temperature
Chosen low enough for freeze-in to set the correct relic density; its value is not derived from first principles in the abstract.
gravitational mass scale for the pseudo-Goldstone boson
Set by hand to the sub-MeV range; no independent calculation of its magnitude is provided.

axioms (2)

domain assumption The 3-3-1 gauge symmetry is spontaneously broken at the TeV scale in the standard way.
Standard assumption of the 3-3-1 literature invoked to keep the model testable at colliders.
ad hoc to paper Gravitational effects generate a tiny explicit breaking of the global symmetry protecting the pseudo-Goldstone boson.
Introduced to produce the sub-MeV mass without additional fields or couplings.

pith-pipeline@v0.9.0 · 5394 in / 1646 out tokens · 52474 ms · 2026-05-10T14:54:11.470340+00:00 · methodology

discussion (0)

Reference graph

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