arxiv: 2605.11124 · v1 · submitted 2026-05-11 · ✦ hep-ph

Recognition: 2 theorem links

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Connecting Neutrino Masses, Dark Matter and Leptogenesis from Delta(54) Flavor with Triple Inverse Seesaw

A. Baruah, H. Bora, N. Bharali, Ng.K. Francis, R. Sarkar, S.K. Jha

Authors on Pith no claims yet

Pith reviewed 2026-05-13 02:21 UTC · model grok-4.3

classification ✦ hep-ph

keywords neutrino massesinverse seesawflavor symmetrydark matterleptogenesisbaryon asymmetrymixing anglesΔ(54)

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The pith

Δ(54) flavor symmetry with triple inverse seesaw generates neutrino masses while linking dark matter relic density to resonant leptogenesis at the TeV scale.

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

The paper constructs an extended model with Δ(54) symmetry and two Higgs doublets that produces light neutrino masses through the triple inverse seesaw. It shows how the same symmetry enforces mixing angles that deviate from tribimaximal values in ways matching current oscillation data, including a nonzero reactor angle and atmospheric angle in the upper octant. The framework also incorporates a dark matter candidate whose relic abundance satisfies cosmological bounds and achieves the observed baryon asymmetry through flavor-dependent resonant leptogenesis when the right-handed neutrino mass is near 10 TeV with a small mass splitting.

Core claim

The model employs Δ(54) flavor symmetry together with a triple inverse seesaw to generate neutrino masses, predicts a nonzero reactor mixing angle and an atmospheric mixing angle in the upper octant together with CP-violating phases consistent with data, satisfies dark matter relic density and active-sterile mixing constraints, and produces the observed baryon asymmetry via resonant leptogenesis at the TeV scale for a right-handed neutrino mass of 10 TeV and appropriate mass splitting.

What carries the argument

The triple inverse seesaw mechanism embedded in Δ(54) flavor symmetry, which simultaneously suppresses neutrino masses, controls mixing parameters, and enables TeV-scale resonant leptogenesis while accommodating a dark matter sector.

If this is right

The reactor angle is predicted to be nonzero while the atmospheric angle lies in the upper octant.
The Jarlskog invariant and CP phase remain consistent with existing neutrino data.
Dark matter relic abundance is achieved alongside active neutrino mixing under standard cosmological limits.
Observed baryon asymmetry is reproduced for a 10 TeV right-handed neutrino mass and small mass splitting.

Where Pith is reading between the lines

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

The TeV-scale leptogenesis window opens the possibility of collider tests for the same particles responsible for neutrino masses.
Similar discrete flavor symmetries might be combined with inverse-seesaw structures to address additional puzzles such as the muon g-2 anomaly.
The tight linkage between dark matter, leptogenesis, and neutrino mixing could reduce the parameter space in future global fits of beyond-Standard-Model scenarios.

Load-bearing premise

The Δ(54) symmetry charge assignments and the triple inverse seesaw parameters can be chosen so that neutrino oscillation data, dark matter relic density, and leptogenesis all hold at once without violating other constraints such as flavor-changing processes.

What would settle it

A precise measurement placing the atmospheric mixing angle in the lower octant, or a failure to observe the predicted level of baryon asymmetry or dark matter relic density for right-handed neutrinos near 10 TeV, would rule out the central claim.

Figures

Figures reproduced from arXiv: 2605.11124 by A. Baruah, H. Bora, N. Bharali, Ng.K. Francis, R. Sarkar, S.K. Jha.

**Figure 1.** Figure 1: Correlation between the parameters a, b, s and M. The best fit value is indicated by the x marker corresponding to χ 2 min. The two real parameters are allowed to run over the ranges: M ∈ [1013 , 1014]eV and s ∈ [108 , 109 ]eV . The term ϕa and ϕb are the phases. The allowed parameter space of the model is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗

**Figure 2.** Figure 2: Correlation among the oscillation parameters predicted by the model at 3 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Figure 3: Correlation between Dirac CP (δCP ) with solar and atmospheric mixing angle respectively (top row). Correlation between Jarlskog invariant (J) with atmospheric mixing angle and δCP respectively (bottom row). The best fit value is indicated by the x marker. 4. Dark Matter Sector A non-resonantly created sterile dark matter (DM) may be easily accommodated within an extended SM of particle physics. Since the… view at source ↗

**Figure 4.** Figure 4: Allowed regions of the parameter MDM . The best fit value is indicated by the x marker. matter mass and the mixing angle. As a non-resonant DM candidate, we have taken into account a sterile neutrino mass matrix, in our model. Therefore mDM will be used to represent the fermion mass [19]. The lightest sterile fermion, dominantly composed of the gauge-singlet fields SL and SR , forms a pseudo-Dirac state wi… view at source ↗

**Figure 5.** Figure 5: Correlation between Active neutrino-DM mixing angle [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

**Figure 6.** Figure 6: Correlation between Relic abundance (ΩDMh 2 ) as a function of dark matter mass (MDM ) and including constraints from Lyman-α and X-ray for NH. 5. Resonant Leptogenesis Fukugita and Yanagida originally proposed the leptogenesis mechanism, which is one of the most commonly accepted explanations for the Baryon Asymmetry of the Universe (BAU). The mass of the lightest right-handed neutrino, M1 = 109 GeV, has… view at source ↗

**Figure 7.** Figure 7: Correlations between the flavor-dependent CP-violating asymmetries [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

**Figure 8.** Figure 8: Correlations between the Baryon Asymmetry ( [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗

read the original abstract

In this present study, an extended Delta 54 flavor symmetry model incorporating two standard model Higgs doublets is investigated. This model generates neutrino masses through the triple inverse seesaw mechanism. It predicts deviations from tribimaximal mixing, yielding a nonzero reactor angle and an atmospheric mixing angle in the upper octant. In addition, the CP-violating phase and the Jarlskog invariant are found to be consistent with current neutrino oscillation data. Our study also includes the dark matter sector by evaluating the relic abundance and active neutrino dark matter mixing under relevant cosmological constraints. Furthermore, baryogenesis is achieved through resonant leptogenesis at the TeV scale including flavor effects. We obtain the observed baryon asymmetry, for right-handed neutrino mass 10 TeV and mass splitting d.

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

Δ(54) model with triple inverse seesaw fits neutrino data and DM relic but leptogenesis relies on a chosen small mass splitting d.

read the letter

The main point is that this paper constructs a Δ(54) flavor model using triple inverse seesaw and two Higgs doublets to explain neutrino masses and mixing while incorporating dark matter and TeV-scale resonant leptogenesis. It gets the observed baryon asymmetry for a right-handed neutrino mass of 10 TeV and a specific mass splitting d. The new element is the unified treatment that predicts an upper octant for the atmospheric mixing angle, a nonzero reactor angle, and consistent CP phase and Jarlskog invariant, all while satisfying relic abundance and producing the correct asymmetry with flavor effects in leptogenesis. The paper does well in detailing the symmetry assignments and showing numerical consistency with current oscillation data and cosmological bounds. The soft spot lies in the leptogenesis sector. Resonant leptogenesis at 10 TeV requires a very small splitting d to generate enough asymmetry, and the description suggests this d is selected to match the target value rather than emerging directly from the flavor symmetry or the scalar vacuum expectation values. If the Δ(54) breaking terms responsible for d also influence the light neutrino mass matrix or the dark matter interactions, the simultaneous fit could be compromised, and the abstract does not clarify how conflicts are avoided. This work is for hep-ph model builders interested in flavor symmetries applied to multiple problems like neutrino masses, dark matter, and baryogenesis. Readers focused on TeV-scale leptogenesis or inverse seesaw constructions could extract useful benchmarks from the predictions. I recommend sending it for peer review. The framework is coherent enough and the checks against data are present, so referees can assess whether the symmetry truly controls the scales without hidden tuning.

Referee Report

1 major / 2 minor

Summary. The manuscript constructs an extended Δ(54) flavor symmetry model with two SM Higgs doublets that realizes neutrino masses via the triple inverse seesaw mechanism. It predicts deviations from tribimaximal mixing (nonzero θ13, θ23 in the upper octant) together with values of δ_CP and the Jarlskog invariant J that are stated to be consistent with oscillation data. The model also incorporates a dark-matter candidate whose relic abundance and active-sterile mixing are checked against cosmological bounds, and it claims to reproduce the observed baryon asymmetry through resonant leptogenesis at the TeV scale for a right-handed neutrino mass of 10 TeV and a mass splitting d.

Significance. If the Δ(54) charge assignments and scalar VEVs simultaneously enforce the required small splitting d for resonant leptogenesis while preserving the predicted mixing angles and DM relic density without additional fine-tuning or conflicts with flavor-violating processes, the work would provide a unified, symmetry-based link among neutrino masses, dark matter, and baryogenesis. The explicit inclusion of flavor effects in the leptogenesis calculation and the numerical checks against relic abundance and oscillation data are constructive elements that strengthen the presentation.

major comments (1)

[Abstract and leptogenesis section] Abstract and the leptogenesis discussion: the statement that the observed baryon asymmetry is obtained “for right-handed neutrino mass 10 TeV and mass splitting d” does not demonstrate that the Δ(54) symmetry or the triple inverse seesaw structure fixes |d| to the narrow range (typically ≲10^{-6}–10^{-8}) required for resonant enhancement at the TeV scale; the splitting appears instead to be chosen by hand to match the target Y_B, which weakens the claimed connection between the flavor symmetry and leptogenesis.

minor comments (2)

[Model and mass-matrix section] The notation for the mass-splitting parameter d should be defined explicitly (e.g., d ≡ (m_{N2} − m_{N1})/m_N) at first use and its relation to the Δ(54)-allowed operators clarified.
[Figures] Figure captions for the mixing-angle and relic-density plots should include the precise parameter values and ranges used, together with a brief statement of the experimental constraints applied.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The major comment highlights an important point regarding the connection between the flavor symmetry and the resonant leptogenesis parameter. We address it point-by-point below and will revise the manuscript to strengthen the presentation.

read point-by-point responses

Referee: [Abstract and leptogenesis section] Abstract and the leptogenesis discussion: the statement that the observed baryon asymmetry is obtained “for right-handed neutrino mass 10 TeV and mass splitting d” does not demonstrate that the Δ(54) symmetry or the triple inverse seesaw structure fixes |d| to the narrow range (typically ≲10^{-6}–10^{-8}) required for resonant enhancement at the TeV scale; the splitting appears instead to be chosen by hand to match the target Y_B, which weakens the claimed connection between the flavor symmetry and leptogenesis.

Authors: We agree that the current wording in the abstract and leptogenesis section could be clarified to better demonstrate the role of the Δ(54) symmetry. In the model, the charge assignments under Δ(54) together with the triple inverse seesaw structure and the VEVs of the two Higgs doublets naturally suppress the mass splitting d between the right-handed neutrinos to the small values required for resonant leptogenesis at the TeV scale, without introducing additional large hierarchies beyond those already present in the scalar potential. The specific numerical value of d is then chosen within this symmetry-allowed window to reproduce the observed baryon asymmetry while remaining consistent with the neutrino mixing predictions and dark-matter constraints. We will revise the abstract and expand the leptogenesis section (including an explicit derivation of the allowed range for d from the flavor charges and VEVs) to make this connection explicit and to address potential concerns about fine-tuning. revision: yes

Circularity Check

1 steps flagged

Baryon asymmetry obtained for chosen 10 TeV RH neutrino mass and splitting d reduces to parameter selection

specific steps

fitted input called prediction [Abstract]
"We obtain the observed baryon asymmetry, for right-handed neutrino mass 10 TeV and mass splitting d."

The paper presents the observed baryon asymmetry as obtained specifically for the selected right-handed neutrino mass of 10 TeV and mass splitting d. This indicates that the values are chosen to reproduce the target Y_B rather than emerging as a parameter-free prediction from the Δ(54) assignments or triple inverse seesaw structure.

full rationale

The derivation chain for leptogenesis success reduces to selecting m_N = 10 TeV and d to match the observed Y_B, as stated in the abstract. Neutrino mass generation via triple inverse seesaw and mixing angle predictions from Δ(54) appear independent of this choice and are not shown to force the specific d needed for resonant leptogenesis. No self-citation chains, ansatz smuggling, or renaming of known results are evident in the provided text. This yields partial circularity confined to the baryogenesis claim.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the choice of Δ(54) symmetry to fix Yukawa textures, the triple inverse seesaw for mass generation, and numerical tuning of right-handed neutrino parameters to match baryon asymmetry; these are not derived from more fundamental principles within the paper.

free parameters (2)

right-handed neutrino mass = 10 TeV
Set to 10 TeV to reproduce observed baryon asymmetry in resonant leptogenesis
mass splitting d
Small splitting parameter required for resonant enhancement of leptogenesis

axioms (2)

domain assumption Δ(54) discrete flavor symmetry governs the Yukawa couplings and scalar potential
Invoked to produce deviations from tribimaximal mixing and constrain the neutrino sector
domain assumption Triple inverse seesaw mechanism generates the observed neutrino mass scale
Assumed as the mass-generation framework without derivation from the symmetry alone

pith-pipeline@v0.9.0 · 5453 in / 1783 out tokens · 73708 ms · 2026-05-13T02:21:36.315640+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
We obtain the observed baryon asymmetry, η_B ≈6×10^{-10}, for right-handed neutrino mass M1=10 TeV and mass splitting d≈10^{-8}.
IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear
The Δ(54) symmetry can manifest itself in heterotic string models... We specifically choose the Majorana mass matrix for right-handed neutrinos, MR, so that these neutrinos have degenerate masses at the dimension five-level.

Reference graph

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