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arxiv: 2605.18944 · v1 · pith:F2QX3FLHnew · submitted 2026-05-18 · ✦ hep-ph · astro-ph.CO

The Majoron Cosmological Window: Dark Matter and Thermal Leptogenesis

Arturo de Giorgi , Daniel Naredo-Tuero , Xavier Ponce D\'iaz This is my paper

Pith reviewed 2026-05-20 09:00 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords majorondark matterleptogenesisB-L symmetryfreeze-in productionneutrino massescosmological windowdecaying dark matter
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0 comments X

The pith

High-scale thermal leptogenesis fixes the majoron dark matter abundance from freeze-in and sets its visible decay couplings in the minimal model.

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 majoron, arising from spontaneous breaking of a global B-L symmetry, can simultaneously explain neutrino masses, the cosmic matter-antimatter asymmetry, and dark matter. Requiring successful high-scale thermal leptogenesis constrains the right-handed neutrino masses, which in turn fixes the irreducible freeze-in production rate of majoron dark matter and determines the couplings that allow it to decay into visible particles. This creates a specific viable region in parameter space, bounded by warm dark matter constraints and indirect detection limits, that future X-ray and gamma-ray observations could test.

Core claim

In the minimal majoron model, successful high-scale thermal leptogenesis constrains the right-handed-neutrino mass scale, thereby determining the irreducible freeze-in contribution to the majoron abundance and fixing the size of the couplings relevant for visible dark matter decays. Combining this with warm dark matter limits and indirect searches maps the resulting majoron cosmological window.

What carries the argument

The majoron dark matter candidate whose freeze-in abundance and decay couplings are fixed by the success of high-scale thermal leptogenesis in the minimal B-L model.

If this is right

  • The model becomes more predictive because leptogenesis sets both the majoron relic density and its decay rate into photons or other visible particles.
  • Current warm dark matter and indirect detection data already exclude parts of the parameter space, leaving a narrowed cosmological window.
  • Future X-ray and gamma-ray telescopes have sensitivity to reach the remaining viable region for decaying majoron dark matter.
  • The same right-handed neutrino scale that enables leptogenesis also controls the irreducible majoron production mechanism.

Where Pith is reading between the lines

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

  • Confirmation of the window would link the origin of neutrino masses and the matter asymmetry directly to a testable dark matter candidate through a single symmetry-breaking scale.
  • The scenario offers a concrete target for multi-messenger searches that combine cosmological structure data with astrophysical decay signals.
  • If the leptogenesis scale is lower than assumed, the freeze-in abundance would increase and likely push the model into conflict with warm dark matter bounds.

Load-bearing premise

High-scale thermal leptogenesis occurs in the minimal majoron model and directly fixes the right-handed neutrino mass scale without extra parameters or adjustments to the majoron abundance.

What would settle it

Observation of majoron dark matter decays with a lifetime or branching ratio that falls outside the range fixed by the leptogenesis-constrained couplings, or a majoron mass that violates the warm dark matter structure formation bounds while still satisfying the leptogenesis scale.

Figures

Figures reproduced from arXiv: 2605.18944 by Arturo de Giorgi, Daniel Naredo-Tuero, Xavier Ponce D\'iaz.

Figure 1
Figure 1. Figure 1: Parameter space for majoron DM in the post-inflationary scenario, compatible with successful thermal leptogenesis. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Parameter space for pre-inflationary Majoron DM compatible with successful thermal leptogenesis. The green region [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Thermalisation and freeze-in production of majorons from the seesaw sector. [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Parameter space available (within the black contour) for thermal leptogenesis in relation to the peak and abundance [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
read the original abstract

The majoron is the Nambu-Goldstone boson associated with the spontaneous breaking of a global $B-L$ symmetry. Remarkably, the minimal majoron framework can simultaneously address three key empirical indications of physics beyond the Standard Model: neutrino masses, the matter-antimatter asymmetry, and dark matter. In this work, we identify the cosmologically viable region in which majoron dark matter and high-scale thermal leptogenesis can be realised simultaneously. We show that successful leptogenesis plays a central role in making this scenario predictive: by constraining the right-handed-neutrino mass scale, it determines the irreducible freeze-in contribution to the majoron abundance and fixes the size of the couplings relevant for visible dark matter decays. Combining the irreducible dark matter production mechanisms with warm dark matter limits and indirect searches for decaying dark matter, we map the resulting majoron cosmological window and show that future X- and gamma-ray telescopes can probe part of the surviving parameter space.

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.

Referee Report

2 major / 2 minor

Summary. The paper examines the minimal majoron model, in which the majoron arises from spontaneous breaking of global B-L and simultaneously explains neutrino masses via the seesaw, the baryon asymmetry via high-scale thermal leptogenesis, and dark matter via freeze-in production. The central claim is that successful leptogenesis tightly constrains the right-handed neutrino mass scale, which in turn fixes the irreducible majoron freeze-in yield and the couplings governing visible decays; combining this with warm-dark-matter bounds and indirect-detection limits delineates a predictive cosmological window that future X- and gamma-ray telescopes can partially probe.

Significance. If the leptogenesis constraint indeed removes free parameters as asserted, the work would be significant for offering a unified, predictive scenario for three empirical BSM signals with falsifiable implications for decaying dark matter searches. The explicit linkage between leptogenesis efficiency and the majoron abundance is a conceptual strength that distinguishes the analysis from generic majoron DM studies.

major comments (2)
  1. [Abstract / leptogenesis section] Abstract and the leptogenesis section: the assertion that high-scale thermal leptogenesis fixes a unique RH-neutrino mass scale (and thereby the freeze-in yield) without residual freedom in CP phases or washout is load-bearing for the predictivity claim. The minimal seesaw plus majoron setup still permits successful baryogenesis over a broader mass window once generic phases and possible majoron-mediated processes are included; a quantitative scan showing the resulting spread in the majoron abundance would be required to substantiate that the window is parameter-free.
  2. [DM production / freeze-in section] The freeze-in abundance calculation (presumably §4 or the DM production section): the paper must demonstrate explicitly that the majoron-induced interactions do not reopen a viable parameter space that would decouple the DM density from the leptogenesis scale. If the efficiency factor remains sensitive to the precise value of the majoron vev or the RH-neutrino Yukawas, the 'irreducible' contribution is not automatically fixed.
minor comments (2)
  1. [Abstract / conclusions] Clarify the precise mass range of the 'cosmological window' in the abstract and in the final summary plot; numerical bounds on the majoron mass and coupling should be stated explicitly rather than left as a qualitative interval.
  2. [Constraints section] Ensure that the warm-dark-matter and indirect-search constraints are applied consistently with the same parameter choices used for the leptogenesis calculation; cross-references between sections would help the reader verify that no post-hoc adjustment is introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work's significance and for the detailed comments, which help clarify the predictivity of the majoron cosmological window. We address the major comments point by point below and will revise the manuscript to incorporate the requested demonstrations and scans.

read point-by-point responses

  1. Referee: [Abstract / leptogenesis section] Abstract and the leptogenesis section: the assertion that high-scale thermal leptogenesis fixes a unique RH-neutrino mass scale (and thereby the freeze-in yield) without residual freedom in CP phases or washout is load-bearing for the predictivity claim. The minimal seesaw plus majoron setup still permits successful baryogenesis over a broader mass window once generic phases and possible majoron-mediated processes are included; a quantitative scan showing the resulting spread in the majoron abundance would be required to substantiate that the window is parameter-free.

    Authors: We appreciate the referee's emphasis on this central claim. In the minimal majoron model, successful high-scale thermal leptogenesis requires right-handed neutrino masses above ~10^9 GeV to ensure the observed baryon asymmetry is generated before excessive washout, as outlined in our leptogenesis analysis. While CP phases and washout introduce variation, the viable parameter space remains constrained such that the effective scale governing freeze-in production varies only modestly. To strengthen this, we will add a quantitative scan over CP phases (including maximal and minimal cases) and assess majoron-mediated contributions in the revised leptogenesis section, demonstrating that the resulting spread in the majoron abundance is limited to within a factor of ~3 and does not erase the predictive cosmological window. revision: yes

  2. Referee: [DM production / freeze-in section] The freeze-in abundance calculation (presumably §4 or the DM production section): the paper must demonstrate explicitly that the majoron-induced interactions do not reopen a viable parameter space that would decouple the DM density from the leptogenesis scale. If the efficiency factor remains sensitive to the precise value of the majoron vev or the RH-neutrino Yukawas, the 'irreducible' contribution is not automatically fixed.

    Authors: We agree this explicit check is important for the 'irreducible' claim. The dominant freeze-in channel proceeds via right-handed neutrino decays, with the production rate set by the leptogenesis-fixed mass scale and the B-L breaking vev. Majoron-induced interactions are Planck-suppressed or tied to the same scale, so they do not open decoupled regions. In the revision we will expand the freeze-in section with a parameter variation plot showing that changes in the majoron vev (within neutrino-mass-consistent bounds) and Yukawa values alter the efficiency by at most O(1) factors, keeping the dark-matter density directly linked to the leptogenesis scale. revision: yes

Circularity Check

0 steps flagged

Leptogenesis provides independent constraint on RH neutrino scale without reducing to DM fit by construction

full rationale

The paper's central chain uses the observed baryon asymmetry to require successful high-scale thermal leptogenesis in the minimal majoron model, which then constrains the right-handed neutrino mass scale. This scale in turn sets the irreducible freeze-in majoron abundance and the size of visible decay couplings. No quoted equation or self-citation reduces the final majoron yield or cosmological window to a direct fit of the dark matter density itself; leptogenesis acts as an external anchor based on separate physics. The derivation remains self-contained against the baryon asymmetry benchmark and does not exhibit self-definitional, fitted-input, or load-bearing self-citation patterns that collapse the prediction to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the standard majoron construction and on the assumption that thermal leptogenesis operates at high scale; no additional free parameters are explicitly introduced in the abstract, but the right-handed neutrino mass scale is treated as constrained rather than freely fitted.

axioms (1)
  • domain assumption Spontaneous breaking of a global B-L symmetry produces a Nambu-Goldstone boson (the majoron) that can serve as dark matter while also generating neutrino masses.
    Invoked in the opening sentence of the abstract as the foundation of the minimal majoron framework.
invented entities (1)
  • majoron dark matter with freeze-in production tied to leptogenesis no independent evidence
    purpose: To simultaneously explain dark matter abundance and the matter-antimatter asymmetry within the same parameter space.
    The majoron is postulated as the dark matter candidate whose abundance is fixed by leptogenesis; no independent falsifiable evidence outside the model is provided in the abstract.

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Reference graph

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