Majoron Dark Matter

• Majoron dark matter is a scenario where the pseudo-Goldstone boson from spontaneous lepton-number breaking serves as a dark matter candidate, naturally linking neutrino mass generation and cosmic phenomenology.
• Its interactions, proportional to the neutrino masses and suppressed by a high lepton-number-breaking scale, result in long lifetimes and distinctive signatures in neutrino, X-ray, and gamma-ray observables.
• A variety of production mechanisms—from misalignment to freeze-in—define mass regimes spanning ultralight to TeV scales, with each regime offering specific implications for dark matter detection and leptogenesis constraints.

Majoron dark matter denotes a class of scenarios in which the Majoron—the Goldstone boson of spontaneously broken global lepton number, or a pseudo–Nambu–Goldstone boson once small explicit breaking is included—constitutes all or part of the cosmological dark matter. In seesaw realizations, the same symmetry breaking that generates Majorana neutrino masses also fixes the Majoron’s leading interactions, so its couplings are typically proportional to neutrino masses and suppressed by the lepton-number-breaking scale. This makes the Majoron naturally long-lived and supports realizations ranging from ultralight misalignment-produced dark matter to keV, MeV, and TeV freeze-in scenarios, with characteristic signatures in neutrino, X-ray, gamma-ray, optical, and birefringence observables (Heeck, 2018, Heeck, 2017, Akita et al., 13 May 2026).

1. Origin in spontaneous lepton-number breaking

The canonical construction introduces a complex singlet scalar whose phase is the Majoron. In representative singlet models one writes

$$\sigma(x)=\frac{1}{\sqrt{2}}\big(v_\phi+\rho(x)\big)e^{iJ(x)/F_J},$$

or equivalently

$\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$

with $F_J\simeq v_\phi$ or $f$ the lepton-number-breaking scale, $\rho$ a heavy radial mode, and $J$ the Majoron itself (Heeck, 2018, Lu et al., 29 Jun 2025). In type-I seesaw form, the relevant Yukawa structure is

$$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$

so that after $\langle \sigma\rangle\neq 0$ one has $M_N\sim y_N f$ and

$$m_\nu \sim \frac{y_\nu^2 v^2}{M_N}\sim \frac{y_\nu^2 v^2}{y_N f}.$$

The Majoron is therefore not an ad hoc dark-sector degree of freedom: it is the angular mode of the order parameter that generates heavy Majorana masses and, via the seesaw, the light-neutrino mass matrix (Heeck, 2018).

If the global symmetry were exact, the Majoron would be massless. Majoron dark matter requires explicit but small lepton-number violation, typically attributed to soft terms, higher-dimensional operators, or quantum-gravity effects. The resulting Majoron mass is therefore treated in much of the literature as a free phenomenological parameter, even when benchmark expressions such as

$\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$0

or soft-breaking relations like $\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$1 are displayed in specific constructions (2004.00599, Giorgi et al., 18 May 2026).

2. Couplings, pseudo-Goldstone structure, and decay channels

At low energies the defining interaction is the Majoron coupling to neutrinos. In standard singlet constructions the effective interaction can be written as

$\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$2

with $\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$3, or equivalently in mass-matrix form

$\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$4

The corresponding tree-level decay width scales as

$\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$5

and in minimal formulations appears as

$\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$6

This scaling is the basic reason Majoron dark matter is long-lived: the coupling is suppressed both by the smallness of $\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$7 and by the largeness of the symmetry-breaking scale (Heeck, 2018, Akita et al., 13 May 2026).

Visible decays are generically loop-induced and model-dependent. One-loop couplings to charged leptons and quarks arise in singlet seesaw models, while the two-photon operator is conveniently parameterized as

$\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$8

In anomaly-enhanced two-Higgs-doublet realizations, one instead writes

$\sigma=\frac{1}{\sqrt{2}}(f+\rho+iJ),$9

with $F_J\simeq v_\phi$0 and benchmark values $F_J\simeq v_\phi$1 explicitly discussed (Lu et al., 29 Jun 2025). By contrast, in minimal singlet models the radiative channel is much more suppressed and often controlled by the triplet admixture or by higher-loop structure (0805.2372, Heeck, 2017).

The phenomenological ordering of channels is therefore clear. Tree-level $F_J\simeq v_\phi$2 usually dominates. Loop-induced $F_J\simeq v_\phi$3, $F_J\simeq v_\phi$4, and $F_J\simeq v_\phi$5 provide the visible probes. Because the neutrino width and the visible widths depend on different parameter combinations, bounds from photons or charged particles do not generally translate into a direct bound on the neutrino line rate (Heeck, 2018, Heeck, 2017).

3. Production mechanisms and mass regimes

Majoron dark matter is not tied to a unique cosmological history. The literature summarized here contains misalignment, thermal and non-thermal freeze-in, UV freeze-in, and specialized “Majorogenesis” mechanisms. The viable phenomenology is strongly mass-regime dependent.

Regime	Dominant production discussed	Characteristic probe
$F_J\simeq v_\phi$6 eV	Misalignment	Oscillatory photon birefringence
$F_J\simeq v_\phi$7 eV	Misalignment with enhanced EM anomaly	IR/optical/UV lines
keV	Freeze-in or cold freeze-in from quasi-degenerate parents	X-ray lines, Lyman-$F_J\simeq v_\phi$8
MeV	Freeze-in, including Higgs decays	Neutrino lines, SN/0$F_J\simeq v_\phi$9
TeV	Non-thermal freeze-in “Majorogenesis”	Neutrino, gamma-ray, cosmic-ray searches

For ultralight and eV-scale realizations, misalignment is central. In the anomaly-enhanced two-Higgs-doublet singlet Majoron model, the relic abundance is

$f$0

which naturally points to $f$1 for $f$2 GeV and $f$3 (Lu et al., 29 Jun 2025). In the ultralight anomalous model designed for birefringence searches, misalignment with $f$4 GeV yields $f$5 eV and an ALP-like photon coupling in the range relevant for optical interferometers (Obata et al., 9 Apr 2026).

In the keV regime, warmness becomes decisive. A generic freeze-in spectrum can be too hot, but quasi-degenerate decays $f$6 with $f$7 produce an unusually cold spectrum with

$f$8

substantially below the thermal value. This mechanism is naturally realized in inverse-seesaw Majoron models where a sterile pseudo-Dirac pair decays off-diagonally into a keV Majoron, thereby evading Lyman-$f$9 bounds while preserving an observable X-ray line (Heeck, 2018).

MeV-scale realizations have also been constructed explicitly. In a Higgs-portal freeze-in scenario, the observed abundance is obtained for

$\rho$0

with production dominated by $\rho$1 decays (Brune et al., 2018). At the opposite end, TeV-scale pseudo-Nambu–Goldstone Majorons require non-thermal production because $\rho$2 GeV and tiny Yukawas make freeze-out ineffective; three viable “Majorogenesis” mechanisms have been proposed: heavy RH-neutrino decays, UV freeze-in through the Higgs–$\rho$3 portal, and resonant annihilation of non-thermal RH neutrinos produced by inflaton decay (2004.00599).

A recent minimal synthesis combines freeze-in and misalignment in the two-RHN singlet seesaw. Remaining agnostic about the origin of $\rho$4, it finds that without fine-tuning of the initial misalignment angle the Majoron mass is bounded by $\rho$5 (Akita et al., 13 May 2026).

4. Signatures, constraints, and observational status

The clearest signature at $\rho$6 is a mono-energetic neutrino line at

$\rho$7

For dark-matter masses above $\rho$8 MeV, Borexino, KamLAND, and Super-Kamiokande can search for this signal, and the neutrino-line channel directly probes the tree-level $\rho$9 coupling rather than UV-sensitive visible operators (Heeck, 2018). For sub-MeV masses, neutrino-line sensitivity deteriorates and the principal indirect probe becomes

$J$0

from $J$1, searched for in X-ray and gamma-ray observatories (0805.2372, Lattanzi et al., 2013).

Cosmological longevity is mandatory. Representative requirements range from $J$2 in generic decaying-DM discussions to $J$3 Gyr from WMAP-9 analyses of invisible decays (Heeck, 2018, Lattanzi et al., 2013). In keV late-decaying majoron dark matter, WMAP-based analyses gave

$J$4

while X-ray line searches constrain $J$5 across the $J$6 keV–$J$7 GeV range (0805.2372, Lattanzi et al., 2013).

A frequently discussed benchmark is the reported $J$8 keV line. If interpreted as $J$9, it corresponds to $$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$0 keV. The interpretation remains unsettled, but it continues to serve as a benchmark for keV-scale Majoron dark matter, including triplet-assisted radiative models and cold freeze-in inverse-seesaw realizations (Heeck, 2018, Queiroz et al., 2014).

The MeV range is constrained in a different way. SN1987A and neutrinoless double beta decay with Majoron emission probe neutrino–Majoron couplings well above the cosmologically preferred $$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$1 range for MeV dark matter, excluding sizeable regions relevant for non-DM Majoron phenomenology but not the deeply feeble-coupling DM limit (Brune et al., 2018). At eV masses in anomaly-enhanced models, the signature shifts to optical and UV photons. JWST blank-sky measurements presently dominate in the relevant $$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$2–$$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$3 eV mass range, already intersecting the $$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$4 benchmark line, while future data can probe the $$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$5 case (Lu et al., 29 Jun 2025). For ultralight anomaly-coupled Majorons, gravitational-wave interferometers become relevant because the coherent field induces oscillatory photon birefringence through

$$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$6

with Advanced LIGO, KAGRA, and future detectors probing the corresponding parameter space (Obata et al., 9 Apr 2026).

5. Model realizations and internal tensions

The simplest realization is the singlet Majoron model: type-I seesaw plus one complex scalar singlet. It is theoretically economical and directly ties dark matter to neutrino mass generation (Heeck, 2017, Akita et al., 13 May 2026). However, phenomenology depends sensitively on the scalar sector and on whether the Majoron remains almost purely singlet or acquires doublet/triplet admixtures.

Triplet-assisted realizations are important because they generate $$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$7 more efficiently. In singlet-plus-triplet seesaw models the Majoron is mostly singlet but carries a small $$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$8 component, which induces couplings to charged fermions and hence an X-ray line. X-ray limits then translate into upper bounds on the triplet vev $$\mathcal{L}\supset - y_\nu \,\overline{L}\tilde H N - \frac{1}{2} y_N\,\sigma\,\overline{N^c}N + \text{h.c.},$$9, with large $\langle \sigma\rangle\neq 0$0 few GeV already disfavored in late-decaying keV Majoron scenarios (0805.2372, Lattanzi et al., 2013).

Inverse-seesaw models add a distinct structural possibility: the Majoron can couple off-diagonally to a quasi-degenerate sterile pseudo-Dirac pair, which simultaneously explains cold keV freeze-in and, in some constructions, supports resonant leptogenesis. A recent UV-freeze-in model with two RH neutrinos and a $\langle \sigma\rangle\neq 0$1 symmetry makes this correlation explicit: the same dimension-5 operators that generate the RHN mass splitting $\langle \sigma\rangle\neq 0$2 also induce the $\langle \sigma\rangle\neq 0$3 process that produces Majoron dark matter (King et al., 2024).

Heavy Majoron WIMP-like scenarios coupled through the Higgs portal are much more constrained. In the simplest singlet Majoron Higgs-portal model, thermally produced Majoron dark matter below $\langle \sigma\rangle\neq 0$4 GeV is excluded by LUX 2013 except in the narrow Higgs-resonance region near $\langle \sigma\rangle\neq 0$5, and future direct detection was already expected to decisively test the $\langle \sigma\rangle\neq 0$6 GeV–$\langle \sigma\rangle\neq 0$7 TeV window (Queiroz et al., 2014). This effectively pushes heavy Majoron dark matter toward freeze-in or other non-thermal histories rather than conventional freeze-out (2004.00599).

Not every Majoron-related dark-sector model makes the Majoron itself the dark matter particle. Some global $\langle \sigma\rangle\neq 0$8 constructions use the Majoron as a light mediator while a different $\langle \sigma\rangle\neq 0$9-stabilized scalar provides the dark matter, leading to semi-annihilation and box-shaped neutrino spectra instead of decaying-Majoron signals. That contrast clarifies that “Majoron dark matter” is a specific subset within a broader Majoron-coupled dark-sector literature (Miyagi et al., 2022).

6. Cosmological window, leptogenesis, and current synthesis

A central modern theme is the simultaneous realization of neutrino masses, dark matter, and baryogenesis. In the minimal singlet-Majoron framework with high-scale thermal leptogenesis, successful leptogenesis constrains the RH-neutrino mass scale and thereby fixes an irreducible freeze-in contribution to the Majoron abundance as well as the size of the loop-induced visible decay couplings. Combining those ingredients with warm-DM limits and indirect searches yields a restricted “Majoron cosmological window,” with future X- and gamma-ray telescopes expected to probe part of the surviving parameter space (Giorgi et al., 18 May 2026).

The recent minimal two-RHN analysis reaches an even sharper conclusion. Without fine-tuning of the initial misalignment angle, one finds

$M_N\sim y_N f$0

When thermal leptogenesis is imposed, successful leptogenesis favors misalignment-dominated production with

$M_N\sim y_N f$1

whereas freeze-in dominated production remains compatible only with a mild fine-tuning of the initial misalignment angle,

$M_N\sim y_N f$2

This sharply distinguishes a low-mass, misalignment-dominated regime from a higher-mass freeze-in regime that becomes increasingly tuned once the RH-neutrino sector is required to generate the baryon asymmetry (Akita et al., 13 May 2026).

More ambitious unified frameworks extend the same logic in different directions. One eV-scale two-Higgs-doublet Majoron model combines misalignment dark matter, thermal leptogenesis, an enhanced electromagnetic anomaly, and the production of Lyman–Werner photons capable of aiding direct-collapse black-hole seed formation (Lu et al., 29 Jun 2025). Another high-scale resonant-leptogenesis construction links UV freeze-in Majoron production directly to the dimension-5 operators that split a quasi-degenerate RH-neutrino pair, yielding a correlated parameter space for neutrino masses, dark matter, and baryon asymmetry (King et al., 2024).

Taken together, these results support a precise but non-universal conclusion. Majoron dark matter is not a single model but a family of pseudo-Goldstone dark-matter scenarios whose viability is controlled by four coupled ingredients: the lepton-number-breaking scale, the explicit breaking that sets $M_N\sim y_N f$3, the production mechanism, and the heavy-neutrino sector. The framework remains viable across a wide mass range, but once relic density, warmness, lifetime, and leptogenesis are imposed simultaneously, the allowed regions become sharply predictive and increasingly accessible to line searches and precision photon-propagation experiments (Giorgi et al., 18 May 2026, Obata et al., 9 Apr 2026).