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arxiv: 2508.02642 · v2 · submitted 2025-08-04 · ✦ hep-ph · astro-ph.CO

Lepton parity dark matter and naturally unstable domain walls

Ernest Ma , Partha Kumar Paul , Narendra Sahu This is my paper

Pith reviewed 2026-05-19 00:46 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords lepton paritydark matterdomain wallsgravitational wavestype I seesawZ2 symmetrystochastic backgroundneutrino masses
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The pith

Residual lepton parity from the type I seesaw stabilizes dark matter without new symmetries and leads to unstable domain walls that annihilate into observable gravitational waves.

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

The paper tries to establish a minimal scenario that ties together neutrino mass generation, dark matter, and gravitational waves using only the standard type I seesaw and its residual symmetry. It shows how the lepton parity acts as a dark matter stabilizing parity for a singlet fermion, avoiding the need to impose extra discrete symmetries by hand. The scalar potential then has an accidental Z2 that breaks to form domain walls, but explicit breaking terms allowed by lepton parity make them unstable so they decay. This decay produces a stochastic gravitational wave background that might be seen in various detectors. A reader would care if this provides a unified and economical explanation for multiple open problems in particle cosmology.

Core claim

The residual symmetry (−1)^L from the type I seesaw acts as the dark parity D=(−1)^{L+2j} to ensure stability of a singlet Majorana fermion S as dark matter, which interacts with a real scalar σ, both even under lepton parity. The scalar potential has an accidental Z2 symmetry that is spontaneously broken, producing domain walls which are rendered unstable by explicit Z2 breaking terms permitted by the lepton parity, resulting in their annihilation and the generation of a stochastic gravitational wave background potentially observable at different experiments.

What carries the argument

The accidental Z2 symmetry in the scalar potential, whose spontaneous breaking creates domain walls made unstable by explicit breaking terms allowed under the lepton parity from the seesaw.

If this is right

  • Dark matter remains stable through the existing lepton parity symmetry without requiring additional discrete symmetries.
  • Domain walls formed from Z2 breaking do not persist due to allowed explicit breaking, resolving potential cosmological issues.
  • The annihilation of these domain walls produces a stochastic gravitational wave background with characteristics observable by experiments such as LISA or SKA.
  • Neutrino masses are generated via the standard type I seesaw mechanism alongside these features.

Where Pith is reading between the lines

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

  • The model suggests that residual symmetries from neutrino mass generation can naturally address dark matter stability and cosmological defects.
  • Similar accidental symmetries in other extensions could lead to testable gravitational wave signals.
  • Future observations of gravitational waves could constrain the parameters of lepton parity models.

Load-bearing premise

The scalar potential possesses an accidental Z2 symmetry whose spontaneous breaking produces domain walls that become unstable due to explicit Z2-breaking terms allowed by the lepton parity.

What would settle it

A specific pattern in the stochastic gravitational wave spectrum, such as a peak frequency and amplitude determined by the scale of the accidental Z2 breaking and the lepton parity violation, that matches or fails to match observations from pulsar timing arrays or space-based interferometers.

Figures

Figures reproduced from arXiv: 2508.02642 by Ernest Ma, Narendra Sahu, Partha Kumar Paul.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. GW spectrum is shown for BP1, BP2, BP3 and BP4 as mentioned in Table [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Allowed values of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

We propose a simple and predictive setup that connects neutrino masses, dark matter (DM), and gravitational waves. A minimal lepton parity DM scenario is considered where the residual symmetry $(-1)^L$ from the type I seesaw acts as the dark parity $D=(-1)^{L+2j}$, ensuring DM stability without imposing any new symmetry. A singlet Majorana fermion $S$ with even lepton parity serves as the DM candidate, interacting via a real scalar $\sigma$ which is also even lepton parity. The scalar potential possesses an accidental $\mathcal{Z}_2$ symmetry, whose spontaneous breaking gives rise to unstable domain walls (DW) in the presence of explicit $\mathcal{Z}_2$ breaking terms allowed by the lepton parity. The subsequent DW annihilation generates a stochastic gravitational wave (GW) background potentially observable at different GW 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.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a minimal extension of the Standard Model with a singlet Majorana fermion S and real scalar σ, both even under lepton parity. The residual (-1)^L symmetry from the type I seesaw is identified as the dark parity D = (-1)^{L+2j} that stabilizes S as dark matter without new imposed symmetries. The scalar potential is shown to possess an accidental Z2 symmetry whose spontaneous breaking produces domain walls; explicit Z2-breaking operators permitted by lepton parity render the walls unstable, with their annihilation generating a stochastic gravitational wave background potentially observable at experiments such as LISA or pulsar timing arrays.

Significance. If the construction holds, the work provides a simple, predictive link between neutrino masses, dark matter stability via residual symmetries, and gravitational wave signals from naturally unstable domain walls. The minimal field content and avoidance of additional discrete symmetries imposed by hand are positive features. The potential for observable GW signals adds phenomenological value, though quantitative predictions will depend on parameter choices fitted to data.

major comments (1)
  1. [§3 (scalar potential)] §3 (scalar potential): The central claim that explicit Z2-breaking operators (e.g., σ^3 or σ^5 terms) are allowed by lepton parity (-1)^L while breaking the accidental Z2 and preserving the dark parity D for S must be demonstrated explicitly. Please provide the lepton parity charge assignments for S and σ, verify that these operators do not violate D, and confirm they do not destabilize the DM candidate or neutrino sector. If such terms are forbidden or absent, the domain walls remain stable and the GW signal vanishes.
minor comments (2)
  1. [Introduction] Clarify the definition and origin of the quantum number j appearing in D = (-1)^{L+2j} in the introduction and model section.
  2. [§3] Add a brief table or explicit listing of all renormalizable and higher-dimensional operators allowed by lepton parity to make the accidental Z2 and its breaking transparent.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for explicit verification of the symmetry assignments. We address the major comment below and will revise the manuscript accordingly to improve clarity.

read point-by-point responses

  1. Referee: [§3 (scalar potential)] §3 (scalar potential): The central claim that explicit Z2-breaking operators (e.g., σ^3 or σ^5 terms) are allowed by lepton parity (-1)^L while breaking the accidental Z2 and preserving the dark parity D for S must be demonstrated explicitly. Please provide the lepton parity charge assignments for S and σ, verify that these operators do not violate D, and confirm they do not destabilize the DM candidate or neutrino sector. If such terms are forbidden or absent, the domain walls remain stable and the GW signal vanishes.

    Authors: We agree that an explicit demonstration strengthens the presentation. In the revised manuscript we will add the following clarification in §3. Both the Majorana fermion S and the real scalar σ are assigned even lepton parity, i.e., charge +1 under the Z_2 lepton parity (-1)^L. The dark parity is D = (-1)^{L+2j}. For the fermion S (j=1/2) this gives D(S)=-1, while for the scalar σ (j=0) one has D(σ)=+1. The operator σ^3 carries total lepton parity (+1)^3=+1 and is therefore allowed by lepton parity; under the accidental Z_2 (σ→-σ) it transforms to -σ^3 and thus breaks the accidental symmetry. The same holds for σ^5. Because these are purely scalar operators they do not couple to S and therefore cannot violate D for the dark-matter candidate. The type-I seesaw sector that generates the residual (-1)^L symmetry is likewise untouched by pure-scalar terms. We will insert a short paragraph containing the charge table and the above verification to make the argument fully explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained model construction

full rationale

The paper constructs a model by assigning lepton parity to fields in a type-I seesaw extension, identifying the residual (-1)^L as dark parity D for the singlet fermion S, and writing a scalar potential for even-parity fields that happens to be invariant under an additional accidental Z2 at renormalizable order. Explicit Z2-breaking operators are then permitted at higher dimension because they respect lepton parity. These steps are direct consequences of the field content and discrete symmetry assignments; no fitted parameter is relabeled as a prediction, no load-bearing premise reduces to a self-citation, and the stochastic GW spectrum follows from the subsequent DW dynamics without being equivalent to the input assumptions by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 2 invented entities

The construction rests on the type I seesaw, an accidental Z2 in the scalar potential, and the assumption that explicit breaking terms allowed by lepton parity suffice to render domain walls unstable; new particles are introduced without independent evidence.

free parameters (1)
  • masses and couplings of S and sigma
    Masses and interaction strengths of the dark-matter fermion and the mediating scalar must be chosen to satisfy relic-density and direct-detection constraints.
axioms (1)
  • domain assumption Type I seesaw mechanism generates the residual lepton parity symmetry (−1)^L
    Invoked to supply the dark parity without new discrete symmetries.
invented entities (2)
  • Singlet Majorana fermion S no independent evidence
    purpose: Dark matter candidate carrying even lepton parity
    Postulated new particle whose stability is protected by the residual symmetry.
  • Real scalar sigma no independent evidence
    purpose: Mediator for DM interactions and source of accidental Z2 symmetry
    Introduced to generate the domain-wall dynamics.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Imprint of matter-antimatter asymmetry on collapsing domain walls

    hep-ph 2026-04 unverdicted novelty 8.0

    Radiative corrections from an asymmetric Dirac fermion generate a bias that collapses domain walls, producing gravitational waves that encode the asymmetry level and temperature.

  2. Cosmological Probes of Lepton Parity Freeze-in Dark Matter: $\Delta N_{\rm eff}$ & Gravitational Waves

    hep-ph 2025-11 unverdicted novelty 5.0

    Lepton parity stabilizes a Majorana fermion as freeze-in dark matter produced via right-handed neutrino or Higgs decays, yielding detectable gravitational waves or ΔN_eff depending on scalar couplings.

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