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arxiv: 2506.23290 · v2 · submitted 2025-06-29 · ✦ hep-ph

Type II Seesaw Leptogenesis in a Majoron background

Maximilian Berbig This is my paper

Pith reviewed 2026-05-19 07:43 UTC · model grok-4.3

classification ✦ hep-ph
keywords leptogenesisType II SeesawMajoronbaryon asymmetrydark matterneutrino masseselectroweak triplet
0
0 comments X p. Extension

The pith

A coherent Majoron background enables spontaneous leptogenesis in the Type II Seesaw with a light triplet scalar.

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

This paper shows how leptogenesis can arise spontaneously in the Type II Seesaw model when the triplet scalar sits in a coherent Majoron background. Inverse decays of the Higgs into the triplet create a chemical potential that the triplet then passes to the leptons through its decays. The setup requires only one triplet scalar, which can be as light as 1 TeV, with its vacuum expectation value between roughly 1 keV and 1 MeV. In the UV completion that includes the Majoron, the same background can also produce the dark matter density through kinetic misalignment. The baryon asymmetry and dark matter can be generated together when the lepton number breaking scale lies between 10^5 and 10^8 GeV and the Majoron mass is between 1 micro-eV and 1 eV.

Core claim

The central discovery is that in the Type II Seesaw featuring an electroweak triplet scalar T in a coherent pseudo Nambu-Goldstone boson background from the Majoron, inverse Higgs-to-T decays generate a chemical potential for T that is transmitted to the lepton sector via the leptonic decays of T. This allows the mechanism to function with a single triplet as light as 1 TeV and v_T in the O(1 keV) to O(1 MeV) window, while the Majoron explains dark matter and enables cogenesis of dark matter and the baryon asymmetry for O(10^5 GeV) < v_σ < O(10^8 GeV) and O(1 eV) > m_j > O(1 μeV).

What carries the argument

The wash-in scenario using inverse Higgs boson decays to the triplet scalar to produce a chemical potential transmitted through T decays in the presence of a coherent Majoron background.

If this is right

  • The doubly charged component of the triplet can decay into both same sign di-leptons and same sign W boson pairs with appreciable rates.
  • Cogenesis of dark matter and baryon asymmetry is possible in the stated parameter windows for the lepton number breaking scale and Majoron mass.
  • The mechanism requires only a single electroweak triplet scalar.
  • Potential experimental distinction from inflationary scenarios through the triplet decay modes.

Where Pith is reading between the lines

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

  • Similar coherent backgrounds might be used in other neutrino mass models to generate asymmetries without high-scale physics.
  • Future collider experiments could search for the doubly charged scalar decays in the indicated vev range to test the proposal.
  • Measurements of dark matter properties could constrain the kinetic misalignment contribution from the Majoron.

Load-bearing premise

The coherent pseudo Nambu-Goldstone boson background must exist long enough for inverse decays to generate the chemical potential for the triplet.

What would settle it

If the doubly charged triplet scalar is not observed to decay into both dileptons and W pairs, or if the Majoron mass and scale do not match the required ranges for dark matter, the mechanism would be disfavored.

read the original abstract

We discuss spontaneous Leptogenesis in the Type II Seesaw model of neutrino masses featuring an electroweak triplet scalar $T$ in a coherent pseudo Nambu-Goldstone boson (pNGB) background. In the "wash-in" scenario the inverse decays of Higgs bosons to $T$ generate a chemical potential for the triplet that is then transmitted to the lepton sector via the leptonic decays of $T$. Our mechanism works with a single triplet that can be as light as 1 TeV, and has a vacuum expectation value $v_T$ in the window $\mathcal{O}(1~\text{keV})<v_T<\mathcal{O}(1~\text{MeV})$. This range of $v_T$ can lead to appreciable decays of the triplet's doubly charged component into both same sign di-leptons and same sign pairs of $W$-bosons, which could potentially allow for an experimental distinction from a recently proposed inflationary Type II Seesaw Affleck-Dine scenario preferring the leptonic mode. In the "singlet-doublet-triplet Majoron" UV-completion of the Type II Seesaw model, the required pNGB is automatically included in the form of the Majoron, that originates from the phase of the lepton number breaking singlet scalar. The coherent motion of the Majoron can furthermore explain the dark matter relic abundance via the kinetic misalignment mechanism. Cogenesis of dark matter and the baryon asymmetry can work for a lepton number breaking scale of $\mathcal{O}(10^5\;\text{GeV})<v_\sigma< \mathcal{O}(10^8~\text{GeV})$ and a Majoron mass of $\mathcal{O}(1~\text{eV}) > m_j >\mathcal{O}(1~\mu\text{eV})$.

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 manuscript proposes spontaneous leptogenesis in the Type II Seesaw model with an electroweak triplet scalar T placed in a coherent pseudo Nambu-Goldstone boson (Majoron) background. In the wash-in scenario, inverse Higgs decays HH → T generate a chemical potential for the triplet that is transmitted to the lepton sector through T → ℓℓ decays. The mechanism operates with a single triplet as light as 1 TeV and v_T in the window O(1 keV) < v_T < O(1 MeV), allowing the doubly-charged component to decay into both same-sign dileptons and same-sign WW pairs. In the singlet-doublet-triplet Majoron UV completion, the Majoron also accounts for the dark matter relic density via kinetic misalignment, with viable cogenesis for O(10^5 GeV) < v_σ < O(10^8 GeV) and O(1 μeV) < m_j < O(1 eV).

Significance. If the wash-in chemical-potential transfer survives in the Majoron background, the work would provide a unified explanation of the baryon asymmetry and dark matter abundance within a minimal Type II Seesaw extension that includes the Majoron automatically. The scenario permits a testable light triplet and offers a potential experimental discriminator via the branching ratios of the doubly-charged scalar. The combination of leptogenesis with kinetic-misalignment dark matter is a novel aspect that could be of interest to the hep-ph community.

major comments (2)
  1. [Abstract (wash-in scenario)] Abstract (wash-in scenario paragraph): the central claim that inverse HH → T decays build a net chemical potential μ_T which is then transmitted to leptons via T decays requires explicit demonstration that the coherent Majoron background does not introduce additional L-violating processes capable of erasing the asymmetry before sphaleron conversion. No rate equations or Boltzmann-equation analysis are referenced in the provided description.
  2. [Abstract (parameter windows)] Parameter windows: the intervals O(1 keV) < v_T < O(1 MeV), O(10^5 GeV) < v_σ < O(10^8 GeV) and O(1 μeV) < m_j < O(1 eV) are stated to simultaneously reproduce the observed baryon asymmetry and DM density. The manuscript should clarify whether these ranges follow from independent constraints or are chosen to fit both observables, and provide a scan or sensitivity analysis showing the mechanism is not finely tuned.
minor comments (2)
  1. [Abstract] The abstract states that the doubly-charged component can decay into both dileptons and WW pairs, but quantitative branching ratios or partial widths as functions of v_T would improve clarity and allow direct comparison with the referenced inflationary Affleck-Dine scenario.
  2. [Notation] Notation for the lepton-number-breaking scale (v_σ) and Majoron mass (m_j) is consistent, but the triplet VEV is written both as v_T and occasionally without subscript; uniform usage throughout would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us improve the presentation. We address each major comment point by point below.

read point-by-point responses

  1. Referee: Abstract (wash-in scenario paragraph): the central claim that inverse HH → T decays build a net chemical potential μ_T which is then transmitted to leptons via T decays requires explicit demonstration that the coherent Majoron background does not introduce additional L-violating processes capable of erasing the asymmetry before sphaleron conversion. No rate equations or Boltzmann-equation analysis are referenced in the provided description.

    Authors: We agree that an explicit demonstration strengthens the argument. The manuscript outlines that the Majoron pNGB background is slowly varying and its L-violating interactions with the lepton sector are suppressed by the small lepton-number breaking scale and the pNGB nature of the field. To address the referee's concern directly, the revised manuscript includes order-of-magnitude estimates comparing the relevant Majoron-induced rates to the Hubble expansion and sphaleron conversion timescales in the temperature regime of interest, showing that the generated chemical potential is preserved. We also reference analogous Boltzmann treatments from spontaneous leptogenesis models with light pNGBs. This addition clarifies the robustness of the wash-in transfer without altering the core mechanism or results. revision: yes

  2. Referee: Parameter windows: the intervals O(1 keV) < v_T < O(1 MeV), O(10^5 GeV) < v_σ < O(10^8 GeV) and O(1 μeV) < m_j < O(1 eV) are stated to simultaneously reproduce the observed baryon asymmetry and DM density. The manuscript should clarify whether these ranges follow from independent constraints or are chosen to fit both observables, and provide a scan or sensitivity analysis showing the mechanism is not finely tuned.

    Authors: These intervals originate from independent constraints rather than joint fitting. The v_T window follows from Type II Seesaw neutrino mass requirements, electroweak precision bounds, and the condition that the doubly-charged scalar has appreciable branching ratios to both same-sign dileptons and WW pairs. The v_σ and m_j ranges are fixed by the kinetic misalignment mechanism to reproduce the observed dark matter relic density. Leptogenesis efficiency holds across this broad interval due to the wash-in nature of the scenario. In the revised manuscript we have explicitly stated the independent origins of each window and added a qualitative sensitivity discussion showing that the baryon asymmetry varies smoothly and remains consistent with observations for parameter variations within the quoted ranges, confirming the absence of fine-tuning. revision: yes

Circularity Check

0 steps flagged

No significant circularity; viable parameter windows derived from external observables

full rationale

The paper presents a leptogenesis mechanism via wash-in from inverse Higgs-to-triplet decays in a coherent Majoron background, with transmission to leptons via T decays, alongside kinetic misalignment for DM. The quoted intervals for v_T, v_σ and m_j are explicitly the ranges in which the computed asymmetries and relic density can simultaneously match the observed baryon asymmetry and DM abundance. This is standard parameter-space exploration against external benchmarks (observed Y_B and Ω_DM), not a self-referential fit where an output is renamed as input or where the central chemical-potential generation reduces to the same equations by construction. No self-citation load-bearing step, no ansatz smuggled via prior work, and no uniqueness theorem invoked. The derivation of μ_T from inverse decays and its transmission remains independent of the specific numerical windows chosen to satisfy observations.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 1 invented entities

The scenario rests on the Type II Seesaw as the neutrino-mass model, the existence of a coherent pNGB background, and three parameter windows chosen to achieve the desired cosmological outcomes.

free parameters (3)
  • v_T = O(1 keV) < v_T < O(1 MeV)
    Window O(1 keV) to O(1 MeV) chosen so that the triplet produces both leptonic and WW decays while enabling the wash-in process.
  • v_sigma = O(10^5 GeV) < v_sigma < O(10^8 GeV)
    Lepton-number breaking scale window selected to allow cogenesis of baryon asymmetry and dark matter.
  • m_j = O(1 eV) > m_j > O(1 μeV)
    Majoron mass window chosen to reproduce the observed dark matter relic density via kinetic misalignment.
axioms (2)
  • domain assumption Type II Seesaw mechanism generates neutrino masses via an electroweak triplet scalar T.
    Core model assumption stated in the title and abstract.
  • ad hoc to paper A coherent pNGB background generates a chemical potential for the triplet via inverse Higgs decays.
    Introduced specifically for the spontaneous leptogenesis scenario.
invented entities (1)
  • Majoron no independent evidence
    purpose: Supplies the coherent pNGB background for leptogenesis and accounts for dark matter via kinetic misalignment.
    Arises automatically from the phase of the lepton-number breaking singlet scalar in the UV completion.

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