Type II Seesaw Leptogenesis in a Majoron background

This paper proposes a mechanism for spontaneous Leptogenesis within the Type II Seesaw model, where a coherent pseudo Nambu-Goldstone boson background enables a "wash-in" scenario that generates the baryon asymmetry via inverse decays of Higgs bosons into a light electroweak triplet scalar with a keV-scale vacuum expectation value.

The Gist

The Big Picture: Solving Three Cosmic Mysteries at Once

Imagine the universe has three massive puzzles that scientists have been trying to solve separately:

1. Why do neutrinos have mass? (They are tiny ghost particles that were thought to be weightless).
2. Why is there more matter than antimatter? (If the Big Bang created equal amounts, they should have annihilated each other, leaving nothing but light. But we are here, made of matter).
3. What is Dark Matter? (The invisible stuff holding galaxies together).

This paper proposes a single, elegant machine—a "Cosmic Swiss Army Knife"—that solves all three problems simultaneously using a specific type of particle called a Triplet and a ghostly field called a Majoron.

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The Characters in Our Story

To understand the mechanism, let's meet the cast of characters:

• The Triplet (The Heavy Hauler): Imagine a heavy truck (the Triplet particle) that can carry cargo. In this model, it's a new type of particle that interacts with the Higgs field (the field that gives other particles mass).
• The Majoron (The Spinning Top): This is a ghostly, invisible particle associated with a hidden symmetry of the universe. Think of it as a giant, invisible spinning top that has been rotating since the early universe.
• The Lepton (The Passenger): These are the particles (like electrons and neutrinos) that make up the "lepton" family.

The Mechanism: How It Works

1. The "Wash-In" Effect (Creating the Imbalance)

Usually, to create an imbalance between matter and antimatter, you need a chaotic, out-of-control explosion (like a car crash). But this paper suggests a smoother process called "Spontaneous Wash-In."

• The Analogy: Imagine a river (the Majoron) flowing very fast. The water is moving so quickly that it creates a current.
• The Process: The Triplet particle (the truck) is sitting in this fast-flowing river. Because the river is spinning and moving, it creates a "chemical potential"—basically, a pressure difference.
• The Result: The Triplet decays, but because of the spinning river, it doesn't decay equally into matter and antimatter. It preferentially dumps leptons (matter) into the universe. It's like a faucet that, due to the spinning water, only lets out hot water and no cold water.

This process is called "Wash-In" because instead of washing away an asymmetry (which usually happens in other theories), the background field actively washes in a new asymmetry.

2. The "Seesaw" (Explaining Neutrino Mass)

The paper uses the Type II Seesaw mechanism.

• The Analogy: Imagine a playground seesaw. On one end is a very heavy weight (the Triplet). On the other end is a tiny feather (the neutrino).
• The Physics: Because the heavy Triplet is so massive, it pushes the neutrino side up, making the neutrino's effective mass incredibly small. This explains why neutrinos are so light compared to other particles.

3. The Dark Matter Connection (The Kinetic Misalignment)

What happens to the spinning Majoron (the top) after it does its job?

• The Analogy: Imagine a spinning top that slows down but never quite stops. It keeps spinning, but its energy is spread out over the whole universe.
• The Result: This slow, coherent spinning motion of the Majoron field is the Dark Matter. It doesn't interact with light, it's invisible, and it has the right amount of "weight" to hold galaxies together. This is called Kinetic Misalignment.

The "Sweet Spot" (Why This Model is Special)

Most theories require these particles to be impossibly heavy (heavier than anything we can build in a lab) or impossibly light. This paper finds a "Goldilocks" zone:

• The Triplet: It can be as light as 1 TeV (about the mass of a proton, but 1,000 times heavier). This is light enough that we might actually find it in particle colliders like the Large Hadron Collider (LHC) soon!
• The Majoron: It is incredibly light (like a feather), but heavy enough to be stable.

How to Tell This Model Apart from Others

The author suggests a way to test if this is the right theory.

• The "Double-Decker" Decay: The Triplet particle has a "double-charged" version (like a double-decker bus).
  • Old Theory: Predicts this bus mostly drops off leptons (electrons/muons).
  • This Theory: Predicts that depending on the exact settings, this bus might drop off pairs of W-bosons (heavy force carriers) just as often as it drops off leptons.
• The Test: If we build a collider and see these double-charged particles decaying into W-bosons, it's a huge hint that this specific "Majoron background" theory is correct.

Summary

This paper proposes a beautiful, unified story:

1. A spinning invisible field (Majoron) acts as a cosmic current.
2. This current pushes a new heavy particle (Triplet) to create more matter than antimatter (Leptogenesis).
3. The heavy particle also explains why neutrinos are light (the Seesaw).
4. The spinning field itself becomes the Dark Matter that holds the universe together.

It's a theory that is testable (we might find the Triplet soon) and solves the three biggest mysteries of cosmology with a single, coherent mechanism.

Technical Summary

1. Problem Statement

The paper addresses three fundamental open questions in particle physics and cosmology simultaneously:

1. Neutrino Mass Origin: Explaining the smallness of neutrino masses via the Type II Seesaw mechanism.
2. Baryon Asymmetry of the Universe (BAU): Explaining the observed matter-antimatter asymmetry ($\Delta B \approx 8.76 \times 10^{-11}$) without requiring the extremely high mass scales ($m_T \gtrsim 10^{10}$ GeV) typically needed for thermal Leptogenesis in the Type II Seesaw.
3. Dark Matter (DM): Identifying a viable Dark Matter candidate within the same framework.

Specific Challenges:

• High Mass Scale: Standard Type II Seesaw Leptogenesis usually requires triplet masses $m_T > 10^{10}$ GeV to generate sufficient CP violation, making the model untestable at colliders.
• Triplet VEV Constraints: The triplet vacuum expectation value (VEV), $v_T$, is tightly constrained by electroweak precision data and lepton flavor violation (LFV).
• Majoron Constraints: Models with a Majoron (the Nambu-Goldstone boson of lepton number breaking) often face constraints from $Z$-boson decays (if the Majoron is part of a triplet) or overclosure of the universe.

2. Methodology and Theoretical Framework

The author proposes a "Spontaneous Wash-In Leptogenesis" scenario within a Singlet-Doublet-Triplet Majoron model.

A. The Model

• Field Content:
  • Standard Model (SM) fields.
  • An electroweak scalar triplet $T$ (hypercharge $Y=1$, lepton number $L=-2$).
  • A complex singlet scalar $\sigma$ (lepton number $L=2$) which breaks $U(1)_L$ spontaneously.
• Mechanism:
  • The lepton number breaking scale $v_\sigma$ generates an effective coupling $\kappa = \lambda_{\sigma HT} v_\sigma / \sqrt{2}$, inducing a small triplet VEV $v_T \propto v_\sigma v_H^2 / m_T^2$.
  • The phase of $\sigma$ corresponds to the Majoron ($j$). Explicit breaking of $U(1)_L$ (via higher-dimensional operators) gives the Majoron a small mass $m_j$, making it a pseudo-Nambu-Goldstone boson (pNGB).
• Majoron Dynamics:
  • The Majoron field undergoes coherent rotation in the early universe, driven by mechanisms like the Affleck-Dine (AD) mechanism or other rotation sources.
  • This rotation creates a time-dependent background velocity $\dot{\theta}$ (where $\theta = j/v_\sigma$).

B. Leptogenesis Mechanism (Wash-In)

Unlike standard thermal Leptogenesis (which relies on out-of-equilibrium decays and CP violation in the decay amplitudes), this scenario uses Spontaneous Baryogenesis:

1. CPT Violation: The coherent motion of the Majoron ($\dot{\theta} \neq 0$) acts as a chemical potential background that spontaneously violates CPT.
2. Chemical Potential Shift: The Majoron rotation shifts the chemical potentials of particles carrying lepton number:
   • $\mu_L \to \mu_L - \dot{\theta}/2$
   • $\mu_T \to \mu_T + \dot{\theta}$
   • $\mu_H$ (Higgs) remains unshifted as it carries no lepton number.
3. Wash-In Process:
   • The process $HH \to T$ (inverse decay of Higgses) becomes sensitive to $\dot{\theta}$ because $\mu_H$ is unshifted while $\mu_T$ is shifted. This generates a non-zero chemical potential for the triplet $T$.
   • The triplet then decays via $T \to L^\dagger L^\dagger$, transferring the asymmetry to the lepton sector.
   • Crucially, this works with a single generation of triplets and does not require CP-violating phases in the Yukawa couplings.

C. Dark Matter Production

• The Majoron rotation is not damped by the Leptogenesis process (negligible back-reaction).
• The Majoron acts as Dark Matter via the Kinetic Misalignment Mechanism (KMM). The initial kinetic energy of the rotating field redshifts slower than radiation, eventually trapping the field and converting kinetic energy into mass energy, reproducing the observed relic abundance.

3. Key Contributions

1. Low-Scale Leptogenesis with a Single Triplet:

   • The paper demonstrates that Leptogenesis can occur with a triplet mass as low as $m_T \sim 1$ TeV, accessible to current and future colliders (LHC, FCC).
   • It eliminates the need for quasi-degenerate triplets (resonant Leptogenesis) or multiple generations.

2. Novel Parameter Space for $v_T$:

   • The model predicts a specific window for the triplet VEV: $O(1 \text{ keV}) < v_T < O(1 \text{ MeV})$.
   • This range is distinct from the "Inflationary Affleck-Dine" Type II Seesaw models (which predict $v_T < 8.5$ keV) and standard thermal scenarios.

3. Cogenesis of DM and Baryon Asymmetry:

   • The framework unifies the origin of neutrino masses, baryon asymmetry, and dark matter.
   • The Majoron serves as the DM candidate, produced via KMM, with a mass range $O(1 \text{ eV}) > m_j > O(1 \mu\text{eV})$ and a lepton number breaking scale $O(10^5 \text{ GeV}) < v_\sigma < O(10^8 \text{ GeV})$.

4. Experimental Discrimination:

   • The paper provides clear signatures to distinguish this model from other non-thermal Type II Seesaw scenarios based on the decay modes of the doubly charged scalar ($h^{\pm\pm}$).

4. Key Results and Constraints

A. Parameter Space Viability

• Strong Wash-In Regime: Both inverse decays ($L^\dagger L^\dagger \leftrightarrow T$ and $HH \leftrightarrow T$) are in equilibrium. This requires:
  $$8.5 \text{ keV} \sqrt{\frac{1 \text{ TeV}}{m_T}} < v_T < 277 \text{ keV} \sqrt{\frac{1 \text{ TeV}}{m_T}} \sqrt{\frac{m_\nu^2}{2.65 \times 10^{-3} \text{ eV}^2}}$$
• Weak Wash-In Regime: One rate is out of equilibrium. This allows for a broader range: $O(1 \text{ keV}) < v_T < O(1 \text{ MeV})$.
• Constraints Satisfied:
  • Electroweak Precision: $v_T < 7$ GeV (satisfied).
  • Lepton Flavor Violation: The predicted rates for $\mu \to e\gamma$ and $\mu-e$ conversion are below current and projected limits (MEG, Mu3e, COMET) for the viable $v_T$ range.
  • Chiral Hypermagnetic Instability: The model avoids overproduction of baryon asymmetry via this instability for the derived parameters.
  • Dark Radiation: Thermalization of Majorons is avoided, keeping $\Delta N_{eff}$ within Planck limits.

B. Phenomenological Signatures

• Triplet Decays: The doubly charged scalar $h^{\pm\pm}$ decays into either same-sign dileptons ($l^\pm l^\pm$) or same-sign $W$ bosons ($W^\pm W^\pm$).
  • The branching ratio depends on $v_T$.
  • For $v_T > 40$ keV, the $W^\pm W^\pm$ mode dominates.
  • For $v_T < 40$ keV, the $l^\pm l^\pm$ mode dominates.
• Distinction from Competing Models:
  • Vs. Inflationary Affleck-Dine (Refs [52-55]): Those models require $v_T < 8.5$ keV, predicting dominant $l^\pm l^\pm$ decays. The proposed model allows $v_T$ up to MeV, allowing dominant $W^\pm W^\pm$ decays.
  • Vs. Resonant Leptogenesis: Resonant scenarios require two nearly degenerate triplets. This model works with a single triplet.

C. Dark Matter Properties

• The Majoron is stable on cosmological timescales ($\tau_j > 250$ Gyr) for the preferred parameters.
• Direct detection via electron recoil is suppressed for sub-eV Majorons but becomes relevant for $v_T \sim O(1 \text{ GeV})$, a region largely ruled out by other constraints.
• Indirect detection (decay to photons/neutrinos) is suppressed due to the small couplings ($1/v_\sigma$).

5. Significance

This work presents a minimal and testable solution to the hierarchy of neutrino masses, the baryon asymmetry, and dark matter.

• Testability: Unlike high-scale seesaw models, this scenario predicts a TeV-scale triplet that can be discovered at the LHC or future colliders.
• Model Discrimination: The specific prediction of the $v_T$ window allows experimentalists to distinguish between different non-thermal Leptogenesis mechanisms by measuring the decay branching ratios of the doubly charged Higgs.
• Unified Framework: It successfully integrates the Majoron (as DM) and the Type II Seesaw without requiring fine-tuned CP phases or multiple heavy generations, relying instead on the coherent dynamics of the early universe.

In summary, the paper establishes that Spontaneous Wash-In Leptogenesis in a Majoron background is a robust, low-scale mechanism that connects the physics of neutrino masses, baryogenesis, and dark matter, offering concrete experimental signatures for the next generation of particle physics experiments.