TeV-scale unification of light dark matter and neutrino mass

This paper demonstrates that TeV-scale heavy neutral leptons in an inverse-seesaw model can simultaneously generate neutrino masses and produce light pseudo-Nambu-Goldstone boson dark matter via freeze-in, establishing a predictive link between neutrino mass generation, dark matter abundance, and decay signatures testable at future colliders and neutrino detectors.

The Gist

The Big Mystery: Two Missing Pieces of the Universe

Imagine the universe is a giant jigsaw puzzle. Scientists have most of the pieces, but two huge ones are missing:

1. Neutrino Mass: We know these ghostly particles exist, but why are they so incredibly light? It’s like finding a feather that weighs less than a single atom.
2. Dark Matter: We know invisible "stuff" holds galaxies together, but we have no idea what it is made of. It’s like knowing a room is full of furniture, but you can’t see or touch any of it.

Usually, physicists treat these as two separate mysteries. This paper proposes a bold idea: What if they are actually connected?

The Main Character: The "Heavy Hubs"

To solve this, the authors introduce a new type of particle called a Heavy Neutral Lepton (HNL).

• The Analogy: Think of the HNL as a "Heavy Hub" or a "Big Brother" to the neutrinos.
• The Scale: These particles are heavy (about 1,000 times the mass of a proton), but not impossibly heavy. They exist at the "TeV scale," which means we might be able to create them in giant particle smashers like the Large Hadron Collider (LHC).

The Three-Way Connection (The Triangle)

The paper argues that these Heavy Hubs connect three different things in a perfect triangle. If you find one, you prove the others exist.

1. Neutrino Mass: The Heavy Hubs interact with regular neutrinos to give them their tiny weight. It’s like a seesaw: the heavier the Hub, the lighter the neutrino becomes.
2. Dark Matter Creation: In the early universe, these Heavy Hubs didn't just sit there. They slowly "leaked" energy to create Dark Matter.
   • The Analogy: Imagine a bucket (Dark Matter) being filled by a slow drip from a tap (the Heavy Hubs). This process is called "freeze-in." It’s not a violent explosion; it’s a slow, steady accumulation.
3. Dark Matter Decay: Dark Matter is usually thought to be perfectly stable. But in this model, the Heavy Hubs act as a bridge that allows Dark Matter to slowly decay back into neutrinos.
   • The Analogy: Think of Dark Matter as a very slow-burning candle. It lasts for billions of years, but eventually, it turns into smoke (neutrinos).

The "Goldstone" Ghost

The Dark Matter particle in this theory is special. It comes from a broken symmetry in the laws of physics (specifically, "Lepton Number").

• The Analogy: Imagine a smooth sheet of fabric (symmetry). If you rip it, a ripple forms. That ripple is a particle called a Majoron.
• Usually, this ripple has no weight. But the authors add a tiny "kink" to the fabric. This gives the ripple just enough weight to be Dark Matter, but not so much that it becomes heavy. It’s a "light" Dark Matter particle (less than the mass of a proton).

Why This Matters (The Prediction)

This isn't just theory; it makes specific predictions that scientists can test.

1. The Weight Limit: Because the math is so tight, the Dark Matter must be light (less than 1 GeV). If it were heavier, the math wouldn't work.
2. The Signal: Since Dark Matter decays into neutrinos, massive underground detectors (like Hyper-Kamiokande, DUNE, and JUNO) should be able to catch these "ghostly" neutrinos coming from space.
3. The Collider: If we build a machine to find the Heavy Hubs (at the LHC), we should also see the neutrino signals from Dark Matter.

The Bottom Line

This paper suggests that the universe is more interconnected than we thought. The same heavy particles that explain why neutrinos have mass are also the factory that made Dark Matter, and the mechanism that lets Dark Matter slowly die.

The Takeaway: If we find the Heavy Hubs in a collider, we should look for a specific whisper from Dark Matter in our neutrino detectors. It’s a unified theory that links the very small (neutrinos), the invisible (dark matter), and the very heavy (collider physics) into one neat package.

Technical Summary

Here is a detailed technical summary of the paper "TeV-scale unification of light dark matter and neutrino mass."

1. Problem Statement

The paper addresses two fundamental open questions in particle physics and cosmology: the origin of neutrino masses and the identity of Dark Matter (DM).

• Neutrino Mass: While neutrino oscillation experiments confirm neutrinos are massive, the mechanism behind their tiny masses remains unclear. The Inverse Seesaw mechanism is a viable candidate that allows for Heavy Neutral Leptons (HNLs) at the TeV scale, making them accessible to colliders. However, standard Inverse Seesaw models do not naturally provide a Dark Matter candidate.
• Dark Matter: The particle nature of DM is unknown. Pseudo-Nambu-Goldstone bosons (pNGBs), such as Majorons arising from spontaneous lepton number breaking, are well-motivated DM candidates. However, in existing constructions, the parameters governing neutrino mass, DM relic abundance, and DM lifetime are typically treated as independent inputs, lacking a direct connection to collider-accessible neutrino mass models.
• The Gap: There is a need for a unified, predictive framework that links neutrino mass generation, DM production, and DM decay, specifically within a TeV-scale scenario testable at current and future experiments.

2. Methodology

The authors propose a minimal extension of the Standard Model (SM) based on the Inverse Seesaw mechanism augmented by a global $U(1)_L$ (Lepton Number) symmetry.

• Field Content: The model introduces three right-handed fermions ($N_R$), three left-handed fermions ($S_L$), and a complex singlet scalar ($\phi$).
• Symmetry Breaking:
  • Spontaneous: The scalar $\phi$ acquires a vacuum expectation value (VEV), $v_\phi$, spontaneously breaking the global $U(1)_L$ symmetry. This generates a massless Nambu-Goldstone boson (NGB).
  • Explicit (Soft): A soft-breaking term ($V_{soft} \propto \text{Re}(\phi)$) is added to the scalar potential. This gives the NGB a small physical mass, turning it into a pseudo-Nambu-Goldstone boson (pNGB), denoted as $\chi$. This $\chi$ serves as the DM candidate.
• Mechanisms:
  • Neutrino Mass: Generated via the Inverse Seesaw mechanism involving $N_R$ and $S_L$. The active neutrino mass is suppressed by the small lepton-number violating parameter $\mu_S$.
  • DM Production: The DM ($\chi$) is produced via the freeze-in mechanism from the annihilation of thermal HNLs ($N N \to \chi \chi$). This is a non-thermal production process.
  • DM Decay: The DM particle decays into active neutrinos ($\chi \to \nu \nu$). This decay is mediated by the same HNLs that generate neutrino masses.

3. Key Contributions

• Unified Framework: The paper establishes a coherent framework where the same TeV-scale HNLs responsible for neutrino mass generation also produce the DM (via freeze-in) and mediate its decay.
• Predictive Correlations: Unlike previous models, this framework creates tight correlations between three sectors: (i) neutrino masses, (ii) DM relic abundance, and (iii) DM lifetime. These cannot be chosen independently; they are determined by the same underlying parameters (Yukawa couplings, VEVs, and mass scales).
• Sub-GeV DM Prediction: For collider-accessible TeV-scale HNLs, the constraints on observed relic density and DM lifetime force the DM mass ($m_\chi$) into the sub-GeV regime.
• Experimental Bridge: The model provides a concrete link between high-energy collider physics (HNL searches), cosmology (relic density), and neutrino astronomy (DM decay signals).

4. Results

• Mass Spectrum:
  • Active neutrino mass: $m_\nu \simeq \mu_S (m_D/m_N)^2$.
  • DM Mass ($m_\chi$): Originates from the soft-breaking term.
  • HNL Mass ($m_N$): Set at the TeV scale.
• DM Lifetime: The decay width $\Gamma_{\chi \to \nu\nu}$ is extremely suppressed by the small neutrino mass and the large symmetry-breaking scale $v_\phi$. The resulting lifetime satisfies experimental lower bounds from Super-Kamiokande.
• Relic Abundance: The correct DM relic density ($\Omega_{DM} h^2 \approx 0.12$) is achieved through the freeze-in annihilation of HNLs. The yield is analytically derived and depends on $m_N$, $v_\phi$, and the scalar mass $m_\rho$.
• Parameter Space Constraints:
  • For $m_N \sim \mathcal{O}(\text{TeV})$, the DM mass $m_\chi$ is constrained to be sub-GeV.
  • Regions $m_\chi \gtrsim 2 \text{ GeV}$ are excluded by Super-Kamiokande data.
  • Regions $30 \text{ MeV} \lesssim m_\chi \lesssim 60 \text{ MeV}$are ruled out by SK$\bar{\nu}_e$ flux data.
  • The allowed sub-GeV region is testable at next-generation detectors.
• Observables: The model predicts observable neutrino signals from DM decay at next-generation neutrino detectors such as Hyper-Kamiokande, DUNE, and JUNO.

5. Significance

• Testability: The framework is highly testable. A discovery of TeV-scale HNLs at colliders (e.g., LHC, muon colliders) would imply a correlated prediction for a neutrino signal from DM decay.
• Multi-Front Approach: It allows for simultaneous testing via collider searches for HNLs and neutrino telescopes searching for DM decay signatures.
• Theoretical Economy: It solves the "independent input" problem of previous pNGB DM models by deriving DM properties directly from the neutrino mass generation sector.
• Cosmological Viability: The use of a linear soft-breaking term allows the model to potentially escape the cosmic domain wall catastrophe while bypassing severe constraints from DM direct detection experiments due to suppressed scattering amplitudes.

In conclusion, this work demonstrates that a minimal extension of the inverse seesaw model can simultaneously explain neutrino masses and Dark Matter phenomenology, creating a predictive bridge between collider physics, cosmology, and neutrino astronomy.