⚛️ high-energy theory

Quasi-Dirac fermion: A source of neutrino mass and dark matter

This paper proposes that TeV-scale quasi-Dirac fermions, arising from lepton-symmetry violations in unified theories, simultaneously generate small radiative neutrino masses and provide a stable dark matter candidate, with their tiny mass splitting ensuring consistency with experimental constraints on dark matter detection and charged lepton flavor violation.

Original authors: Nguyen Thi Nguyet Nga, Nguyen Huy Thao, Phung Van Dong

Published 2026-03-16

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CC BY 4.0

Original authors: Nguyen Thi Nguyet Nga, Nguyen Huy Thao, Phung Van Dong

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: Two Missing Pieces of the Puzzle

Imagine the Standard Model of physics as a giant, incredibly detailed LEGO castle. It explains almost everything we see in the universe: stars, planets, and the atoms inside us. However, there are two missing bricks that the castle doesn't have:

Neutrino Mass: We know tiny particles called neutrinos exist, but for a long time, we thought they were weightless. Experiments proved they actually have a tiny, tiny mass. The current castle doesn't explain how they get this weight.
Dark Matter: We know there is invisible "stuff" holding galaxies together, but we don't know what it is. The current castle has no room for this invisible guest.

Previous attempts to fix the castle (like the "Seesaw Mechanism") tried to add a heavy new brick to explain the neutrino weight. But this created a new problem: to make the math work, the new brick had to be so weakly connected to the rest of the castle that it couldn't possibly be the Dark Matter we are looking for. It was like trying to build a bridge with a rope that is too weak to hold a person.

The New Solution: The "Quasi-Dirac" Twin

The authors of this paper propose a clever new design. Instead of adding a single, heavy brick, they introduce a pair of twins who are almost, but not quite, identical.

1. The "Quasi-Dirac" Twins

Imagine you have two twins, N1 and N2.

In a normal world, they would be exact opposites (like a particle and its anti-particle).
In this new model, they are "Quasi-Dirac" twins. They are so similar that they act like a single unit, but there is a tiny, tiny difference between them (like one twin having a mole on the left cheek and the other on the right).

This tiny difference is the key. Because they are so similar, they cancel each other out in most calculations. But because they aren't exactly the same, that tiny leftover difference is what gives the neutrino its small mass.

The Analogy: Think of a seesaw where the two sides are almost perfectly balanced. If you put a heavy rock on one side, the seesaw tips wildly. But if you have two heavy rocks that are almost the same weight, the seesaw stays mostly flat. The tiny difference in weight is what causes the slight wobble we see (the neutrino mass).

2. Solving the Neutrino Mystery

In previous models, to get the neutrino mass small enough, the connection between the new particles and the old ones had to be incredibly weak (like a whisper). This made it impossible for these particles to be Dark Matter.

In this new "Quasi-Dirac" model, the twins cancel out most of the mass effect. This means the connection (the "whisper") can actually be a loud shout (a strong connection).

Result: We can explain the tiny neutrino mass without needing the connection to be impossibly weak. This makes the model much more realistic.

3. Solving the Dark Matter Mystery

Now, let's look at the Dark Matter candidate. In this model, there is a new particle (let's call it A, a scalar particle) that is stable and invisible.

The Abundance Problem: Dark Matter needs to exist in just the right amount in the universe. Too much, and the universe collapses; too little, and galaxies fly apart.
The Solution: The authors show that particle A can annihilate (destroy itself) with other particles in the early universe at just the right rate to leave behind the perfect amount of Dark Matter we see today.
The Detection Problem: Scientists are trying to catch Dark Matter by seeing it bounce off normal atoms. Previous models predicted it would bounce too hard (violating experimental limits).
The Fix: Because the "twins" (N1 and N2) are so similar, they create a "shield" that prevents the Dark Matter from bouncing off atoms too violently. It allows the Dark Matter to interact just enough to be detected, but not so much that it breaks the rules of current experiments.

The "Lepton-Like" Rule

Why do these twins exist? The paper suggests a new "rule of the universe" (a symmetry).

Imagine a rule that says, "Particles must come in pairs to keep the balance."
If you try to break this rule (by making the twins too different), the universe gets messy.
Because the rule is so strict, the twins must be almost identical. This strictness is what naturally creates the "Quasi-Dirac" state, solving the math problems without needing to fine-tune numbers by hand.

Why This Matters

This paper is like finding a new blueprint for the LEGO castle that fixes two broken windows with a single, elegant piece of plastic.

It explains the neutrino mass without needing impossible "weak whispers."
It provides a Dark Matter candidate that fits the amount we see in the universe.
It respects the limits of what scientists have already seen in experiments (like the MEG experiment looking for rare particle decays).

The Bottom Line

The authors propose that the universe contains a pair of "almost identical" heavy particles. Their near-perfect similarity cancels out most of their effects, leaving just a tiny ripple that gives neutrinos their mass. Meanwhile, a related invisible particle acts as the Dark Matter, interacting with the universe in a way that is perfectly balanced—strong enough to exist, but subtle enough to have remained hidden until now.

This "Quasi-Dirac" idea turns a mathematical headache into a beautiful, symmetrical solution.

1. Problem Statement

The Standard Model (SM) fails to explain two fundamental phenomena: the origin of small neutrino masses and the nature of dark matter (DM).

The Seesaw Mechanism Issue: While the canonical seesaw mechanism explains small neutrino masses ( $m_\nu \sim 0.1$ eV) by introducing heavy right-handed neutrinos ( $\nu_R$ ) at the GUT scale ( $M \sim 10^{14}$ GeV), it fails to accommodate TeV-scale physics required for Dark Matter. To explain neutrino masses at the TeV scale, the Yukawa coupling ( $h$ ) must be unnaturally small ( $h \sim 10^{-6}$ ), which is inconsistent with Renormalization Group Equation (RGE) running and charged-lepton flavor violation (cLFV) limits.
The Scotogenic Mechanism Issue: The scotogenic model (radiative neutrino mass generation with a $Z_2$ $Z_{2}$ symmetry) allows for TeV-scale new physics. However, it faces phenomenological hurdles:
1. Overproduction of DM: Fermionic DM candidates ( $\nu_R$ ) typically overclose the universe unless fine-tuned co-annihilation occurs.
2. cLFV Constraints: To satisfy limits on processes like $\mu \to e\gamma$ , the Yukawa coupling $h$ must be very small ( $h \lesssim 0.05$ ), which often renders the DM candidate unstable or unable to achieve the correct relic density.
3. Scalar DM Constraints: Scalar DM candidates often suffer from large scattering cross-sections with nuclei via $Z$ -exchange unless specific mass splittings are engineered, requiring large couplings that may conflict with other bounds.

The authors argue that the loop suppression in standard scotogenic models is insufficient to naturally satisfy all neutrino mass, DM abundance, and cLFV constraints simultaneously without fine-tuning.

2. Methodology and Model Construction

The authors propose a Quasi-Dirac Scotogenic Model, a generalization of the standard scotogenic framework.

Field Content:
- Standard Model fields: Even under a discrete $Z_2$ symmetry.
- Inert Higgs Doublet ( $\eta$ ): Odd under $Z_2$ . Contains physical scalars $S$ (CP-even), $A$ (CP-odd), and $H^-$ (charged).
- New Fermions ( $N_L, N_R$ ): A vector-like pair for each family, odd under $Z_2$ .
Symmetry Structure:
- A Lepton-like symmetry is introduced (approximate global symmetry). In the limit where certain parameters vanish, the theory conserves this symmetry.
- Mass Terms: The Lagrangian includes a large Dirac mass term $M \bar{N}_L N_R$ (conserving the symmetry) and small Majorana mass terms $\mu_L \bar{N}_L N_L^c$ and $\mu_R \bar{N}_R^c N_R$ (violating the symmetry).
- Hierarchy: The model assumes $\mu_{L,R} \ll M$ . This hierarchy is "technically natural" (protected by the symmetry) and leads to the formation of Quasi-Dirac fermions ( $N_1, N_2$ ) with nearly degenerate masses separated by $\Delta M \sim \mu$ .
Neutrino Mass Generation:
- Neutrino masses are generated radiatively via one-loop diagrams involving the inert scalars ( $\eta$ ) and the quasi-Dirac fermions ( $N_{1,2}$ ).
- Crucially, the contribution to the neutrino mass from the two nearly degenerate states ( $N_1$ and $N_2$ ) largely cancels out due to their opposite signs in the Majorana sector, leaving a residual mass proportional to the small splitting $\mu/M$ .
- This results in a Radiative Inverse Seesaw mechanism, distinct from the standard radiative canonical seesaw.

3. Key Contributions

Novel Radiative Inverse Seesaw: The paper demonstrates that introducing quasi-Dirac fermions in a scotogenic setup naturally suppresses neutrino mass by a factor of $\Delta M / M \sim 10^{-5}$ in addition to the standard loop factor ( $1/16\pi^2$ ).
Resolution of Coupling Tension: This double suppression allows the Yukawa coupling ( $h$ $h$ ) between the dark fermions and standard leptons to be sizable ( $h \sim 0.05$ $h \sim 0.05$ ). This value is consistent with:
- RGE running constraints.
- Charged-lepton flavor violation limits (e.g., $\mu \to e\gamma$ ).
- The requirement for correct Dark Matter annihilation rates.
Unified Dark Matter Scenario:
- Fermionic DM: The quasi-Dirac nature allows the fermion to be a viable DM candidate without overproduction issues, as the annihilation cross-section is enhanced by the larger allowed coupling $h$ .
- Scalar DM: The model also accommodates the lightest inert scalar ( $A$ ) as a DM candidate. The mass splitting between $S$ and $A$ (induced by $\lambda_5$ ) kinematically suppresses $Z$ -mediated scattering, satisfying direct detection limits.

4. Results and Phenomenological Analysis

Neutrino Mass: The derived neutrino mass formula is:
$m_\nu \sim \frac{\lambda_5 h^2}{16\pi^2} \frac{v^2}{M} \left( \frac{\mu}{M} \right)$
With $M \sim \text{TeV}$ , $\mu \sim 10 \text{ MeV}$ , and $h \sim 0.05$ , the model successfully reproduces $m_\nu \sim 0.1$ eV.
Dark Matter Relic Density:
- The scalar DM candidate ( $A$ ) annihilates via gauge portals ($ZZ, WW$) and Higgs portals ( $HH, t\bar{t}$ ).
- For a gauge-portal dominated scenario, the correct relic density ( $\Omega h^2 \approx 0.11$ ) is achieved for a DM mass $m_A \approx 568$ GeV.
- For a Higgs-portal dominated scenario, $m_A \approx 1.39(\lambda_3 - \lambda_5) \text{ TeV}$ .
Direct Detection:
- The model predicts a spin-independent scattering cross-section $\sigma_{SI} \sim 10^{-46} \text{ cm}^2$ for $m_A \approx 568$ GeV.
- This falls within the sensitivity range of current experiments (e.g., XENONnT, LZ) and satisfies the upper bounds, provided the coupling difference $\lambda_3 - \lambda_5 \approx 0.025$ .
Lepton Flavor Violation (cLFV):
- The branching ratio for $\mu \to e\gamma$ is calculated. With $h \sim 0.05$ and $m_{H^-} \sim 770$ GeV, the prediction $Br(\mu \to e\gamma) \lesssim 4.2 \times 10^{-13}$ is consistent with current experimental limits (MEG collaboration).

5. Significance and Conclusion

This work provides a theoretically robust and phenomenologically viable framework that unifies the explanation of neutrino mass and dark matter at the TeV scale.

Theoretical Innovation: It introduces a "Quasi-Dirac" approximation into the scotogenic mechanism, effectively realizing a Radiative Inverse Seesaw. This distinguishes it from previous models where small Majorana masses were the sole source of suppression.
Phenomenological Viability: By allowing larger Yukawa couplings ( $h \sim 0.05$ ) than standard scotogenic models, the model solves the "overproduction" problem of fermionic DM and satisfies cLFV constraints without fine-tuning.
Experimental Testability: The model predicts specific mass ranges for Dark Matter ( $\sim 568$ GeV or $\sim 1$ TeV) and scattering cross-sections that are currently accessible to direct detection experiments. It also predicts specific signatures for cLFV processes that can be tested in future high-precision experiments.
Broader Context: The authors note that such neutral vector-like fermions appear naturally in various BSM extensions (e.g., Dark $U(1)$ , 3-3-1-1 models, Trinification), suggesting that the quasi-Dirac mechanism is a generalizable feature for solving the neutrino/DM puzzle in unified theories.

In summary, the paper demonstrates that Quasi-Dirac fermions offer a natural mechanism to suppress neutrino masses while maintaining large couplings necessary for viable Dark Matter phenomenology, bridging the gap between neutrino physics and cosmology.