⚛️ phenomenology

Right-handed neutrino dark matter consistent with the generation of baryon number asymmetry

This paper investigates the possibility that right-handed neutrinos serve as a unified solution to three fundamental Standard Model problems—neutrino mass generation, baryon asymmetry, and dark matter—by analyzing their mass matrix structure within the scotogenic model.

Original authors: Daijiro Suematsu

Published 2026-02-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Daijiro Suematsu

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 Picture: Solving Three Mysteries with One Key

Imagine the Standard Model of physics is like a giant, complex puzzle that explains almost everything about the universe. But there are three missing pieces that don't fit:

Neutrino Mass: We know tiny particles called neutrinos have mass, but the puzzle says they should be weightless.
Dark Matter: We know there is invisible "stuff" holding galaxies together, but we can't see it or touch it.
The Matter-Antimatter Imbalance: The Big Bang should have created equal amounts of matter and antimatter, which would have destroyed each other. But somehow, we are here, made of matter.

This paper proposes a clever solution: Three right-handed neutrinos (a specific type of particle we've never seen) could be the "Master Keys" that unlock all three mysteries at once, without needing to invent any new, complicated rules.

The Cast of Characters

To understand the story, let's meet the players in this cosmic drama:

The Standard Neutrinos (The Left-Handed Ones): These are the famous, ghostly particles that pass through your hand right now. They are light and interact very weakly.
The Right-Handed Neutrinos (The Heavy Twins): Imagine these as the "big brothers" of the standard neutrinos. They are heavy, invisible, and don't talk to normal matter (nuclei) at all.
- N2 and N3 (The Heavy Hitters): These two are heavy (about 3,000 times heavier than a proton). They are the "actors" who perform a play that explains why the universe is full of matter instead of antimatter.
- N1 (The Silent Guardian): This is the lightest one. It is the Dark Matter candidate. Because it's so shy and doesn't interact with anything, it floats around the universe as the invisible glue holding galaxies together.
The Inert Doublet (The "η" or "Eta"): Think of this as a special, invisible shield or a "magic box" that only the right-handed neutrinos can open. It helps generate the mass for the neutrinos.

The Plot: How It All Works

1. The Ghostly Mass (Neutrino Oscillations)

In the standard puzzle, neutrinos shouldn't have mass. But in this story, the "magic box" (the inert doublet) and the heavy twins (N2, N3) interact in a secret loop. It's like a game of "telephone" where the message gets distorted, giving the light neutrinos a tiny bit of weight. This explains why they wiggle and change flavors as they travel through space.

2. The Great Imbalance (Leptogenesis)

How did we get more matter than antimatter?
Imagine the heavy twin N2 is a ticking time bomb. When it decays (explodes), it doesn't just split evenly; it has a slight bias. It prefers to spit out "matter" over "antimatter."

The Catch: Usually, these heavy twins are too heavy to decay slowly enough to make a difference.
The Trick: The author suggests that N2 and the "magic box" (η) are almost exactly the same weight. This creates a "traffic jam" (a technical term: degeneracy). It slows down N2's decay just enough so that the bias can actually build up a surplus of matter before the universe cools down. This surplus becomes the stars and us.

3. The Invisible Guardian (Dark Matter)

Now, what about the lightest twin, N1?

The Problem: Usually, to be Dark Matter, a particle needs to be produced in the exact right amount in the early universe. If it interacts too much, it disappears; too little, and there isn't enough to hold galaxies together.
The Solution: N1 is so shy it barely interacts at all. It's like a ghost that never touches anything.
The "Freeze-in" Mechanism: Instead of N1 being produced by colliding with other particles (like a snowball fight), it is slowly "leaking" into existence from the decay of the heavier particles (N2 and the magic box η).
- Analogy: Imagine a leaky faucet in a bathtub. The water (Dark Matter) doesn't come from a bucket being poured in; it slowly drips in over time. By the time the universe cools down, the tub is filled to the exact right level to be Dark Matter.

The "Magic" of the Solution

The most brilliant part of this paper is how it solves a contradiction.

Usually, if you want a particle to be Dark Matter, you need to tune its interactions perfectly. But if you tune it to be Dark Matter, you often break the rules for explaining the matter-antimatter imbalance.

This paper says: "Don't worry about N1's interactions!"

N1 is so weakly interacting that it doesn't mess up the "matter creation" play performed by N2.
N1 just waits in the wings, slowly accumulating from the leftovers of the N2 show.
Because N1 doesn't touch nuclei, we can't detect it with current experiments (which is good, because it means we haven't ruled it out yet!).

The Conclusion

The author, Daijiro Suematsu, is essentially saying:

"We don't need to invent a whole new universe of physics. We just need three right-handed neutrinos. Two of them act as the directors of the 'Matter Creation' play, and the third one quietly becomes the invisible Dark Matter that holds the universe together. They all work together in a delicate dance of mass and timing, solving three of the biggest mysteries in physics with a single, elegant idea."

It's a "three birds with one stone" scenario, where the stone is a specific type of neutrino that has been hiding in plain sight in our theories all along.

1. Problem Statement

The Standard Model (SM) fails to explain three major observational phenomena:

Neutrino Mass: Oscillation experiments confirm non-zero neutrino masses, which the SM cannot generate without extension.
Baryon Asymmetry: The universe exhibits a significant matter-antimatter asymmetry, unexplained by SM CP violation.
Dark Matter (DM): Astrophysical observations confirm the existence of DM, but the SM offers no viable candidate.

Previous extensions often address these issues separately or require complex model extensions (e.g., introducing new gauge interactions like $U(1)'$ ) to reconcile Dark Matter stability with Leptogenesis and neutrino mass generation. Specifically, in the Scotogenic model (a radiative neutrino mass model with an inert doublet scalar $\eta$ and right-handed neutrinos $N_k$ ), a tension exists:

To generate sufficient DM relic abundance via thermal freeze-out, the lightest right-handed neutrino ( $N_1$ ) requires large Yukawa couplings ( $h_{\alpha 1}$ ).
Large Yukawa couplings induce excessive Lepton Flavor Violation (LFV), such as $\mu \to e\gamma$ , which violates experimental bounds.
Conversely, small Yukawa couplings (required to satisfy LFV bounds) make $N_1$ under-abundant in standard freeze-out scenarios.
Additionally, generating sufficient baryon asymmetry via Leptogenesis at the TeV scale is difficult due to washout effects and the need for CP asymmetry.

2. Methodology

The author analyzes the original Scotogenic model without introducing new gauge interactions or extending the particle content beyond the standard three right-handed neutrinos ( $N_{1,2,3}$ ) and one inert doublet scalar ( $\eta$ ).

Key Theoretical Framework:

Symmetry: A discrete $Z_2$ symmetry ensures the stability of the lightest $Z_2$ -odd particle (assumed to be $N_1$ ).
Mass Ordering: The study assumes a specific mass hierarchy: $M_1 < M_{\eta_R} < M_2 < M_3$ , where $M_{\eta_R}$ is the mass of the real part of the neutral inert scalar.
Neutrino Mass Generation: Neutrino masses are generated radiatively at the one-loop level. The author derives the structure of the neutrino mass matrix $M_\nu$ and links it to the Yukawa couplings $h_{\alpha k}$ and the mixing matrix $U$ .
Mass Degeneracy: To facilitate Leptogenesis at the TeV scale, the model assumes near-degeneracy between the second right-handed neutrino and the inert scalar ( $M_2 \simeq M_{\eta_R}$ ) and potentially between $N_2$ and $N_3$ for resonant enhancement.

Analytical Approach:

Neutrino Sector: The author fixes the flavor mixing and mass eigenvalues using neutrino oscillation data (normal ordering). A specific texture for Yukawa couplings is proposed (involving tribimaximal mixing limits) to allow for a zero mass eigenvalue ( $m_1 \approx 0$ ) while satisfying LFV constraints with complex phases.
Dark Matter Relic Abundance: Instead of standard freeze-out, the paper investigates the Freeze-in mechanism and the contribution of late-time decays.
- The Boltzmann equations for the number densities of $N_1$ and $\eta_R$ are solved numerically.
- The study considers two regimes:
  - $h_1$ is large enough for $\eta_R$ to decay into $N_1$ before freeze-out.
  - $h_1$ is small, where $\eta_R$ freezes out and decays later, contributing to the $N_1$ abundance.
Leptogenesis Consistency: The CP asymmetry ( $\epsilon$ ) generated by the out-of-equilibrium decay of $N_2$ is calculated. The author checks if the generated lepton asymmetry survives washout processes and if the subsequent production of $\eta_R$ (from $N_2$ decay) disrupts the $N_1$ DM abundance.

3. Key Contributions

Unified Solution without Extensions: The paper demonstrates that the original Scotogenic model (without new gauge symmetries) can simultaneously explain neutrino masses, baryon asymmetry, and Dark Matter using only three right-handed neutrinos and an inert doublet.
Resolution of the LFV-Density Tension: The author shows that $N_1$ can be a viable DM candidate with very small Yukawa couplings ( $h_1 \ll 1$ ). This suppresses LFV processes ( $\mu \to e\gamma$ ) to unobservable levels while still achieving the correct relic density via the decay of the heavier inert scalar $\eta_R$ .
Role of $\eta_R$ Co-annihilation: A crucial contribution is the identification of the $\eta_R$ co-annihilation and its subsequent decay as the primary driver for the $N_1$ relic abundance. The DM abundance is not determined solely by $N_1$ interactions but by the interplay between $N_1$ , $\eta_R$ , and the couplings $\lambda_3, \lambda_4$ .
Leptogenesis at TeV Scale: The paper establishes conditions under which successful Leptogenesis can occur at the TeV scale. This requires:
- Strict mass degeneracy between $N_2$ and $\eta_R$ (to suppress the $N_2$ decay width and ensure out-of-equilibrium conditions).
- Resonant enhancement of CP asymmetry via $N_3$ (since $N_1$ is stable).
Decoupling of Direct Detection and Relic Density: The model predicts that $N_1$ has no interaction with nuclei (as it only interacts via Yukawa couplings to leptons and scalars). Thus, it evades direct detection constraints, yet its abundance is determined by the thermal history of its "mother" particle, $\eta_R$ .

4. Results

Parameter Space:
- Masses: $M_2 \simeq M_3 \simeq M_{\eta_R} \approx 3$ TeV. $M_1$ can range from keV to TeV scales.
- Couplings:
  - $h_2, h_3 \approx 10^{-3}$ (fixed by neutrino oscillation data).
  - $h_1$ is tuned to be very small ( $10^{-9}$ to $10^{-6}$ ) to satisfy LFV bounds and achieve the correct DM abundance via freeze-in/decay.
  - $\lambda_5 \approx -10^{-3}$ (drives neutrino mass).
  - $\lambda_3, \lambda_4$ are tuned to control the $\eta_R$ co-annihilation cross-section.
Relic Abundance:
- For $M_1 \sim$ TeV, the correct abundance is achieved when $\eta_R$ freezes out and decays into $N_1$ . The couplings $\lambda_3, \lambda_4$ must be tuned so that the freeze-out density of $\eta_R$ matches the required $N_1$ density.
- For $M_1 \sim$ keV, $h_1$ can be larger ( $10^{-5}$ ) while still satisfying constraints, as the suppression factor in the neutrino mass formula ( $\Lambda_1 \propto M_1/M_{\eta_R}$ ) allows for consistency.
Leptogenesis:
- With mass degeneracy $\delta_2 = (M_2 - M_{\eta_R})/M_2 \sim 10^{-5}$ and resonant enhancement from $N_3$ ( $\delta_3 \sim 10^{-9}$ ), the CP asymmetry $\epsilon \sim O(10^{-7})$ is achieved.
- This generates a lepton asymmetry $Y_L \sim O(10^{-10})$ , sufficient to explain the baryon asymmetry via sphaleron processes.
- Numerical solutions of the coupled Boltzmann equations confirm that the late-time production of $\eta_R$ from $N_2$ decay does not spoil the $N_1$ abundance if parameters are tuned correctly.
Phenomenology:
- LFV ( $\mu \to e\gamma$ ): The branching ratio is predicted to be $\sim O(10^{-19})$ , far below current experimental limits ( $\sim 10^{-13}$ ).
- Electric Dipole Moment (EDM): Predicted to be $\sim O(10^{-35})$ cm, also unobservable.
- Collider Signals: The inert scalars ( $\eta^\pm, \eta_R, \eta_I$ ) could be produced at future colliders, but distinguishing this model from scenarios where $\eta_R$ is the DM is difficult due to the small $h_1$ .

5. Significance

This work provides a minimalist and elegant solution to three of the most pressing problems in particle physics within a single framework.

Minimalism: It avoids the need for ad-hoc extensions (like new gauge groups) often required to stabilize DM or generate sufficient asymmetry.
Experimental Viability: By predicting a DM candidate ( $N_1$ ) that is "sterile" to nuclei, it naturally explains the null results of direct detection experiments (like XENON or LUX) while remaining consistent with cosmological observations.
Interconnected Dynamics: It highlights a novel mechanism where the Dark Matter abundance is dictated by the thermal history and decay of a heavier scalar partner, rather than the DM particle's own annihilation cross-section.
Testability: While direct detection is impossible, the model predicts specific mass scales (TeV) for the inert doublet and right-handed neutrinos, making it a target for future high-energy colliders (e.g., FCC, ILC) and precision measurements of LFV and EDMs in the distant future.

In conclusion, the paper establishes that the lightest right-handed neutrino in the original Scotogenic model is a robust Dark Matter candidate that is fully consistent with neutrino oscillation data and the generation of the baryon asymmetry of the universe.