Unified Origin of Dirac Neutrino and Asymmetric Dark Matter Masses via a Dirac-Type Leptogenesis

This paper proposes a unified framework based on an extended $U(1)_X$ Froggatt-Nielsen mechanism and a $\mathbb{Z}_4$ symmetry that simultaneously explains the origins of light Dirac neutrino masses, GeV-scale asymmetric dark matter, and the baryon asymmetry of the Universe through Dirac-type leptogenesis with exact lepton-number conservation.

The Gist

Imagine the universe as a giant, complex machine that started with a perfect balance: equal amounts of matter and antimatter, and no "ghostly" particles like dark matter. But today, we live in a universe made almost entirely of matter, and we know there is a massive amount of invisible "dark matter" holding galaxies together.

For decades, physicists have struggled to explain three big mysteries at once:

1. Why do neutrinos (tiny ghost particles) have such tiny masses?
2. What is dark matter, and why does it weigh about as much as a few atoms?
3. Why is there more matter than antimatter?

This paper proposes a beautiful, unified solution: All three mysteries are actually the same story, told from different angles.

Here is the story, broken down with simple analogies:

1. The "Froggatt-Nielsen" Filter (The Great Suppressor)

Imagine you have a very powerful water hose (representing the fundamental forces of nature) spraying water (mass) at a garden. You want the flowers (neutrinos) to get just a tiny, gentle mist, but you want the heavy rocks (dark matter) to get a steady stream, and you want the trees (heavy neutrinos) to get a massive gush.

In the Standard Model, it's hard to get these different amounts of water without building three different hoses. This paper suggests using a special filter (called the Froggatt-Nielsen mechanism).

• This filter is based on a hidden rule (a symmetry called $U(1)_X$).
• When the water tries to pass through, the filter blocks most of it.
• For the light neutrinos, the filter is so strong that only a tiny, tiny drop gets through (explaining why they are so light).
• For the dark matter, the filter lets through just enough to give it a mass of about 1–2 GeV (roughly the weight of a few protons).
• The Magic: The same filter that makes the neutrinos light automatically sets the weight of the dark matter. They are two sides of the same coin.

2. The "Lepton Ledger" (The Cosmic Accounting)

In the early universe, the authors imagine a heavy, unstable particle (a "Heavy Neutrino") that was like a giant, overfilled bank account. This particle decayed (broke apart) into two different types of "currency":

1. Visible Currency: Regular matter (leptons) that eventually became the protons and neutrons in our bodies.
2. Dark Currency: The dark matter particles (called $\chi$).

Usually, if you create matter, you create an equal amount of antimatter, and they cancel each other out. But here, the universe played a trick. Because of a strict rule called Lepton Number Conservation, the universe couldn't just create matter out of nothing. It had to create a "debt."

• The heavy neutrino decayed, creating a surplus of "Visible Matter" and a matching surplus of "Dark Matter."
• Because the total "account" had to balance to zero, the amount of Dark Matter created was mathematically locked to the amount of Visible Matter.
• The Result: This explains why Dark Matter is about 5 times heavier than normal matter. It's not a coincidence; it's a direct consequence of the same event that created the matter in our bodies!

3. The "Ghostly Door" (Why We Don't See Dark Matter)

If Dark Matter and Normal Matter were created together, why don't they bump into each other constantly? Why is Dark Matter so "dark"?

The paper suggests a one-way door (or a very high wall).

• The interactions between our world and the dark world are suppressed by that same "filter" mentioned earlier.
• It's like trying to talk to someone in a soundproof room through a wall made of lead. You can shout, but they can barely hear you.
• This explains why Dark Matter doesn't clump with normal matter and why it's so hard to detect in labs. It only interacts very weakly, mostly through a "loop" (a complex, indirect path) involving a new, light particle (a scalar $\eta$).

4. The "Cleanup Crew" (Getting Rid of the Excess)

When the heavy neutrinos decayed, they didn't just create the "good" Dark Matter (the asymmetric part). They also created a "symmetric" part (equal amounts of Dark Matter and Anti-Dark Matter). If this symmetric part remained, it would ruin the math and make the universe too heavy.

The paper introduces a cleanup crew:

• There is a light, invisible particle (the scalar $\eta$) that acts like a vacuum cleaner.
• The symmetric Dark Matter particles found each other, bumped into this vacuum cleaner, and annihilated (destroyed each other), turning into pure energy.
• The "good" Dark Matter (the asymmetric part) was safe because it didn't have a partner to annihilate with.
• The Result: Only the "good" Dark Matter survived, exactly matching the amount needed to hold galaxies together.

Why This Matters

This model is elegant because it doesn't require inventing three separate, unrelated theories.

• One mechanism explains why neutrinos are light.
• One mechanism explains why Dark Matter weighs what it weighs.
• One event explains why we exist (the matter/antimatter imbalance).

The Bottom Line:
The universe is like a perfectly tuned instrument. The "tuning" that makes the notes of neutrinos so quiet also determines the weight of the invisible strings (Dark Matter) that hold the instrument together. This paper gives us a blueprint for how to tune that instrument, and it predicts that future experiments (like new underground detectors) might finally "hear" the Dark Matter particles by listening for the faint vibrations they cause when they bump into atoms.

Technical Summary

Here is a detailed technical summary of the paper "Unified Origin of Dirac Neutrino and Asymmetric Dark Matter Masses via a Dirac-Type Leptogenesis" by Ishida, Ohki, and Uemura.

1. Problem Statement

The paper addresses three fundamental open questions in particle physics and cosmology that the Standard Model (SM) fails to explain simultaneously:

1. Neutrino Masses: The origin of tiny neutrino masses and whether neutrinos are Dirac or Majorana particles.
2. Baryon Asymmetry of the Universe (BAU): The dynamical origin of the matter-antimatter asymmetry.
3. Dark Matter (DM): The particle identity of Dark Matter, specifically the "Asymmetric Dark Matter" (ADM) scenario where the DM relic density is linked to the baryon asymmetry.

Existing models often treat these problems separately or require ad-hoc scales. Specifically, connecting Dirac neutrino masses (which require exact lepton number conservation) with ADM and leptogenesis is challenging because conventional Dirac leptogenesis often struggles to generate sufficient asymmetry without violating constraints or requiring unnatural hierarchies between the DM mass scale (GeV) and the leptogenesis scale ($10^{10}$ GeV).

2. Methodology and Model Construction

The authors propose a unified framework extending the SM with specific symmetries and particle content to solve these problems simultaneously.

A. Symmetry Structure

• $U(1)_X$ (Froggatt-Nielsen-like): A gauged, non-anomalous symmetry introduced to generate hierarchical Yukawa couplings and suppress operators. It is spontaneously broken by a scalar singlet $S$ at a high scale $v_S$.
• $U(1)_L$ (Global Lepton Number): Exact global symmetry ensuring neutrinos remain Dirac particles (forbidding Majorana mass terms).
• $Z_4^D$ (Discrete Symmetry): Stabilizes the dark sector, ensuring the stability of the lightest dark fermion.

B. Particle Content

• SM Fields: Standard leptons ($\ell_L$) and Higgs ($H$).
• Neutrino Sector: Right-handed neutrinos ($\nu_R$) and heavy singlet fermions ($N_{L,R}$).
• Dark Sector: Chiral fermions $\chi_{L,R}$ (ADM candidate) and $\psi_{L,R}$ (heavier partners).
• Scalar Sector:
  • $S$: Breaks $U(1)_X$, generates heavy neutrino masses.
  • $\phi$: Mediates interactions between dark sector and heavy neutrinos (no VEV).
  • $\eta$: Complex scalar (with real part $\eta_R$ and imaginary part $\eta_I$) mediating dark matter self-interactions and annihilation.

C. Mass Generation Mechanisms

The model utilizes a Dirac Seesaw mechanism combined with the Froggatt-Nielsen (FN) suppression:

• Neutrino Masses: Generated via higher-dimensional operators suppressed by the ratio $\langle S \rangle / \Lambda$ (where $\Lambda \sim M_{Pl}$). The light neutrino mass is $m_\nu \sim \epsilon \delta v_S$, where $\epsilon = v_{EW}/v_S$ and $\delta = \langle S \rangle/\Lambda$.
• ADM Mass: The dark fermion $\chi$ acquires a mass $m_\chi \sim \delta v_S$.
• Unified Hierarchy: The model naturally explains the hierarchy $m_\nu / m_{ADM} \sim v_{EW} / v_S < 10^{-10}$, linking the sub-eV neutrino mass, the GeV-scale ADM mass, and the $10^{10}$ GeV leptogenesis scale through a single set of suppression parameters.

3. Key Mechanisms and Dynamics

A. Dirac Leptogenesis

• Process: Asymmetry is generated via the out-of-equilibrium, CP-violating decays of the lightest heavy Dirac neutrino ($\nu_h^1$).
• Decay Channels: $\nu_h^1 \to \ell_L H$ (SM sector) and $\nu_h^1 \to \chi \phi^*$ (Dark sector).
• Asymmetry Sharing: Since total lepton number is conserved, the generated asymmetry is shared between the visible and dark sectors. The CP asymmetry parameters $\epsilon$ are generated at the one-loop level involving both SM Yukawas ($Y$) and dark couplings ($g$).
• Sphaleron Conversion: The SM lepton asymmetry is partially converted into a baryon asymmetry via electroweak sphalerons. The dark sector asymmetry remains as the ADM relic density.
• Decoupling: The model ensures the dark and visible sectors remain chemically decoupled after asymmetry generation due to the extreme suppression of DM-number-changing processes (suppressed by $\delta^4$).

B. Dark Matter Relic Density

• Asymmetric Component: The relic density is determined by the initial asymmetry, leading to a predicted mass $m_\chi \approx 1.8$ GeV to match the observed $\Omega_{DM}/\Omega_B \approx 5$.
• Symmetric Component: The symmetric component of $\chi$ (particle-antiparticle pairs) must be efficiently annihilated to avoid overclosing the universe.
• Annihilation: The symmetric component annihilates via $\chi \bar{\chi} \to \eta_I \eta_I$ (mediated by $\psi$). The model requires the mediator $\eta_I$ to be light ($m_{\eta_I} < m_\chi/2$) and the Yukawa couplings to be sufficiently strong ($|f| \gtrsim 0.15$) to ensure the symmetric component freezes out early, leaving a "fully asymmetric" dark matter scenario.

4. Results and Numerical Analysis

• Baryon Asymmetry: Numerical scans over Yukawa couplings ($10^{-4} < |Y|, |g| < 1$) and heavy neutrino masses ($M_1$) show that the observed baryon-to-photon ratio ($\eta_B \approx 6.1 \times 10^{-10}$) is successfully reproduced for$M_1 \gtrsim 10^{10}$ GeV.
• ADM Mass: The framework predicts a GeV-scale ADM mass ($m_\chi \sim 1.8$ GeV) naturally, consistent with the relation $m_\chi \approx (5 \times 28/79) m_p$.
• Direct Detection:
  • DM-nucleon scattering occurs via a one-loop Higgs-mediated process (involving $\eta_I$ and $\psi$ in the loop).
  • The spin-independent cross-section $\sigma_{SI}$ is suppressed but within the sensitivity range of future sub-GeV experiments (e.g., DarkSide-50, DS-LM).
  • Current constraints (DS-50, CRESST-III) exclude parts of the parameter space, particularly for larger portal couplings ($\lambda_{H\eta}$).
• Cosmological Constraints:
  • BBN: The freeze-out temperature of the symmetric component is $T_f \gtrsim 60$ MeV, safely above the BBN scale, avoiding constraints on extra relativistic degrees of freedom.
  • $\Delta N_{eff}$: The contribution of right-handed neutrinos to the effective number of neutrino species is calculated to be $\Delta N_{eff} \approx 0.1$, consistent with current CMB bounds ($|\Delta N_{eff}| < 0.17$).
  • Higgs Invisible Decay: The decay $h \to \eta_I \eta_I$ constrains the portal coupling $\lambda_{H\eta} \lesssim 10^{-2}$, which is consistent with direct detection limits.

5. Significance and Conclusion

Key Contributions:

1. Unified Origin: The paper provides a rare, unified explanation for the origins of neutrino mass, baryon asymmetry, and dark matter mass using a single symmetry-breaking scale ($v_S$) and a Froggatt-Nielsen mechanism.
2. Dirac Leptogenesis with ADM: It successfully implements Dirac leptogenesis where the asymmetry resides in the dark sector rather than the right-handed neutrinos, avoiding the washout problems typical of Majorana models while maintaining exact lepton number conservation.
3. Testability: The model predicts a specific mass range for ADM ($\sim 1-2$ GeV) and a distinct direct detection signature (loop-suppressed, sub-GeV) that is accessible to next-generation experiments, distinguishing it from WIMP paradigms.
4. Theoretical Consistency: The model is anomaly-free, requires no additional SM-charged scalars (minimizing flavor/precision constraints), and naturally explains the hierarchy between the Planck scale, the leptogenesis scale, and the GeV scale without ad-hoc parameters.

Significance:
This work demonstrates that Dirac neutrinos and Asymmetric Dark Matter are not just compatible but can be dynamically linked through a high-scale leptogenesis mechanism. It offers a compelling alternative to the WIMP paradigm and Majorana neutrino scenarios, providing a "testable connection" between neutrino physics and the dark sector that can be probed by upcoming low-mass dark matter searches and precision cosmological measurements (e.g., CMB-S4).