Cogenesis of visible and dark matter in type-I Dirac seesaw

This paper proposes a novel cogenesis framework based on the type-I Dirac seesaw mechanism, where the out-of-equilibrium decays of heavy vector-like fermions simultaneously generate the baryon asymmetry and an asymmetric dark matter component, allowing for successful cogenesis with dark matter masses ranging from 100 MeV to 39 TeV while remaining testable through neutrino, dark matter, CMB, and gravitational wave observations.

The Gist

The Big Picture: Solving Two Mysteries at Once

Imagine the universe is a giant party. We know two things about the guests:

1. The Visible Guests (Baryons): These are the people we can see—stars, planets, you, and me. They make up about 20% of the "matter" at the party.
2. The Invisible Guests (Dark Matter): These are the mysterious guests we can't see, but we know they are there because they are holding the party together (gravity). They make up about 80% of the matter.

The Mystery: Scientists have always wondered why these two groups exist in such a specific ratio. Why is there roughly 5 times more invisible matter than visible matter? It's like finding a room with 500 ghosts for every 100 humans. It seems too perfect to be a coincidence.

The Paper's Idea: This paper proposes a "Cogenesis" theory. "Co" means together. Instead of the visible and invisible guests arriving separately, the authors suggest they were born together from the same event, like twins separated at birth.

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The Cast of Characters

To explain how this happens, the authors introduce a new "play" involving some new actors:

1. The Heavy Hitters (Vector-like Fermions, $N$): Imagine these as massive, unstable "parent" particles that existed right after the Big Bang. They are the main characters.
2. The Standard Neutrinos ($\nu_R$): The "right-handed" cousins of the tiny particles we know.
3. The Dark Matter Twins ($\chi$ and $\phi$):
   • $\chi$ (Chi): The Dark Matter particle (the ghost).
   • $\phi$ (Phi): A heavier "sibling" or companion particle that helps $\chi$ interact.

The Plot: The Great Decay Party

The story happens in the very early universe, when things were hot and chaotic.

1. The Parents Decay (The Birth of Asymmetry)
The heavy "Parent" particles ($N$) are unstable. They decay (break apart) into three different types of children:

• Group A: Visible matter particles (Leptons).
• Group B: Right-handed neutrinos.
• Group C: Dark Matter particles ($\chi$).

2. The "CP Asymmetry" (The Unfair Coin Flip)
In physics, usually, if a parent decays, it creates equal amounts of matter and antimatter (like flipping a coin and getting 50% heads and 50% tails). If that happened here, the matter and antimatter would cancel each other out, leaving an empty universe.

But, the authors propose a trick. Because of a specific mechanism (the Dirac Seesaw), the "coin" is slightly weighted.

• When the heavy parent decays, it creates slightly more matter than antimatter for the visible group.
• Simultaneously, it creates slightly more antimatter than matter for the dark matter group (or vice versa, depending on the specific math).

The Analogy: Imagine a baker making two types of cookies: Chocolate (Visible) and Vanilla (Dark).

• The baker has a rule: "For every 100 Chocolate cookies, I must make 100 Vanilla cookies."
• However, the baker is slightly clumsy. He accidentally makes 101 Chocolate cookies and 99 Vanilla cookies.
• The "extra" Chocolate cookies become our visible universe.
• The "missing" Vanilla cookies (the antimatter that didn't get made) leave behind a net surplus of Vanilla cookies that become our Dark Matter.

3. The Connection
Because the total number of "cookies" (lepton number) must stay balanced, the extra visible matter is mathematically linked to the extra dark matter. This explains why the ratio is roughly 5:1. The "weight" of the Dark Matter particle determines how many of them are needed to balance the equation.

The Cleanup Crew: Getting Rid of the "Symmetric" Part

There is a problem. Even with the "unfair coin flip," the decay still produces a lot of equal amounts of matter and antimatter (the 99 Vanilla and 99 Anti-Vanilla). If they stay, they will annihilate each other and disappear, or worse, ruin the delicate balance of the early universe.

The Solution: The paper introduces a "Cleanup Crew" (a light scalar particle called $\phi_1$).

• This particle acts like a vacuum cleaner. It forces the equal, symmetric parts of the Dark Matter to annihilate each other before the universe cools down too much (specifically, before Big Bang Nucleosynthesis, the time when the first atoms formed).
• Result: The "junk" (symmetric matter) is swept away. Only the "special" leftovers (the asymmetric matter) remain. This ensures that today, Dark Matter is almost entirely made of the "survivors" from that early imbalance.

The Constraints: How Big Can the Ghost Be?

The authors ran complex computer simulations (like a massive digital weather forecast) to see what sizes of Dark Matter particles would work.

• The Lower Limit (100 MeV): If the Dark Matter particle is too light (like a feather), the "vacuum cleaner" can't clean up the symmetric junk fast enough. The universe would be ruined. So, the ghost must be at least as heavy as 100 MeV (about the weight of a proton).
• The Upper Limit (39 TeV): If the Dark Matter particle is too heavy (like a boulder), the laws of physics (specifically "unitarity") say it's impossible to create enough of them to fill the universe. So, the ghost can't be heavier than 39 TeV.

The Sweet Spot: The Dark Matter particle must be somewhere between 100 MeV and 39 TeV.

How Can We Test This?

The authors don't just make up a story; they suggest ways to prove it:

1. Neutrino Experiments: The model predicts that the lightest neutrino has a very specific, tiny mass. Experiments like KATRIN are looking for this.
2. Double Beta Decay: The model says a specific type of radioactive decay (neutrinoless double beta decay) should never happen. If we see it, the model is wrong. If we don't see it, the model gets a point.
3. Gravitational Waves: The "birth" of this universe scenario might have created ripples in space-time (gravitational waves) that future detectors could hear.
4. Dark Matter Self-Interaction: The model suggests Dark Matter particles might bump into each other (like ghosts bumping into ghosts) via a light force carrier. This could explain why galaxies look the way they do.

Summary

This paper suggests that the visible universe and the invisible dark universe are twins. They were born from the same unstable particles in the early universe. A slight "bias" in how these particles decayed created a surplus of visible matter and a surplus of dark matter. A cosmic "cleanup crew" removed the unwanted leftovers, leaving us with the specific ratio of matter we see today.

It's a unified theory that ties the smallest particles (neutrinos) to the biggest mystery (dark matter) into one elegant, testable package.

Technical Summary

1. Problem Statement

The paper addresses two fundamental mysteries in cosmology:

1. Dark Matter (DM): The existence of non-baryonic, non-luminous matter dominating the universe's mass.
2. Baryon Asymmetry of the Universe (BAU): The observed matter-antimatter imbalance.

While these are often studied separately, their similar order of magnitude abundances ($\Omega_{DM} \approx 5 \Omega_B$) suggest a common origin, known as cogenesis. Existing models often rely on Majorana neutrinos (violating lepton number) or specific WIMP paradigms. This paper proposes a novel mechanism within the Type-I Dirac Seesaw framework, which preserves total lepton number (producing light Dirac neutrinos) and generates asymmetries in both the visible (baryon/lepton) and dark sectors simultaneously.

2. Methodology and Model Setup

Model Extension

The authors extend the Standard Model (SM) with the following minimal ingredients:

• Three heavy vector-like fermions ($N$): Responsible for the Dirac seesaw mechanism and generating asymmetries.
• Three right-handed neutrinos ($\nu_R$): The SM neutrino counterparts.
• One singlet scalar ($\eta$): Facilitates the Dirac mass generation.
• Dark Sector:
  • Dirac fermion Dark Matter ($\chi$): The DM candidate.
  • Heavier scalar companion ($\phi$): Couples $\chi$ to $N$.
  • Light scalar mediator ($\phi_1$): Introduced to annihilate the symmetric component of DM and enable self-interactions.

Mechanism of Cogenesis

The core mechanism relies on the out-of-equilibrium decays of the heavy vector-like fermions ($N$) into three distinct channels:

1. $N \to L H$ (Left-handed lepton doublet + Higgs) $\to$ Generates Lepton Asymmetry ($\epsilon_L$).
2. $N \to \nu_R \eta$ (Right-handed neutrino + singlet scalar) $\to$ Generates Right-handed Asymmetry ($\epsilon_R$).
3. $N \to \chi \phi$ (Dark fermion + dark scalar) $\to$ Generates Dark Matter Asymmetry ($\epsilon_\chi$).

Key Constraint: Since the model preserves total lepton number (Dirac nature), the sum of CP asymmetries must vanish:
$$\epsilon_L + \epsilon_R + \epsilon_\chi = 0$$
This creates a competitive dynamic where asymmetries are generated but can also be washed out if the sectors reach equilibrium.

Computational Approach

• Boltzmann Equations: The authors solve a set of coupled Boltzmann equations numerically to track the evolution of the number densities of $N$, $L$, $\nu_R$, and $\chi$. This includes terms for decay, inverse decay, and scattering (washout) processes.
• MCMC Scan: A Markov Chain Monte Carlo (MCMC) analysis is performed over a 9-dimensional parameter space (including neutrino masses, heavy fermion masses, Yukawa couplings, and the Casas-Ibarra rotation angle) to find regions consistent with observed BAU and DM relic density.
• Constraints:
  • BBN Constraint: The symmetric component of DM must annihilate efficiently before Big Bang Nucleosynthesis (BBN) to avoid disrupting light element abundances.
  • Unitarity Bound: The mass of Asymmetric Dark Matter (ADM) is constrained by partial-wave unitarity limits on the annihilation cross-section.

3. Key Contributions

1. Novel Dirac Cogenesis Framework: The paper establishes a viable cogenesis mechanism where light Dirac neutrinos are generated via a Type-I seesaw, avoiding the lepton number violation typical of Majorana seesaw models.
2. Interplay of Three Sectors: Unlike simpler models, this framework explicitly models the interplay between the left-handed lepton sector, the right-handed neutrino sector, and the dark sector, showing how CP asymmetries are distributed and washed out among them.
3. Symmetric Component Annihilation: The introduction of the light scalar $\phi_1$ provides a mechanism for the symmetric part of the DM to annihilate ($\bar{\chi}\chi \to \phi_1\phi_1$), ensuring the present-day DM is purely asymmetric.
4. Phenomenological Viability: The model connects the DM mass range to fundamental constraints (BBN and Unitarity) and predicts specific signatures for direct detection, gravitational waves, and neutrino experiments.

4. Results

Parameter Space and Mass Bounds

The successful cogenesis is realized within a specific mass range for the Dark Matter particle ($\chi$):
$$100 \text{ MeV} \lesssim m_\chi \lesssim 39 \text{ TeV}$$

• Lower Bound ($\sim 100$ MeV): Arises from the requirement that the symmetric component of DM must annihilate efficiently before the BBN epoch. Lower masses lead to insufficient annihilation, leaving a symmetric relic that violates observational limits.
• Upper Bound ($\sim 39$ TeV): Derived from the unitarity bound on the asymmetric DM mass. For $s$-wave annihilation, the mass cannot exceed $\sim 110$ TeV, but the requirement to annihilate the symmetric component down to negligible levels tightens this to $\sim 39$ TeV.

Neutrino Mass Implications

• The model favors a lightest active neutrino mass ($m_1$) in the range $10^{-10} \text{ eV} \lesssim m_1 \lesssim 10^{-3} \text{ eV}$.
• For the viable parameter space, the sum of neutrino masses is $\sum m_i \approx 59$ meV. This is consistent with current Planck bounds but within the projected sensitivity of future experiments like the Simons Observatory.

Benchmark Points

The authors provide four benchmark points (BP1–BP4) spanning DM masses from $\sim 200$ MeV to $\sim 10$ TeV. In all cases, the calculated baryon asymmetry ($\eta_B \approx 6 \times 10^{-10}$) and the ratio of DM to baryon relic density ($R \approx 5.36$) match observational data.

5. Significance and Detection Prospects

The proposed model is highly testable across multiple experimental frontiers:

• Direct Detection: The light scalar $\phi_1$ mixes with the SM Higgs, allowing for Spin-Independent Direct Detection (SIDD). The predicted cross-sections are within reach of current and future experiments (e.g., PandaX-4T), particularly for DM masses $< 460$ GeV.
• Gravitational Waves (GW): The spontaneous breaking of discrete symmetries (required for the model) leads to the formation of domain walls. Their subsequent annihilation generates a stochastic gravitational wave background detectable by current and future GW observatories.
• Cosmic Microwave Background (CMB): The presence of light Dirac neutrinos contributes to the effective number of relativistic species ($N_{eff}$). The model predicts $\Delta N_{eff} \sim 0.14$, which is within the sensitivity of future CMB experiments (CMB-S4, CMB-HD).
• Neutrinoless Double Beta Decay ($0\nu\beta\beta$): Since the model conserves global lepton number, it predicts a vanishing rate for $0\nu\beta\beta$. A positive detection of this process would falsify the model.
• Neutrino Mass Scale: The upper bound on the lightest neutrino mass ($m_1 \lesssim 10^{-3}$ eV) can be tested by experiments like KATRIN.

Conclusion

This paper successfully demonstrates that a Type-I Dirac seesaw mechanism can simultaneously explain the origin of light neutrino masses, the baryon asymmetry, and the dark matter abundance. By linking the DM mass to unitarity and BBN constraints, the model offers a narrow, testable window for DM masses ($100$ MeV – $39$ TeV) and provides distinct signatures in neutrino physics, gravitational wave astronomy, and direct detection experiments.