Baryogenesis and Dark Matter from light Sterile Neutrinos

This paper proposes a mechanism where light sterile neutrinos below the electroweak scale simultaneously explain the universe's baryon asymmetry and dark matter abundance by behaving as Dirac particles at high temperatures and viable warm dark matter at low temperatures, while analyzing general initial conditions and specific ultraviolet completions under cosmological constraints.

The Gist

The Big Picture: Solving Two Mysteries at Once

Imagine the universe is a giant, messy attic. Physicists have been trying to clean it up, but they are stuck on two specific, stubborn piles of junk:

1. The "Missing Matter" Pile (Dark Matter): We know there is invisible stuff holding galaxies together, but we don't know what it is.
2. The "Missing People" Pile (Baryon Asymmetry): The universe is made of matter (us, stars, planets), but the Big Bang should have created equal amounts of matter and antimatter. They should have canceled each other out, leaving nothing but light. But somehow, matter won. Where did all the antimatter go?

Usually, scientists treat these two piles as separate problems. This paper proposes a clever solution: What if the same tiny particle is responsible for both?

The Star of the Show: The "Ghostly Twin" Neutrino

To solve this, the authors introduce a character called the Sterile Neutrino.

• The Regular Neutrino: Think of these as "social butterflies." They interact with other particles (like the Higgs boson) but are very shy and hard to catch.
• The Sterile Neutrino: This is the "ghost." It doesn't interact with anything except gravity. It's invisible, making it a perfect candidate for Dark Matter.

The paper suggests these ghosts have a mass somewhere between a feather and a small rock (specifically, in the keV range). This makes them "Warm Dark Matter"—not too fast, not too slow, just right to form the structure of the universe.

The Magic Trick: The "Chameleon" Particle

Here is the tricky part. To explain why we have more matter than antimatter, the universe needs a mechanism that creates an imbalance. Usually, this requires heavy particles that decay in a specific way.

The authors propose a Chameleon Mechanism:

• At High Temperatures (The Early Universe): When the universe was a scorching hot soup, these sterile neutrinos acted like Dirac particles (a specific type of particle that has a distinct "antiparticle" twin). In this mode, they could participate in a process called Leptogenesis.
  • Analogy: Imagine a factory producing red and blue balls. Due to a tiny glitch in the machine (CP violation), it accidentally produces slightly more red balls than blue ones. The blue balls (antimatter) get destroyed or washed away, leaving a surplus of red balls (matter). This surplus eventually becomes the stars and galaxies we see today.
• At Low Temperatures (Today): As the universe cooled down, the sterile neutrinos switched costumes. They started acting like Majorana particles (particles that are their own antiparticles).
  • Analogy: The factory stops making the "glitch" happen. The remaining red balls (the surplus matter) and the few blue balls that survived stop interacting with each other. They just sit there, floating around as invisible "ghosts." These ghosts are our Dark Matter.

The genius of this idea is that the "glitch" that created the matter surplus also left behind the ghosts that make up the dark matter. One mechanism solves both problems.

The Two Blueprints (UV Completions)

The authors didn't just dream this up; they built two specific "blueprints" (models) to show how this could work in real physics.

1. The "Inflaton Factory" (Primordial Dirac Leptogenesis):
   Imagine the universe started with a giant, unstable balloon called the Inflaton. When it popped (reheating), it didn't just make regular particles; it also made a special "shadow" particle (a scalar doublet). This shadow particle decayed into our sterile neutrinos. The authors showed that if you tweak the recipe just right, you get the perfect amount of matter surplus and the perfect amount of dark matter.

2. The "Phantom Sector" (Minimal Phantom Sector):
   Imagine the Standard Model (our known physics) is a house. The authors added a "Phantom Room" next door. This room has its own furniture (new particles) that can talk to the main house but only through a secret door. Heavy particles in this Phantom Room decayed, creating the imbalance of matter and the leftover dark matter.

Why This Matters (The Constraints)

The authors had to make sure their idea didn't break the rules of the universe. They checked:

• The X-Ray Rule: If these ghosts decay, they should emit X-rays. We haven't seen them, so the ghosts must be very stable and have very weak connections to regular matter. The model fits this.
• The Structure Rule: Dark matter can't be too "hot" (moving too fast), or it would wash away the small galaxies we see. The model predicts "warm" ghosts, which fits the data perfectly.
• The Neutrino Mass Rule: The model must also explain why regular neutrinos have mass. The math checks out.

The Takeaway

This paper is like finding a Swiss Army Knife for cosmology. Instead of needing two different tools to fix the "Missing Matter" and "Missing People" problems, the authors found one tool (light sterile neutrinos with a tiny twist of mass) that does both jobs.

They showed that if these particles exist, they could have:

1. Created the imbalance that let us exist (Baryogenesis).
2. Left behind a leftover population that acts as the invisible glue of the universe (Dark Matter).

It's a simple, elegant, and flexible idea that connects the very beginning of the universe to the dark sky we see today.

Technical Summary

1. Problem Statement

The paper addresses two fundamental puzzles in cosmology and particle physics: the origin of the baryon asymmetry of the Universe (BAU) and the nature of Dark Matter (DM).

• The Challenge: Standard mechanisms for baryogenesis (e.g., Electroweak Baryogenesis or high-scale Majorana Leptogenesis) typically do not naturally explain the DM abundance. Conversely, standard DM candidates (like WIMPs) do not explain the BAU.
• The Specific Gap: Previous low-scale models like the $\nu$MSM (Neutrino Minimal Standard Model) can explain both but require widely separated production epochs (DM at $\sim 100$ MeV, BAU at $> 100$ GeV) and severe parameter tuning.
• The Goal: Propose a unified, minimal framework where sterile neutrinos with masses below the electroweak scale simultaneously generate the BAU and the DM relic density through closely related dynamics, avoiding the need for separate production mechanisms or heavy new physics scales.

2. Methodology

The authors employ a hybrid approach combining effective field theory (EFT) analysis with specific Ultraviolet (UV) completions.

A. General Framework (Low-Energy Effective Theory)

• Core Mechanism: The model utilizes Dirac Leptogenesis combined with small Majorana mass terms.
  • High Temperatures ($T > T_{EW}$): The sterile neutrinos behave effectively as Dirac particles. Small Yukawa couplings keep them out of equilibrium, allowing CP-violating decays/oscillations to generate a lepton asymmetry ($L$) without washing it out (since total lepton number is approximately conserved).
  • Low Temperatures ($T < T_{EW}$): Small Majorana mass terms ($m_N \ll T_{EW}$) become relevant. These terms convert the remaining out-of-equilibrium sterile neutrino population into Warm Dark Matter (WDM).
• Key Assumption: The paper assumes unspecified UV dynamics generate both symmetric (particle + antiparticle) and asymmetric (particle - antiparticle) sterile neutrino populations at high temperatures. These serve as initial conditions for the subsequent evolution.
• Formalism: The authors derive a relation between the baryon asymmetry yield ($Y_B$) and the DM relic density ($\Omega_{DM}$) based on the branching ratios of parent particle decays and the CP-asymmetry parameter ($\epsilon_{CP}$).

B. Constraint Analysis

The authors systematically scan the low-energy parameter space (Yukawa couplings $y_\nu$, sterile masses $m_N$, and mixing angles $\theta$) against:

1. Leptogenesis Viability: Ensuring left-right equilibration processes do not wash out the asymmetry before the Electroweak Phase Transition (EWPT).
2. Dark Matter Stability: Ensuring the lightest sterile state is long-lived (lifetime $> t_{universe}$).
3. Astrophysical Bounds: Lyman-$\alpha$ forest constraints (limiting free-streaming length) and X-ray limits (constraining active-sterile mixing via radiative decays).
4. Cosmological Bounds: Constraints on the effective number of relativistic species ($N_{eff}$) from CMB data (Planck).
5. Neutrino Mass Generation: Consistency with observed light neutrino oscillation data using the Casas-Ibarra parametrization.

C. UV Completions

To demonstrate the robustness of the mechanism, the authors apply their framework to two specific UV models:

1. Primordial Dirac Leptogenesis: A scenario where a singlet inflaton decays into a scalar doublet $\hat{h}$, which subsequently decays into sterile neutrinos.
2. Minimal Phantom Sector: A model extending the SM with a complex scalar $\Phi$ and a Weyl fermion $s_R$, generating Dirac neutrino masses and sterile populations via heavy Dirac fermion decays.

3. Key Contributions

• Unified Mechanism: The paper establishes that small Majorana masses are the "missing link" that allows Dirac leptogenesis to simultaneously produce Dark Matter. The Majorana terms do not disrupt the high-temperature asymmetry generation but convert the symmetric remnant into viable WDM at low temperatures.
• Relaxation of Tuning: Unlike the $\nu$MSM, this mechanism does not require the BAU and DM to be produced at vastly different epochs; they originate from the same primordial population dynamics.
• Parameter Space Mapping: The authors provide a rigorous mapping of the viable parameter space, showing that:
  • The lightest sterile neutrino ($N_1$) must be in the keV range (specifically $m_{N1} \gtrsim 7.5$ keV to satisfy Lyman-$\alpha$ bounds).
  • Heavier sterile states ($N_{2,3}$) must be in the GeV range to generate light neutrino masses and facilitate leptogenesis.
  • Active-sterile mixing angles must be extremely small ($\sin^2 2\theta \lesssim 10^{-11}$ for keV states) to evade X-ray bounds, which is naturally achieved by the model's structure.
• UV Model Validation: The authors show that adding small Majorana masses to existing Dirac leptogenesis models (Primordial and Phantom Sector) resolves previous tensions between DM production, neutrino mass generation, and X-ray constraints.

4. Results

• Mass Hierarchy: The model predicts a hierarchical sterile neutrino spectrum:
  • $m_{N1} \sim \text{keV}$ (Dark Matter candidate, Warm DM).
  • $m_{N2,3} \sim \text{GeV}$ (Responsible for light neutrino masses and leptogenesis).
• Free-Streaming Length: For production via the decay of a heavy parent particle (freeze-in), the resulting momentum distribution yields a free-streaming length $\lambda_{FS} \sim 0.01 - 0.1$ Mpc, classifying the DM as Warm Dark Matter, consistent with structure formation constraints.
• Washout Constraints: Successful leptogenesis requires the Yukawa couplings of the heavy states to be small enough to prevent washout ($y_\nu \lesssim 10^{-8}$) but large enough to decay before Big Bang Nucleosynthesis (BBN) or neutrino decoupling ($y_\nu \gtrsim 10^{-7}$ for GeV masses).
• Viable Regions:
  • In the Primordial Dirac Leptogenesis model, a viable region exists if the production of the DM candidate is decoupled from the light neutrino mass generation mechanism (e.g., via a non-thermal production of the scalar $\hat{h}$).
  • In the Minimal Phantom Sector, the introduction of Majorana masses relaxes the bounds on the CP-asymmetry parameter, allowing for viable parameter space with $M_1$ (heavy fermion mass) in the TeV range.

5. Significance

• Theoretical Economy: The paper demonstrates that a Type-I Seesaw extension with light sterile neutrinos and small Majorana masses is sufficient to solve the BAU and DM puzzles simultaneously without invoking complex new sectors or high-energy scales.
• Testability:
  • X-ray Astronomy: The model predicts specific mixing angles for keV sterile neutrinos that are within the reach of future X-ray telescopes (though currently constrained).
  • Laboratory Experiments: The GeV-scale sterile neutrinos ($N_{2,3}$) could be probed by future beam-dump experiments or collider searches for Heavy Neutral Leptons (HNLs), although their mixing is predicted to be very small.
  • Cosmology: Future precision measurements of $N_{eff}$ and Lyman-$\alpha$ data will further constrain the free-streaming properties of the WDM candidate.
• Paradigm Shift: It challenges the strict dichotomy between Dirac and Majorana neutrinos in cosmology, showing that a "hybrid" nature (Dirac at high $T$, Majorana at low $T$) is technically natural and phenomenologically powerful.

In conclusion, the paper provides a robust, minimal, and flexible mechanism where light sterile neutrinos act as the bridge between the origin of matter and the nature of dark matter, utilizing small Majorana masses to transition from a Dirac leptogenesis regime to a Warm Dark Matter candidate.